diff --git a/.gitattributes b/.gitattributes
index ed554a29615c1a82335a909c3ed8049ee67e94c0..6450fddb0a448ba2c899376c3ef59b9680c8c5ca 100644
--- a/.gitattributes
+++ b/.gitattributes
@@ -334,3 +334,4 @@ parrot/lib/python3.10/site-packages/transformers/models/speecht5/__pycache__/mod
 parrot/lib/python3.10/site-packages/transformers/utils/__pycache__/dummy_tf_objects.cpython-310.pyc filter=lfs diff=lfs merge=lfs -text
 parrot/lib/python3.10/site-packages/transformers/__pycache__/modeling_tf_utils.cpython-310.pyc filter=lfs diff=lfs merge=lfs -text
 parrot/lib/python3.10/site-packages/transformers/__pycache__/trainer.cpython-310.pyc filter=lfs diff=lfs merge=lfs -text
+moondream/lib/python3.10/site-packages/numpy.libs/libopenblas64_p-r0-0cf96a72.3.23.dev.so filter=lfs diff=lfs merge=lfs -text
diff --git a/llava_next/lib/python3.10/site-packages/fsspec-2024.10.0.dist-info/INSTALLER b/llava_next/lib/python3.10/site-packages/fsspec-2024.10.0.dist-info/INSTALLER
new file mode 100644
index 0000000000000000000000000000000000000000..a1b589e38a32041e49332e5e81c2d363dc418d68
--- /dev/null
+++ b/llava_next/lib/python3.10/site-packages/fsspec-2024.10.0.dist-info/INSTALLER
@@ -0,0 +1 @@
+pip
diff --git a/llava_next/lib/python3.10/site-packages/fsspec-2024.10.0.dist-info/METADATA b/llava_next/lib/python3.10/site-packages/fsspec-2024.10.0.dist-info/METADATA
new file mode 100644
index 0000000000000000000000000000000000000000..0d1df093f7d53ef7a17e51be10495f060c5a86dc
--- /dev/null
+++ b/llava_next/lib/python3.10/site-packages/fsspec-2024.10.0.dist-info/METADATA
@@ -0,0 +1,278 @@
+Metadata-Version: 2.3
+Name: fsspec
+Version: 2024.10.0
+Summary: File-system specification
+Project-URL: Changelog, https://filesystem-spec.readthedocs.io/en/latest/changelog.html
+Project-URL: Documentation, https://filesystem-spec.readthedocs.io/en/latest/
+Project-URL: Homepage, https://github.com/fsspec/filesystem_spec
+Maintainer-email: Martin Durant <mdurant@anaconda.com>
+License: BSD 3-Clause License
+        
+        Copyright (c) 2018, Martin Durant
+        All rights reserved.
+        
+        Redistribution and use in source and binary forms, with or without
+        modification, are permitted provided that the following conditions are met:
+        
+        * Redistributions of source code must retain the above copyright notice, this
+          list of conditions and the following disclaimer.
+        
+        * Redistributions in binary form must reproduce the above copyright notice,
+          this list of conditions and the following disclaimer in the documentation
+          and/or other materials provided with the distribution.
+        
+        * Neither the name of the copyright holder nor the names of its
+          contributors may be used to endorse or promote products derived from
+          this software without specific prior written permission.
+        
+        THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+        AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+        IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+        DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
+        FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+        DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+        SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+        CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+        OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+        OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+License-File: LICENSE
+Keywords: file
+Classifier: Development Status :: 4 - Beta
+Classifier: Intended Audience :: Developers
+Classifier: License :: OSI Approved :: BSD License
+Classifier: Operating System :: OS Independent
+Classifier: Programming Language :: Python :: 3.8
+Classifier: Programming Language :: Python :: 3.9
+Classifier: Programming Language :: Python :: 3.10
+Classifier: Programming Language :: Python :: 3.11
+Classifier: Programming Language :: Python :: 3.12
+Requires-Python: >=3.8
+Provides-Extra: abfs
+Requires-Dist: adlfs; extra == 'abfs'
+Provides-Extra: adl
+Requires-Dist: adlfs; extra == 'adl'
+Provides-Extra: arrow
+Requires-Dist: pyarrow>=1; extra == 'arrow'
+Provides-Extra: dask
+Requires-Dist: dask; extra == 'dask'
+Requires-Dist: distributed; extra == 'dask'
+Provides-Extra: dev
+Requires-Dist: pre-commit; extra == 'dev'
+Requires-Dist: ruff; extra == 'dev'
+Provides-Extra: doc
+Requires-Dist: numpydoc; extra == 'doc'
+Requires-Dist: sphinx; extra == 'doc'
+Requires-Dist: sphinx-design; extra == 'doc'
+Requires-Dist: sphinx-rtd-theme; extra == 'doc'
+Requires-Dist: yarl; extra == 'doc'
+Provides-Extra: dropbox
+Requires-Dist: dropbox; extra == 'dropbox'
+Requires-Dist: dropboxdrivefs; extra == 'dropbox'
+Requires-Dist: requests; extra == 'dropbox'
+Provides-Extra: entrypoints
+Provides-Extra: full
+Requires-Dist: adlfs; extra == 'full'
+Requires-Dist: aiohttp!=4.0.0a0,!=4.0.0a1; extra == 'full'
+Requires-Dist: dask; extra == 'full'
+Requires-Dist: distributed; extra == 'full'
+Requires-Dist: dropbox; extra == 'full'
+Requires-Dist: dropboxdrivefs; extra == 'full'
+Requires-Dist: fusepy; extra == 'full'
+Requires-Dist: gcsfs; extra == 'full'
+Requires-Dist: libarchive-c; extra == 'full'
+Requires-Dist: ocifs; extra == 'full'
+Requires-Dist: panel; extra == 'full'
+Requires-Dist: paramiko; extra == 'full'
+Requires-Dist: pyarrow>=1; extra == 'full'
+Requires-Dist: pygit2; extra == 'full'
+Requires-Dist: requests; extra == 'full'
+Requires-Dist: s3fs; extra == 'full'
+Requires-Dist: smbprotocol; extra == 'full'
+Requires-Dist: tqdm; extra == 'full'
+Provides-Extra: fuse
+Requires-Dist: fusepy; extra == 'fuse'
+Provides-Extra: gcs
+Requires-Dist: gcsfs; extra == 'gcs'
+Provides-Extra: git
+Requires-Dist: pygit2; extra == 'git'
+Provides-Extra: github
+Requires-Dist: requests; extra == 'github'
+Provides-Extra: gs
+Requires-Dist: gcsfs; extra == 'gs'
+Provides-Extra: gui
+Requires-Dist: panel; extra == 'gui'
+Provides-Extra: hdfs
+Requires-Dist: pyarrow>=1; extra == 'hdfs'
+Provides-Extra: http
+Requires-Dist: aiohttp!=4.0.0a0,!=4.0.0a1; extra == 'http'
+Provides-Extra: libarchive
+Requires-Dist: libarchive-c; extra == 'libarchive'
+Provides-Extra: oci
+Requires-Dist: ocifs; extra == 'oci'
+Provides-Extra: s3
+Requires-Dist: s3fs; extra == 's3'
+Provides-Extra: sftp
+Requires-Dist: paramiko; extra == 'sftp'
+Provides-Extra: smb
+Requires-Dist: smbprotocol; extra == 'smb'
+Provides-Extra: ssh
+Requires-Dist: paramiko; extra == 'ssh'
+Provides-Extra: test
+Requires-Dist: aiohttp!=4.0.0a0,!=4.0.0a1; extra == 'test'
+Requires-Dist: numpy; extra == 'test'
+Requires-Dist: pytest; extra == 'test'
+Requires-Dist: pytest-asyncio!=0.22.0; extra == 'test'
+Requires-Dist: pytest-benchmark; extra == 'test'
+Requires-Dist: pytest-cov; extra == 'test'
+Requires-Dist: pytest-mock; extra == 'test'
+Requires-Dist: pytest-recording; extra == 'test'
+Requires-Dist: pytest-rerunfailures; extra == 'test'
+Requires-Dist: requests; extra == 'test'
+Provides-Extra: test-downstream
+Requires-Dist: aiobotocore<3.0.0,>=2.5.4; extra == 'test-downstream'
+Requires-Dist: dask-expr; extra == 'test-downstream'
+Requires-Dist: dask[dataframe,test]; extra == 'test-downstream'
+Requires-Dist: moto[server]<5,>4; extra == 'test-downstream'
+Requires-Dist: pytest-timeout; extra == 'test-downstream'
+Requires-Dist: xarray; extra == 'test-downstream'
+Provides-Extra: test-full
+Requires-Dist: adlfs; extra == 'test-full'
+Requires-Dist: aiohttp!=4.0.0a0,!=4.0.0a1; extra == 'test-full'
+Requires-Dist: cloudpickle; extra == 'test-full'
+Requires-Dist: dask; extra == 'test-full'
+Requires-Dist: distributed; extra == 'test-full'
+Requires-Dist: dropbox; extra == 'test-full'
+Requires-Dist: dropboxdrivefs; extra == 'test-full'
+Requires-Dist: fastparquet; extra == 'test-full'
+Requires-Dist: fusepy; extra == 'test-full'
+Requires-Dist: gcsfs; extra == 'test-full'
+Requires-Dist: jinja2; extra == 'test-full'
+Requires-Dist: kerchunk; extra == 'test-full'
+Requires-Dist: libarchive-c; extra == 'test-full'
+Requires-Dist: lz4; extra == 'test-full'
+Requires-Dist: notebook; extra == 'test-full'
+Requires-Dist: numpy; extra == 'test-full'
+Requires-Dist: ocifs; extra == 'test-full'
+Requires-Dist: pandas; extra == 'test-full'
+Requires-Dist: panel; extra == 'test-full'
+Requires-Dist: paramiko; extra == 'test-full'
+Requires-Dist: pyarrow; extra == 'test-full'
+Requires-Dist: pyarrow>=1; extra == 'test-full'
+Requires-Dist: pyftpdlib; extra == 'test-full'
+Requires-Dist: pygit2; extra == 'test-full'
+Requires-Dist: pytest; extra == 'test-full'
+Requires-Dist: pytest-asyncio!=0.22.0; extra == 'test-full'
+Requires-Dist: pytest-benchmark; extra == 'test-full'
+Requires-Dist: pytest-cov; extra == 'test-full'
+Requires-Dist: pytest-mock; extra == 'test-full'
+Requires-Dist: pytest-recording; extra == 'test-full'
+Requires-Dist: pytest-rerunfailures; extra == 'test-full'
+Requires-Dist: python-snappy; extra == 'test-full'
+Requires-Dist: requests; extra == 'test-full'
+Requires-Dist: smbprotocol; extra == 'test-full'
+Requires-Dist: tqdm; extra == 'test-full'
+Requires-Dist: urllib3; extra == 'test-full'
+Requires-Dist: zarr; extra == 'test-full'
+Requires-Dist: zstandard; extra == 'test-full'
+Provides-Extra: tqdm
+Requires-Dist: tqdm; extra == 'tqdm'
+Description-Content-Type: text/markdown
+
+# filesystem_spec
+
+[![PyPI version](https://badge.fury.io/py/fsspec.svg)](https://pypi.python.org/pypi/fsspec/)
+[![Anaconda-Server Badge](https://anaconda.org/conda-forge/fsspec/badges/version.svg)](https://anaconda.org/conda-forge/fsspec)
+![Build](https://github.com/fsspec/filesystem_spec/workflows/CI/badge.svg)
+[![Docs](https://readthedocs.org/projects/filesystem-spec/badge/?version=latest)](https://filesystem-spec.readthedocs.io/en/latest/?badge=latest)
+
+A specification for pythonic filesystems.
+
+## Install
+
+```bash
+pip install fsspec
+```
+
+would install the base fsspec. Various optionally supported features might require specification of custom
+extra require, e.g. `pip install fsspec[ssh]` will install dependencies for `ssh` backends support.
+Use `pip install fsspec[full]` for installation of all known extra dependencies.
+
+Up-to-date package also provided through conda-forge distribution:
+
+```bash
+conda install -c conda-forge fsspec
+```
+
+
+## Purpose
+
+To produce a template or specification for a file-system interface, that specific implementations should follow,
+so that applications making use of them can rely on a common behaviour and not have to worry about the specific
+internal implementation decisions with any given backend. Many such implementations are included in this package,
+or in sister projects such as `s3fs` and `gcsfs`.
+
+In addition, if this is well-designed, then additional functionality, such as a key-value store or FUSE
+mounting of the file-system implementation may be available for all implementations "for free".
+
+## Documentation
+
+Please refer to [RTD](https://filesystem-spec.readthedocs.io/en/latest/?badge=latest)
+
+## Develop
+
+fsspec uses GitHub Actions for CI. Environment files can be found
+in the "ci/" directory. Note that the main environment is called "py38",
+but it is expected that the version of python installed be adjustable at
+CI runtime. For local use, pick a version suitable for you.
+
+```bash
+# For a new environment (mamba / conda).
+mamba create -n fsspec -c conda-forge  python=3.9 -y
+conda activate fsspec
+
+# Standard dev install with docs and tests.
+pip install -e ".[dev,doc,test]"
+
+# Full tests except for downstream
+pip install s3fs
+pip uninstall s3fs
+pip install -e .[dev,doc,test_full]
+pip install s3fs --no-deps
+pytest -v
+
+# Downstream tests.
+sh install_s3fs.sh
+# Windows powershell.
+install_s3fs.sh
+```
+
+### Testing
+
+Tests can be run in the dev environment, if activated, via ``pytest fsspec``.
+
+The full fsspec suite requires a system-level docker, docker-compose, and fuse
+installation. If only making changes to one backend implementation, it is
+not generally necessary to run all tests locally.
+
+It is expected that contributors ensure that any change to fsspec does not
+cause issues or regressions for either other fsspec-related packages such
+as gcsfs and s3fs, nor for downstream users of fsspec. The "downstream" CI
+run and corresponding environment file run a set of tests from the dask
+test suite, and very minimal tests against pandas and zarr from the
+test_downstream.py module in this repo.
+
+### Code Formatting
+
+fsspec uses [Black](https://black.readthedocs.io/en/stable) to ensure
+a consistent code format throughout the project.
+Run ``black fsspec`` from the root of the filesystem_spec repository to
+auto-format your code. Additionally, many editors have plugins that will apply
+``black`` as you edit files. ``black`` is included in the ``tox`` environments.
+
+Optionally, you may wish to setup [pre-commit hooks](https://pre-commit.com) to
+automatically run ``black`` when you make a git commit.
+Run ``pre-commit install --install-hooks`` from the root of the
+filesystem_spec repository to setup pre-commit hooks. ``black`` will now be run
+before you commit, reformatting any changed files. You can format without
+committing via ``pre-commit run`` or skip these checks with ``git commit
+--no-verify``.
diff --git a/llava_next/lib/python3.10/site-packages/fsspec-2024.10.0.dist-info/RECORD b/llava_next/lib/python3.10/site-packages/fsspec-2024.10.0.dist-info/RECORD
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diff --git a/llava_next/lib/python3.10/site-packages/fsspec-2024.10.0.dist-info/REQUESTED b/llava_next/lib/python3.10/site-packages/fsspec-2024.10.0.dist-info/REQUESTED
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/llava_next/lib/python3.10/site-packages/fsspec-2024.10.0.dist-info/WHEEL b/llava_next/lib/python3.10/site-packages/fsspec-2024.10.0.dist-info/WHEEL
new file mode 100644
index 0000000000000000000000000000000000000000..cdd68a497cdfa8d3f2b837225beacef711b85047
--- /dev/null
+++ b/llava_next/lib/python3.10/site-packages/fsspec-2024.10.0.dist-info/WHEEL
@@ -0,0 +1,4 @@
+Wheel-Version: 1.0
+Generator: hatchling 1.25.0
+Root-Is-Purelib: true
+Tag: py3-none-any
diff --git a/llava_next/lib/python3.10/site-packages/fsspec-2024.10.0.dist-info/licenses/LICENSE b/llava_next/lib/python3.10/site-packages/fsspec-2024.10.0.dist-info/licenses/LICENSE
new file mode 100644
index 0000000000000000000000000000000000000000..67590a5e5be5a5a2dde3fe53a7512e404a896c22
--- /dev/null
+++ b/llava_next/lib/python3.10/site-packages/fsspec-2024.10.0.dist-info/licenses/LICENSE
@@ -0,0 +1,29 @@
+BSD 3-Clause License
+
+Copyright (c) 2018, Martin Durant
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met:
+
+* Redistributions of source code must retain the above copyright notice, this
+  list of conditions and the following disclaimer.
+
+* Redistributions in binary form must reproduce the above copyright notice,
+  this list of conditions and the following disclaimer in the documentation
+  and/or other materials provided with the distribution.
+
+* Neither the name of the copyright holder nor the names of its
+  contributors may be used to endorse or promote products derived from
+  this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
+FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
diff --git a/llava_next/lib/python3.10/site-packages/latex2mathml-3.77.0.dist-info/INSTALLER b/llava_next/lib/python3.10/site-packages/latex2mathml-3.77.0.dist-info/INSTALLER
new file mode 100644
index 0000000000000000000000000000000000000000..a1b589e38a32041e49332e5e81c2d363dc418d68
--- /dev/null
+++ b/llava_next/lib/python3.10/site-packages/latex2mathml-3.77.0.dist-info/INSTALLER
@@ -0,0 +1 @@
+pip
diff --git a/llava_next/lib/python3.10/site-packages/latex2mathml-3.77.0.dist-info/LICENSE b/llava_next/lib/python3.10/site-packages/latex2mathml-3.77.0.dist-info/LICENSE
new file mode 100644
index 0000000000000000000000000000000000000000..9d3cfcd8f611756af3e638a7f12dc0a8646add7e
--- /dev/null
+++ b/llava_next/lib/python3.10/site-packages/latex2mathml-3.77.0.dist-info/LICENSE
@@ -0,0 +1,21 @@
+MIT License
+
+Copyright (c) 2016 Ronie Martinez
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
diff --git a/llava_next/lib/python3.10/site-packages/latex2mathml-3.77.0.dist-info/METADATA b/llava_next/lib/python3.10/site-packages/latex2mathml-3.77.0.dist-info/METADATA
new file mode 100644
index 0000000000000000000000000000000000000000..7917e3db6789f1633f2f038b8aff90f6d22b1632
--- /dev/null
+++ b/llava_next/lib/python3.10/site-packages/latex2mathml-3.77.0.dist-info/METADATA
@@ -0,0 +1,172 @@
+Metadata-Version: 2.1
+Name: latex2mathml
+Version: 3.77.0
+Summary: Pure Python library for LaTeX to MathML conversion
+Home-page: https://github.com/roniemartinez/latex2mathml
+License: MIT
+Keywords: latex,mathml
+Author: Ronie Martinez
+Author-email: ronmarti18@gmail.com
+Requires-Python: >=3.8.1,<4.0.0
+Classifier: Development Status :: 5 - Production/Stable
+Classifier: License :: OSI Approved :: MIT License
+Classifier: Programming Language :: Python :: 3
+Classifier: Programming Language :: Python :: 3.9
+Classifier: Programming Language :: Python :: 3.10
+Classifier: Programming Language :: Python :: 3.11
+Classifier: Programming Language :: Python :: 3.12
+Classifier: Programming Language :: Python :: 3.8
+Classifier: Programming Language :: Python :: Implementation :: CPython
+Classifier: Topic :: Scientific/Engineering :: Mathematics
+Classifier: Topic :: Software Development :: Libraries :: Python Modules
+Classifier: Topic :: Text Processing :: Markup :: HTML
+Classifier: Topic :: Text Processing :: Markup :: LaTeX
+Project-URL: Donate, https://www.buymeacoffee.com/roniemartinez
+Project-URL: Repository, https://github.com/roniemartinez/latex2mathml
+Description-Content-Type: text/markdown
+
+<table>
+    <tr>
+        <td>License</td>
+        <td><img src='https://img.shields.io/pypi/l/latex2mathml.svg?style=for-the-badge' alt="License"></td>
+        <td>Version</td>
+        <td><img src='https://img.shields.io/pypi/v/latex2mathml.svg?logo=pypi&style=for-the-badge' alt="Version"></td>
+    </tr>
+    <tr>
+        <td>Github Actions</td>
+        <td><img src='https://img.shields.io/github/actions/workflow/status/roniemartinez/latex2mathml/python.yml?branch=master&label=actions&logo=github%20actions&style=for-the-badge' alt="Github Actions"></td>
+        <td>Coverage</td>
+        <td><img src='https://img.shields.io/codecov/c/github/roniemartinez/latex2mathml/master?label=codecov&logo=codecov&style=for-the-badge' alt="CodeCov"></td>
+    </tr>
+    <tr>
+        <td>Supported versions</td>
+        <td><img src='https://img.shields.io/pypi/pyversions/latex2mathml.svg?logo=python&style=for-the-badge' alt="Python Versions"></td>
+        <td>Wheel</td>
+        <td><img src='https://img.shields.io/pypi/wheel/latex2mathml.svg?style=for-the-badge' alt="Wheel"></td>
+    </tr>
+    <tr>
+        <td>Status</td>
+        <td><img src='https://img.shields.io/pypi/status/latex2mathml.svg?style=for-the-badge' alt="Status"></td>
+        <td>Downloads</td>
+        <td><img src='https://img.shields.io/pypi/dm/latex2mathml.svg?style=for-the-badge' alt="Downloads"></td>
+    </tr>
+    <tr>
+        <td>All Contributors</td>
+        <td><a href="#contributors-"><img src='https://img.shields.io/github/all-contributors/roniemartinez/latex2mathml?style=for-the-badge' alt="All Contributors"></a></td>
+    </tr>
+</table>
+
+# latex2mathml
+
+Pure Python library for LaTeX to MathML conversion
+
+## Installation
+
+```bash
+pip install latex2mathml
+```
+
+## Usage
+
+### Python
+
+```python
+import latex2mathml.converter
+
+latex_input = "<your_latex_string>"
+mathml_output = latex2mathml.converter.convert(latex_input)
+```
+
+### Command-line
+
+```shell
+% latex2mathml -h
+usage: latex2mathml [-h] [-V] [-b] [-t TEXT | -f FILE | -s]
+
+Pure Python library for LaTeX to MathML conversion
+
+options:
+  -h, --help            show this help message and exit
+  -V, --version         Show version
+  -b, --block           Display block
+
+required arguments:
+  -t TEXT, --text TEXT  Text
+  -f FILE, --file FILE  File
+  -s, --stdin           Stdin
+```
+
+## References
+### LaTeX
+
+- https://en.wikibooks.org/wiki/LaTeX/Mathematics
+- http://artofproblemsolving.com/wiki/index.php?title=Main_Page
+- http://milde.users.sourceforge.net/LUCR/Math/
+- https://math-linux.com/latex-26/faq/latex-faq/article/latex-derivatives-limits-sums-products-and-integrals
+- https://www.tutorialspoint.com/tex_commands
+- https://www.giss.nasa.gov/tools/latex/ltx-86.html
+- https://ftp.gwdg.de/pub/ctan/info/l2tabu/english/l2tabuen.pdf
+
+### MathML
+
+- http://www.xmlmind.com/tutorials/MathML/
+
+
+## Author
+
+- [Ronie Martinez](mailto:ronmarti18@gmail.com)
+
+## Contributors ✨
+
+Thanks goes to these wonderful people ([emoji key](https://allcontributors.org/docs/en/emoji-key)):
+
+<!-- ALL-CONTRIBUTORS-LIST:START - Do not remove or modify this section -->
+<!-- prettier-ignore-start -->
+<!-- markdownlint-disable -->
+<table>
+  <tbody>
+    <tr>
+      <td align="center" valign="top" width="14.28%"><a href="https://ron.sh"><img src="https://avatars.githubusercontent.com/u/2573537?v=4?s=100" width="100px;" alt="Ronie Martinez"/><br /><sub><b>Ronie Martinez</b></sub></a><br /><a href="#maintenance-roniemartinez" title="Maintenance">🚧</a> <a href="https://github.com/roniemartinez/latex2mathml/commits?author=roniemartinez" title="Code">💻</a> <a href="#infra-roniemartinez" title="Infrastructure (Hosting, Build-Tools, etc)">🚇</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="https://anwen.cc/"><img src="https://avatars.githubusercontent.com/u/1472850?v=4?s=100" width="100px;" alt="askender"/><br /><sub><b>askender</b></sub></a><br /><a href="https://github.com/roniemartinez/latex2mathml/commits?author=askender" title="Documentation">📖</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="https://github.com/06180339"><img src="https://avatars.githubusercontent.com/u/25408501?v=4?s=100" width="100px;" alt="06180339"/><br /><sub><b>06180339</b></sub></a><br /><a href="https://github.com/roniemartinez/latex2mathml/commits?author=06180339" title="Code">💻</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="https://github.com/chaihahaha"><img src="https://avatars.githubusercontent.com/u/24356676?v=4?s=100" width="100px;" alt="chaihahaha"/><br /><sub><b>chaihahaha</b></sub></a><br /><a href="https://github.com/roniemartinez/latex2mathml/commits?author=chaihahaha" title="Code">💻</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="https://github.com/huangradio"><img src="https://avatars.githubusercontent.com/u/63624395?v=4?s=100" width="100px;" alt="HQY"/><br /><sub><b>HQY</b></sub></a><br /><a href="https://github.com/roniemartinez/latex2mathml/issues?q=author%3Ahuangradio" title="Bug reports">🐛</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="https://github.com/Sun-ZhenXing"><img src="https://avatars.githubusercontent.com/u/44517244?v=4?s=100" width="100px;" alt="鸭梨"/><br /><sub><b>鸭梨</b></sub></a><br /><a href="https://github.com/roniemartinez/latex2mathml/issues?q=author%3ASun-ZhenXing" title="Bug reports">🐛</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="https://github.com/oliverstefanov"><img src="https://avatars.githubusercontent.com/u/33491656?v=4?s=100" width="100px;" alt="oliverstefanov"/><br /><sub><b>oliverstefanov</b></sub></a><br /><a href="https://github.com/roniemartinez/latex2mathml/issues?q=author%3Aoliverstefanov" title="Bug reports">🐛</a></td>
+    </tr>
+    <tr>
+      <td align="center" valign="top" width="14.28%"><a href="https://github.com/ghost"><img src="https://avatars.githubusercontent.com/u/10137?v=4?s=100" width="100px;" alt="Deleted user"/><br /><sub><b>Deleted user</b></sub></a><br /><a href="https://github.com/roniemartinez/latex2mathml/issues?q=author%3Aghost" title="Bug reports">🐛</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="https://github.com/cesaryuan"><img src="https://avatars.githubusercontent.com/u/35998162?v=4?s=100" width="100px;" alt="Cesaryuan"/><br /><sub><b>Cesaryuan</b></sub></a><br /><a href="https://github.com/roniemartinez/latex2mathml/issues?q=author%3Acesaryuan" title="Bug reports">🐛</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="https://github.com/tonystank3000"><img src="https://avatars.githubusercontent.com/u/6315974?v=4?s=100" width="100px;" alt="TonyStank"/><br /><sub><b>TonyStank</b></sub></a><br /><a href="https://github.com/roniemartinez/latex2mathml/issues?q=author%3Atonystank3000" title="Bug reports">🐛</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="https://polarwinkel.de"><img src="https://avatars.githubusercontent.com/u/1512713?v=4?s=100" width="100px;" alt="Dirk Winkel"/><br /><sub><b>Dirk Winkel</b></sub></a><br /><a href="https://github.com/roniemartinez/latex2mathml/issues?q=author%3Apolarwinkel" title="Bug reports">🐛</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="https://github.com/sinslu"><img src="https://avatars.githubusercontent.com/u/12248270?v=4?s=100" width="100px;" alt="sinslu"/><br /><sub><b>sinslu</b></sub></a><br /><a href="https://github.com/roniemartinez/latex2mathml/issues?q=author%3Asinslu" title="Bug reports">🐛</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="https://ubavic.rs"><img src="https://avatars.githubusercontent.com/u/53820106?v=4?s=100" width="100px;" alt="Nikola Ubavić"/><br /><sub><b>Nikola Ubavić</b></sub></a><br /><a href="https://github.com/roniemartinez/latex2mathml/issues?q=author%3Aubavic" title="Bug reports">🐛</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="https://github.com/abhisheksia"><img src="https://avatars.githubusercontent.com/u/68808662?v=4?s=100" width="100px;" alt="abhisheksia"/><br /><sub><b>abhisheksia</b></sub></a><br /><a href="https://github.com/roniemartinez/latex2mathml/issues?q=author%3Aabhisheksia" title="Bug reports">🐛</a></td>
+    </tr>
+    <tr>
+      <td align="center" valign="top" width="14.28%"><a href="http://denissalem.tuxfamily.org"><img src="https://avatars.githubusercontent.com/u/4476506?v=4?s=100" width="100px;" alt="Denis Salem"/><br /><sub><b>Denis Salem</b></sub></a><br /><a href="https://github.com/roniemartinez/latex2mathml/issues?q=author%3ADenisSalem" title="Bug reports">🐛</a> <a href="https://github.com/roniemartinez/latex2mathml/commits?author=DenisSalem" title="Code">💻</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="https://clontz.org"><img src="https://avatars.githubusercontent.com/u/1559632?v=4?s=100" width="100px;" alt="Steven Clontz"/><br /><sub><b>Steven Clontz</b></sub></a><br /><a href="https://github.com/roniemartinez/latex2mathml/issues?q=author%3AStevenClontz" title="Bug reports">🐛</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="https://github.com/yuwenjun1"><img src="https://avatars.githubusercontent.com/u/43265090?v=4?s=100" width="100px;" alt="空白"/><br /><sub><b>空白</b></sub></a><br /><a href="https://github.com/roniemartinez/latex2mathml/issues?q=author%3Ayuwenjun1" title="Bug reports">🐛</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="https://github.com/amuramatsu"><img src="https://avatars.githubusercontent.com/u/6500918?v=4?s=100" width="100px;" alt="MURAMATSU Atshshi"/><br /><sub><b>MURAMATSU Atshshi</b></sub></a><br /><a href="https://github.com/roniemartinez/latex2mathml/issues?q=author%3Aamuramatsu" title="Bug reports">🐛</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="https://github.com/leingang"><img src="https://avatars.githubusercontent.com/u/570942?v=4?s=100" width="100px;" alt="leingang"/><br /><sub><b>leingang</b></sub></a><br /><a href="https://github.com/roniemartinez/latex2mathml/issues?q=author%3Aleingang" title="Bug reports">🐛</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="https://github.com/Nigel-Amers"><img src="https://avatars.githubusercontent.com/u/14248498?v=4?s=100" width="100px;" alt="Nigel Amers"/><br /><sub><b>Nigel Amers</b></sub></a><br /><a href="https://github.com/roniemartinez/latex2mathml/issues?q=author%3ANigel-Amers" title="Bug reports">🐛</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="https://github.com/retsyo"><img src="https://avatars.githubusercontent.com/u/7960913?v=4?s=100" width="100px;" alt="retsyo"/><br /><sub><b>retsyo</b></sub></a><br /><a href="https://github.com/roniemartinez/latex2mathml/issues?q=author%3Aretsyo" title="Bug reports">🐛</a></td>
+    </tr>
+    <tr>
+      <td align="center" valign="top" width="14.28%"><a href="https://github.com/miakramer"><img src="https://avatars.githubusercontent.com/u/16845265?v=4?s=100" width="100px;" alt="Mia Kramer"/><br /><sub><b>Mia Kramer</b></sub></a><br /><a href="https://github.com/roniemartinez/latex2mathml/commits?author=miakramer" title="Code">💻</a> <a href="https://github.com/roniemartinez/latex2mathml/commits?author=miakramer" title="Documentation">📖</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="http://cnx.gdn"><img src="https://avatars.githubusercontent.com/u/13689192?v=4?s=100" width="100px;" alt="Nguyễn Gia Phong"/><br /><sub><b>Nguyễn Gia Phong</b></sub></a><br /><a href="https://github.com/roniemartinez/latex2mathml/issues?q=author%3AMcSinyx" title="Bug reports">🐛</a> <a href="https://github.com/roniemartinez/latex2mathml/commits?author=McSinyx" title="Code">💻</a> <a href="https://github.com/roniemartinez/latex2mathml/commits?author=McSinyx" title="Tests">⚠️</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="https://cdelker.github.io"><img src="https://avatars.githubusercontent.com/u/44102190?v=4?s=100" width="100px;" alt="Collin Delker"/><br /><sub><b>Collin Delker</b></sub></a><br /><a href="https://github.com/roniemartinez/latex2mathml/issues?q=author%3Acdelker" title="Bug reports">🐛</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="https://github.com/jiotv321"><img src="https://avatars.githubusercontent.com/u/118644533?v=4?s=100" width="100px;" alt="jiotv321"/><br /><sub><b>jiotv321</b></sub></a><br /><a href="https://github.com/roniemartinez/latex2mathml/issues?q=author%3Ajiotv321" title="Bug reports">🐛</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="https://github.com/felixonmars"><img src="https://avatars.githubusercontent.com/u/1006477?v=4?s=100" width="100px;" alt="Felix Yan"/><br /><sub><b>Felix Yan</b></sub></a><br /><a href="https://github.com/roniemartinez/latex2mathml/commits?author=felixonmars" title="Code">💻</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="https://rob-blackbourn.github.io/blog/"><img src="https://avatars.githubusercontent.com/u/2880305?v=4?s=100" width="100px;" alt="Rob Blackbourn"/><br /><sub><b>Rob Blackbourn</b></sub></a><br /><a href="https://github.com/roniemartinez/latex2mathml/commits?author=rob-blackbourn" title="Code">💻</a></td>
+    </tr>
+  </tbody>
+</table>
+
+<!-- markdownlint-restore -->
+<!-- prettier-ignore-end -->
+
+<!-- ALL-CONTRIBUTORS-LIST:END -->
+
+This project follows the [all-contributors](https://github.com/all-contributors/all-contributors) specification. Contributions of any kind welcome!
+
diff --git a/llava_next/lib/python3.10/site-packages/latex2mathml-3.77.0.dist-info/RECORD b/llava_next/lib/python3.10/site-packages/latex2mathml-3.77.0.dist-info/RECORD
new file mode 100644
index 0000000000000000000000000000000000000000..605ade09a686ec29b20e9133aa304c5c0723c2a7
--- /dev/null
+++ b/llava_next/lib/python3.10/site-packages/latex2mathml-3.77.0.dist-info/RECORD
@@ -0,0 +1,25 @@
+../../../bin/l2m,sha256=tiRsFHuNF2Y1lraq2gGaQg1Zkg_6YLd9DEP9CMfowBM,237
+../../../bin/latex2mathml,sha256=tiRsFHuNF2Y1lraq2gGaQg1Zkg_6YLd9DEP9CMfowBM,237
+latex2mathml-3.77.0.dist-info/INSTALLER,sha256=zuuue4knoyJ-UwPPXg8fezS7VCrXJQrAP7zeNuwvFQg,4
+latex2mathml-3.77.0.dist-info/LICENSE,sha256=SsHh2gf2s0PVQZHF4XFoQFNOCFkbP56uyQ1oAM3EdUM,1071
+latex2mathml-3.77.0.dist-info/METADATA,sha256=8I_5snYGZtFTF_ZdrISzE_x4L1PcEc9WFhHJfwkOUhA,14844
+latex2mathml-3.77.0.dist-info/RECORD,,
+latex2mathml-3.77.0.dist-info/REQUESTED,sha256=47DEQpj8HBSa-_TImW-5JCeuQeRkm5NMpJWZG3hSuFU,0
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+latex2mathml/converter.py,sha256=a3CTyam1xFz2oPkNVxklSXuPny_DmqnALLsDTRLVmeI,23219
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+latex2mathml/tokenizer.py,sha256=FtlIzWm279chdDE6SrIohMDeHIcwT8GCeyNqexxHu94,2360
+latex2mathml/unimathsymbols.txt,sha256=dO-JVO-vAdwfsTExPvbX97dBxPeOMPbW02ALndWlWu4,216334
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diff --git a/llava_next/lib/python3.10/site-packages/latex2mathml-3.77.0.dist-info/REQUESTED b/llava_next/lib/python3.10/site-packages/latex2mathml-3.77.0.dist-info/REQUESTED
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index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/llava_next/lib/python3.10/site-packages/latex2mathml-3.77.0.dist-info/WHEEL b/llava_next/lib/python3.10/site-packages/latex2mathml-3.77.0.dist-info/WHEEL
new file mode 100644
index 0000000000000000000000000000000000000000..7c881525d384f1537e81e8a783c8433a748a7089
--- /dev/null
+++ b/llava_next/lib/python3.10/site-packages/latex2mathml-3.77.0.dist-info/WHEEL
@@ -0,0 +1,4 @@
+Wheel-Version: 1.0
+Generator: poetry-core 1.8.1
+Root-Is-Purelib: true
+Tag: py3-none-any
diff --git a/llava_next/lib/python3.10/site-packages/latex2mathml-3.77.0.dist-info/entry_points.txt b/llava_next/lib/python3.10/site-packages/latex2mathml-3.77.0.dist-info/entry_points.txt
new file mode 100644
index 0000000000000000000000000000000000000000..85a36b00804610159704e4c3a7ed8a7f8df730b3
--- /dev/null
+++ b/llava_next/lib/python3.10/site-packages/latex2mathml-3.77.0.dist-info/entry_points.txt
@@ -0,0 +1,4 @@
+[console_scripts]
+l2m=latex2mathml.converter:main
+latex2mathml=latex2mathml.converter:main
+
diff --git a/llava_next/lib/python3.10/site-packages/psutil/__pycache__/__init__.cpython-310.pyc b/llava_next/lib/python3.10/site-packages/psutil/__pycache__/__init__.cpython-310.pyc
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index 0000000000000000000000000000000000000000..29125b2b72040e9959618468268d2baf24c95d18
Binary files /dev/null and b/llava_next/lib/python3.10/site-packages/psutil/__pycache__/__init__.cpython-310.pyc differ
diff --git a/llava_next/lib/python3.10/site-packages/pydantic-2.9.2.dist-info/INSTALLER b/llava_next/lib/python3.10/site-packages/pydantic-2.9.2.dist-info/INSTALLER
new file mode 100644
index 0000000000000000000000000000000000000000..a1b589e38a32041e49332e5e81c2d363dc418d68
--- /dev/null
+++ b/llava_next/lib/python3.10/site-packages/pydantic-2.9.2.dist-info/INSTALLER
@@ -0,0 +1 @@
+pip
diff --git a/llava_next/lib/python3.10/site-packages/pydantic-2.9.2.dist-info/METADATA b/llava_next/lib/python3.10/site-packages/pydantic-2.9.2.dist-info/METADATA
new file mode 100644
index 0000000000000000000000000000000000000000..01bf37ad28fe9f4725ca0c53609a57d8d96d9990
--- /dev/null
+++ b/llava_next/lib/python3.10/site-packages/pydantic-2.9.2.dist-info/METADATA
@@ -0,0 +1,1469 @@
+Metadata-Version: 2.3
+Name: pydantic
+Version: 2.9.2
+Summary: Data validation using Python type hints
+Project-URL: Homepage, https://github.com/pydantic/pydantic
+Project-URL: Documentation, https://docs.pydantic.dev
+Project-URL: Funding, https://github.com/sponsors/samuelcolvin
+Project-URL: Source, https://github.com/pydantic/pydantic
+Project-URL: Changelog, https://docs.pydantic.dev/latest/changelog/
+Author-email: Samuel Colvin <s@muelcolvin.com>, Eric Jolibois <em.jolibois@gmail.com>, Hasan Ramezani <hasan.r67@gmail.com>, Adrian Garcia Badaracco <1755071+adriangb@users.noreply.github.com>, Terrence Dorsey <terry@pydantic.dev>, David Montague <david@pydantic.dev>, Serge Matveenko <lig@countzero.co>, Marcelo Trylesinski <marcelotryle@gmail.com>, Sydney Runkle <sydneymarierunkle@gmail.com>, David Hewitt <mail@davidhewitt.io>, Alex Hall <alex.mojaki@gmail.com>
+License-Expression: MIT
+License-File: LICENSE
+Classifier: Development Status :: 5 - Production/Stable
+Classifier: Environment :: Console
+Classifier: Environment :: MacOS X
+Classifier: Framework :: Hypothesis
+Classifier: Framework :: Pydantic
+Classifier: Intended Audience :: Developers
+Classifier: Intended Audience :: Information Technology
+Classifier: Intended Audience :: System Administrators
+Classifier: License :: OSI Approved :: MIT License
+Classifier: Operating System :: POSIX :: Linux
+Classifier: Operating System :: Unix
+Classifier: Programming Language :: Python
+Classifier: Programming Language :: Python :: 3
+Classifier: Programming Language :: Python :: 3 :: Only
+Classifier: Programming Language :: Python :: 3.8
+Classifier: Programming Language :: Python :: 3.9
+Classifier: Programming Language :: Python :: 3.10
+Classifier: Programming Language :: Python :: 3.11
+Classifier: Programming Language :: Python :: 3.12
+Classifier: Programming Language :: Python :: 3.13
+Classifier: Programming Language :: Python :: Implementation :: CPython
+Classifier: Programming Language :: Python :: Implementation :: PyPy
+Classifier: Topic :: Internet
+Classifier: Topic :: Software Development :: Libraries :: Python Modules
+Requires-Python: >=3.8
+Requires-Dist: annotated-types>=0.6.0
+Requires-Dist: pydantic-core==2.23.4
+Requires-Dist: typing-extensions>=4.12.2; python_version >= '3.13'
+Requires-Dist: typing-extensions>=4.6.1; python_version < '3.13'
+Provides-Extra: email
+Requires-Dist: email-validator>=2.0.0; extra == 'email'
+Provides-Extra: timezone
+Requires-Dist: tzdata; (python_version >= '3.9' and sys_platform == 'win32') and extra == 'timezone'
+Description-Content-Type: text/markdown
+
+# Pydantic
+[![CI](https://img.shields.io/github/actions/workflow/status/pydantic/pydantic/ci.yml?branch=main&logo=github&label=CI)](https://github.com/pydantic/pydantic/actions?query=event%3Apush+branch%3Amain+workflow%3ACI)
+[![Coverage](https://coverage-badge.samuelcolvin.workers.dev/pydantic/pydantic.svg)](https://coverage-badge.samuelcolvin.workers.dev/redirect/pydantic/pydantic)
+[![pypi](https://img.shields.io/pypi/v/pydantic.svg)](https://pypi.python.org/pypi/pydantic)
+[![CondaForge](https://img.shields.io/conda/v/conda-forge/pydantic.svg)](https://anaconda.org/conda-forge/pydantic)
+[![downloads](https://static.pepy.tech/badge/pydantic/month)](https://pepy.tech/project/pydantic)
+[![versions](https://img.shields.io/pypi/pyversions/pydantic.svg)](https://github.com/pydantic/pydantic)
+[![license](https://img.shields.io/github/license/pydantic/pydantic.svg)](https://github.com/pydantic/pydantic/blob/main/LICENSE)
+[![Pydantic v2](https://img.shields.io/endpoint?url=https://raw.githubusercontent.com/pydantic/pydantic/main/docs/badge/v2.json)](https://docs.pydantic.dev/latest/contributing/#badges)
+
+Data validation using Python type hints.
+
+Fast and extensible, Pydantic plays nicely with your linters/IDE/brain.
+Define how data should be in pure, canonical Python 3.8+; validate it with Pydantic.
+
+## Pydantic Company :rocket:
+
+We've started a company based on the principles that I believe have led to Pydantic's success.
+Learn more from the [Company Announcement](https://blog.pydantic.dev/blog/2023/02/16/company-announcement--pydantic/).
+
+## Pydantic V1.10 vs. V2
+
+Pydantic V2 is a ground-up rewrite that offers many new features, performance improvements, and some breaking changes compared to Pydantic V1.
+
+If you're using Pydantic V1 you may want to look at the
+[pydantic V1.10 Documentation](https://docs.pydantic.dev/) or,
+[`1.10.X-fixes` git branch](https://github.com/pydantic/pydantic/tree/1.10.X-fixes). Pydantic V2 also ships with the latest version of Pydantic V1 built in so that you can incrementally upgrade your code base and projects: `from pydantic import v1 as pydantic_v1`.
+
+## Help
+
+See [documentation](https://docs.pydantic.dev/) for more details.
+
+## Installation
+
+Install using `pip install -U pydantic` or `conda install pydantic -c conda-forge`.
+For more installation options to make Pydantic even faster,
+see the [Install](https://docs.pydantic.dev/install/) section in the documentation.
+
+## A Simple Example
+
+```py
+from datetime import datetime
+from typing import List, Optional
+from pydantic import BaseModel
+
+class User(BaseModel):
+    id: int
+    name: str = 'John Doe'
+    signup_ts: Optional[datetime] = None
+    friends: List[int] = []
+
+external_data = {'id': '123', 'signup_ts': '2017-06-01 12:22', 'friends': [1, '2', b'3']}
+user = User(**external_data)
+print(user)
+#> User id=123 name='John Doe' signup_ts=datetime.datetime(2017, 6, 1, 12, 22) friends=[1, 2, 3]
+print(user.id)
+#> 123
+```
+
+## Contributing
+
+For guidance on setting up a development environment and how to make a
+contribution to Pydantic, see
+[Contributing to Pydantic](https://docs.pydantic.dev/contributing/).
+
+## Reporting a Security Vulnerability
+
+See our [security policy](https://github.com/pydantic/pydantic/security/policy).
+
+## Changelog
+
+## v2.9.2 (2024-09-17)
+
+[GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.9.2)
+
+### What's Changed
+
+#### Fixes
+* Do not error when trying to evaluate annotations of private attributes by [@Viicos](https://github.com/Viicos) in [#10358](https://github.com/pydantic/pydantic/pull/10358)
+* Adding notes on designing sound `Callable` discriminators by [@sydney-runkle](https://github.com/sydney-runkle) in [#10400](https://github.com/pydantic/pydantic/pull/10400)
+* Fix serialization schema generation when using `PlainValidator` by [@Viicos](https://github.com/Viicos) in [#10427](https://github.com/pydantic/pydantic/pull/10427)
+* Fix `Union` serialization warnings by [@sydney-runkle](https://github.com/sydney-runkle) in [pydantic/pydantic-core#1449](https://github.com/pydantic/pydantic-core/pull/1449)
+* Fix variance issue in `_IncEx` type alias, only allow `True` by [@Viicos](https://github.com/Viicos) in [#10414](https://github.com/pydantic/pydantic/pull/10414)
+* Fix `ZoneInfo` validation with various invalid types by [@sydney-runkle](https://github.com/sydney-runkle) in [#10408](https://github.com/pydantic/pydantic/pull/10408)
+
+## v2.9.1 (2024-09-09)
+
+[GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.9.1)
+
+### What's Changed
+
+#### Fixes
+* Fix Predicate issue in v2.9.0 by [@sydney-runkle](https://github.com/sydney-runkle) in [#10321](https://github.com/pydantic/pydantic/pull/10321)
+* Fixing `annotated-types` bound to `>=0.6.0` by [@sydney-runkle](https://github.com/sydney-runkle) in [#10327](https://github.com/pydantic/pydantic/pull/10327)
+* Turn `tzdata` install requirement into optional `timezone` dependency by [@jakob-keller](https://github.com/jakob-keller) in [#10331](https://github.com/pydantic/pydantic/pull/10331)
+* Fix `IncExc` type alias definition by [@Viicos](https://github.com/Viicos) in [#10339](https://github.com/pydantic/pydantic/pull/10339)
+* Use correct types namespace when building namedtuple core schemas by [@Viicos](https://github.com/Viicos) in [#10337](https://github.com/pydantic/pydantic/pull/10337)
+* Fix evaluation of stringified annotations during namespace inspection by [@Viicos](https://github.com/Viicos) in [#10347](https://github.com/pydantic/pydantic/pull/10347)
+* Fix tagged union serialization with alias generators by [@sydney-runkle](https://github.com/sydney-runkle) in [pydantic/pydantic-core#1442](https://github.com/pydantic/pydantic-core/pull/1442)
+
+## v2.9.0 (2024-09-05)
+
+[GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.9.0)
+
+The code released in v2.9.0 is practically identical to that of v2.9.0b2.
+
+### What's Changed
+
+#### Packaging
+
+* Bump `ruff` to `v0.5.0` and `pyright` to `v1.1.369` by [@sydney-runkle](https://github.com/sydney-runkle) in [#9801](https://github.com/pydantic/pydantic/pull/9801)
+* Bump `pydantic-extra-types` to `v2.9.0` by [@sydney-runkle](https://github.com/sydney-runkle) in [#9832](https://github.com/pydantic/pydantic/pull/9832)
+* Support compatibility with `pdm v2.18.1` by [@Viicos](https://github.com/Viicos) in [#10138](https://github.com/pydantic/pydantic/pull/10138)
+* Bump `v1` version stub to `v1.10.18` by [@sydney-runkle](https://github.com/sydney-runkle) in [#10214](https://github.com/pydantic/pydantic/pull/10214)
+* Bump `pydantic-core` to `v2.23.2` by [@sydney-runkle](https://github.com/sydney-runkle) in [#10311](https://github.com/pydantic/pydantic/pull/10311)
+
+#### New Features
+
+* Add support for `ZoneInfo` by [@Youssefares](https://github.com/Youssefares) in [#9896](https://github.com/pydantic/pydantic/pull/9896)
+* Add `Config.val_json_bytes` by [@josh-newman](https://github.com/josh-newman) in [#9770](https://github.com/pydantic/pydantic/pull/9770)
+* Add DSN for Snowflake by [@aditkumar72](https://github.com/aditkumar72) in [#10128](https://github.com/pydantic/pydantic/pull/10128)
+* Support `complex` number by [@changhc](https://github.com/changhc) in [#9654](https://github.com/pydantic/pydantic/pull/9654)
+* Add support for `annotated_types.Not` by [@aditkumar72](https://github.com/aditkumar72) in [#10210](https://github.com/pydantic/pydantic/pull/10210)
+* Allow `WithJsonSchema` to inject `$ref`s w/ `http` or `https` links by [@dAIsySHEng1](https://github.com/dAIsySHEng1) in [#9863](https://github.com/pydantic/pydantic/pull/9863)
+* Allow validators to customize validation JSON schema by [@Viicos](https://github.com/Viicos) in [#10094](https://github.com/pydantic/pydantic/pull/10094)
+* Support parametrized `PathLike` types by [@nix010](https://github.com/nix010) in [#9764](https://github.com/pydantic/pydantic/pull/9764)
+* Add tagged union serializer that attempts to use `str` or `callable` discriminators to select the correct serializer by [@sydney-runkle](https://github.com/sydney-runkle) in in [pydantic/pydantic-core#1397](https://github.com/pydantic/pydantic-core/pull/1397)
+
+#### Changes
+
+* Breaking Change: Merge `dict` type `json_schema_extra` by [@sydney-runkle](https://github.com/sydney-runkle) in [#9792](https://github.com/pydantic/pydantic/pull/9792)
+  * For more info (how to replicate old behavior) on this change, see [here](https://docs.pydantic.dev/dev/concepts/json_schema/#merging-json_schema_extra)
+* Refactor annotation injection for known (often generic) types by [@sydney-runkle](https://github.com/sydney-runkle) in [#9979](https://github.com/pydantic/pydantic/pull/9979)
+* Move annotation compatibility errors to validation phase by [@sydney-runkle](https://github.com/sydney-runkle) in [#9999](https://github.com/pydantic/pydantic/pull/9999)
+* Improve runtime errors for string constraints like `pattern` for incompatible types by [@sydney-runkle](https://github.com/sydney-runkle) in [#10158](https://github.com/pydantic/pydantic/pull/10158)
+* Remove `'allOf'` JSON schema workarounds by [@dpeachey](https://github.com/dpeachey) in [#10029](https://github.com/pydantic/pydantic/pull/10029)
+* Remove `typed_dict_cls` data from `CoreMetadata` by [@sydney-runkle](https://github.com/sydney-runkle) in [#10180](https://github.com/pydantic/pydantic/pull/10180)
+* Deprecate passing a dict to the `Examples` class by [@Viicos](https://github.com/Viicos) in [#10181](https://github.com/pydantic/pydantic/pull/10181)
+* Remove `initial_metadata` from internal metadata construct by [@sydney-runkle](https://github.com/sydney-runkle) in [#10194](https://github.com/pydantic/pydantic/pull/10194)
+* Use `re.Pattern.search` instead of `re.Pattern.match` for consistency with `rust` behavior by [@tinez](https://github.com/tinez) in [pydantic/pydantic-core#1368](https://github.com/pydantic/pydantic-core/pull/1368)
+* Show value of wrongly typed data in `pydantic-core` serialization warning by [@BoxyUwU](https://github.com/BoxyUwU) in [pydantic/pydantic-core#1377](https://github.com/pydantic/pydantic-core/pull/1377)
+* Breaking Change: in `pydantic-core`, change `metadata` type hint in core schemas from `Any` -> `Dict[str, Any] | None` by [@sydney-runkle](https://github.com/sydney-runkle) in [pydantic/pydantic-core#1411](https://github.com/pydantic/pydantic-core/pull/1411)
+* Raise helpful warning when `self` isn't returned from model validator by [@sydney-runkle](https://github.com/sydney-runkle) in [#10255](https://github.com/pydantic/pydantic/pull/10255)
+
+#### Performance
+
+* Initial start at improving import times for modules, using caching primarily by [@sydney-runkle](https://github.com/sydney-runkle) in [#10009](https://github.com/pydantic/pydantic/pull/10009)
+* Using cached internal import for `BaseModel` by [@sydney-runkle](https://github.com/sydney-runkle) in [#10013](https://github.com/pydantic/pydantic/pull/10013)
+* Simplify internal generics logic - remove generator overhead by [@sydney-runkle](https://github.com/sydney-runkle) in [#10059](https://github.com/pydantic/pydantic/pull/10059)
+* Remove default module globals from types namespace by [@sydney-runkle](https://github.com/sydney-runkle) in [#10123](https://github.com/pydantic/pydantic/pull/10123)
+* Performance boost: skip caching parent namespaces in most cases by [@sydney-runkle](https://github.com/sydney-runkle) in [#10113](https://github.com/pydantic/pydantic/pull/10113)
+* Update ns stack with already copied ns by [@sydney-runkle](https://github.com/sydney-runkle) in [#10267](https://github.com/pydantic/pydantic/pull/10267)
+
+##### Minor Internal Improvements
+* ⚡️ Speed up `multiple_of_validator()` by 31% in `pydantic/_internal/_validators.py` by [@misrasaurabh1](https://github.com/misrasaurabh1) in [#9839](https://github.com/pydantic/pydantic/pull/9839)
+* ⚡️ Speed up `ModelPrivateAttr.__set_name__()` by 18% in `pydantic/fields.py` by [@misrasaurabh1](https://github.com/misrasaurabh1) in [#9841](https://github.com/pydantic/pydantic/pull/9841)
+* ⚡️ Speed up `dataclass()` by 7% in `pydantic/dataclasses.py` by [@misrasaurabh1](https://github.com/misrasaurabh1) in [#9843](https://github.com/pydantic/pydantic/pull/9843)
+* ⚡️ Speed up function `_field_name_for_signature` by 37% in `pydantic/_internal/_signature.py` by [@misrasaurabh1](https://github.com/misrasaurabh1) in [#9951](https://github.com/pydantic/pydantic/pull/9951)
+* ⚡️ Speed up method `GenerateSchema._unpack_refs_defs` by 26% in `pydantic/_internal/_generate_schema.py` by [@misrasaurabh1](https://github.com/misrasaurabh1) in [#9949](https://github.com/pydantic/pydantic/pull/9949)
+* ⚡️ Speed up function `apply_each_item_validators` by 100% in `pydantic/_internal/_generate_schema.py` by [@misrasaurabh1](https://github.com/misrasaurabh1) in [#9950](https://github.com/pydantic/pydantic/pull/9950)
+* ⚡️ Speed up method `ConfigWrapper.core_config` by 28% in `pydantic/_internal/_config.py` by [@misrasaurabh1](https://github.com/misrasaurabh1) in [#9953](https://github.com/pydantic/pydantic/pull/9953)
+
+#### Fixes
+
+* Respect `use_enum_values` on `Literal` types by [@kwint](https://github.com/kwint) in [#9787](https://github.com/pydantic/pydantic/pull/9787)
+* Prevent type error for exotic `BaseModel/RootModel` inheritance by [@dmontagu](https://github.com/dmontagu) in [#9913](https://github.com/pydantic/pydantic/pull/9913)
+* Fix typing issue with field_validator-decorated methods by [@dmontagu](https://github.com/dmontagu) in [#9914](https://github.com/pydantic/pydantic/pull/9914)
+* Replace `str` type annotation with `Any` in validator factories in documentation on validators by [@maximilianfellhuber](https://github.com/maximilianfellhuber) in [#9885](https://github.com/pydantic/pydantic/pull/9885)
+* Fix `ComputedFieldInfo.wrapped_property` pointer when a property setter is assigned by [@tlambert03](https://github.com/tlambert03) in [#9892](https://github.com/pydantic/pydantic/pull/9892)
+* Fix recursive typing of `main.IncEnx` by [@tlambert03](https://github.com/tlambert03) in [#9924](https://github.com/pydantic/pydantic/pull/9924)
+* Allow usage of `type[Annotated[...]]` by [@Viicos](https://github.com/Viicos) in [#9932](https://github.com/pydantic/pydantic/pull/9932)
+* `mypy` plugin: handle frozen fields on a per-field basis by [@dmontagu](https://github.com/dmontagu) in [#9935](https://github.com/pydantic/pydantic/pull/9935)
+* Fix typo in `invalid-annotated-type` error code by [@sydney-runkle](https://github.com/sydney-runkle) in [#9948](https://github.com/pydantic/pydantic/pull/9948)
+* Simplify schema generation for `uuid`, `url`, and `ip` types by [@sydney-runkle](https://github.com/sydney-runkle) in [#9975](https://github.com/pydantic/pydantic/pull/9975)
+* Move `date` schemas to `_generate_schema.py` by [@sydney-runkle](https://github.com/sydney-runkle) in [#9976](https://github.com/pydantic/pydantic/pull/9976)
+* Move `decimal.Decimal` validation to `_generate_schema.py` by [@sydney-runkle](https://github.com/sydney-runkle) in [#9977](https://github.com/pydantic/pydantic/pull/9977)
+* Simplify IP address schema in `_std_types_schema.py` by [@sydney-runkle](https://github.com/sydney-runkle) in [#9959](https://github.com/pydantic/pydantic/pull/9959)
+* Fix type annotations for some potentially generic `GenerateSchema.match_type` options by [@sydney-runkle](https://github.com/sydney-runkle) in [#9961](https://github.com/pydantic/pydantic/pull/9961)
+* Add class name to "has conflict" warnings by [@msabramo](https://github.com/msabramo) in [#9964](https://github.com/pydantic/pydantic/pull/9964)
+* Fix `dataclass` ignoring `default_factory` passed in Annotated by [@kc0506](https://github.com/kc0506) in [#9971](https://github.com/pydantic/pydantic/pull/9971)
+* Fix `Sequence` ignoring `discriminator` by [@kc0506](https://github.com/kc0506) in [#9980](https://github.com/pydantic/pydantic/pull/9980)
+* Fix typing for `IPvAnyAddress` and `IPvAnyInterface` by [@haoyun](https://github.com/haoyun) in [#9990](https://github.com/pydantic/pydantic/pull/9990)
+* Fix false positives on v1 models in `mypy` plugin for `from_orm` check requiring from_attributes=True config by [@radekwlsk](https://github.com/radekwlsk) in [#9938](https://github.com/pydantic/pydantic/pull/9938)
+* Apply `strict=True` to `__init__` in `mypy` plugin by [@kc0506](https://github.com/kc0506) in [#9998](https://github.com/pydantic/pydantic/pull/9998)
+* Refactor application of `deque` annotations by [@sydney-runkle](https://github.com/sydney-runkle) in [#10018](https://github.com/pydantic/pydantic/pull/10018)
+* Raise a better user error when failing to evaluate a forward reference by [@Viicos](https://github.com/Viicos) in [#10030](https://github.com/pydantic/pydantic/pull/10030)
+* Fix evaluation of `__pydantic_extra__` annotation in specific circumstances by [@Viicos](https://github.com/Viicos) in [#10070](https://github.com/pydantic/pydantic/pull/10070)
+* Fix `frozen` enforcement for `dataclasses` by [@sydney-runkle](https://github.com/sydney-runkle) in [#10066](https://github.com/pydantic/pydantic/pull/10066)
+* Remove logic to handle unused `__get_pydantic_core_schema__` signature by [@Viicos](https://github.com/Viicos) in [#10075](https://github.com/pydantic/pydantic/pull/10075)
+* Use `is_annotated` consistently by [@Viicos](https://github.com/Viicos) in [#10095](https://github.com/pydantic/pydantic/pull/10095)
+* Fix `PydanticDeprecatedSince26` typo by [@kc0506](https://github.com/kc0506) in [#10101](https://github.com/pydantic/pydantic/pull/10101)
+* Improve `pyright` tests, refactor model decorators signatures by [@Viicos](https://github.com/Viicos) in [#10092](https://github.com/pydantic/pydantic/pull/10092)
+* Fix `ip` serialization logic by [@sydney-runkle](https://github.com/sydney-runkle) in [#10112](https://github.com/pydantic/pydantic/pull/10112)
+* Warn when frozen defined twice for `dataclasses` by [@mochi22](https://github.com/mochi22) in [#10082](https://github.com/pydantic/pydantic/pull/10082)
+* Do not compute JSON Schema default when plain serializers are used with `when_used` set to `'json-unless-none'` and the default value is `None` by [@Viicos](https://github.com/Viicos) in [#10121](https://github.com/pydantic/pydantic/pull/10121)
+* Fix `ImportString` special cases by [@sydney-runkle](https://github.com/sydney-runkle) in [#10137](https://github.com/pydantic/pydantic/pull/10137)
+* Blacklist default globals to support exotic user code with `__` prefixed annotations by [@sydney-runkle](https://github.com/sydney-runkle) in [#10136](https://github.com/pydantic/pydantic/pull/10136)
+* Handle `nullable` schemas with `serialization` schema available during JSON Schema generation by [@Viicos](https://github.com/Viicos) in [#10132](https://github.com/pydantic/pydantic/pull/10132)
+* Reorganize `BaseModel` annotations by [@kc0506](https://github.com/kc0506) in [#10110](https://github.com/pydantic/pydantic/pull/10110)
+* Fix core schema simplification when serialization schemas are involved in specific scenarios by [@Viicos](https://github.com/Viicos) in [#10155](https://github.com/pydantic/pydantic/pull/10155)
+* Add support for stringified annotations when using `PrivateAttr` with `Annotated` by [@Viicos](https://github.com/Viicos) in [#10157](https://github.com/pydantic/pydantic/pull/10157)
+* Fix JSON Schema `number` type for literal and enum schemas by [@Viicos](https://github.com/Viicos) in [#10172](https://github.com/pydantic/pydantic/pull/10172)
+* Fix JSON Schema generation of fields with plain validators in serialization mode by [@Viicos](https://github.com/Viicos) in [#10167](https://github.com/pydantic/pydantic/pull/10167)
+* Fix invalid JSON Schemas being generated for functions in certain scenarios by [@Viicos](https://github.com/Viicos) in [#10188](https://github.com/pydantic/pydantic/pull/10188)
+* Make sure generated JSON Schemas are valid in tests by [@Viicos](https://github.com/Viicos) in [#10182](https://github.com/pydantic/pydantic/pull/10182)
+* Fix key error with custom serializer by [@sydney-runkle](https://github.com/sydney-runkle) in [#10200](https://github.com/pydantic/pydantic/pull/10200)
+* Add 'wss' for allowed schemes in NatsDsn by [@swelborn](https://github.com/swelborn) in [#10224](https://github.com/pydantic/pydantic/pull/10224)
+* Fix `Mapping` and `MutableMapping` annotations to use mapping schema instead of dict schema by [@sydney-runkle](https://github.com/sydney-runkle) in [#10020](https://github.com/pydantic/pydantic/pull/10020)
+* Fix JSON Schema generation for constrained dates by [@Viicos](https://github.com/Viicos) in [#10185](https://github.com/pydantic/pydantic/pull/10185)
+* Fix discriminated union bug regression when using enums by [@kfreezen](https://github.com/kfreezen) in [pydantic/pydantic-core#1286](https://github.com/pydantic/pydantic-core/pull/1286)
+* Fix `field_serializer` with computed field when using `*` by [@nix010](https://github.com/nix010) in [pydantic/pydantic-core#1349](https://github.com/pydantic/pydantic-core/pull/1349)
+* Try each option in `Union` serializer before inference by [@sydney-runkle](https://github.com/sydney-runkle) in [pydantic/pydantic-core#1398](https://github.com/pydantic/pydantic-core/pull/1398)
+* Fix `float` serialization behavior in `strict` mode by [@sydney-runkle](https://github.com/sydney-runkle) in [pydantic/pydantic-core#1400](https://github.com/pydantic/pydantic-core/pull/1400)
+* Introduce `exactness` into Decimal validation logic to improve union validation behavior by [@sydney-runkle](https://github.com/sydney-runkle) in in [pydantic/pydantic-core#1405](https://github.com/pydantic/pydantic-core/pull/1405)
+* Fix new warnings assertions to use `pytest.warns()` by [@mgorny](https://github.com/mgorny) in [#10241](https://github.com/pydantic/pydantic/pull/10241)
+* Fix a crash when cleaning the namespace in `ModelMetaclass` by [@Viicos](https://github.com/Viicos) in [#10242](https://github.com/pydantic/pydantic/pull/10242)
+* Fix parent namespace issue with model rebuilds by [@sydney-runkle](https://github.com/sydney-runkle) in [#10257](https://github.com/pydantic/pydantic/pull/10257)
+* Remove defaults filter for namespace by [@sydney-runkle](https://github.com/sydney-runkle) in [#10261](https://github.com/pydantic/pydantic/pull/10261)
+* Use identity instead of equality after validating model in `__init__` by [@Viicos](https://github.com/Viicos) in [#10264](https://github.com/pydantic/pydantic/pull/10264)
+* Support `BigInt` serialization for `int` subclasses by [@kxx317](https://github.com/kxx317) in [pydantic/pydantic-core#1417](https://github.com/pydantic/pydantic-core/pull/1417)
+* Support signature for wrap validators without `info` by [@sydney-runkle](https://github.com/sydney-runkle) in [#10277](https://github.com/pydantic/pydantic/pull/10277)
+* Ensure `__pydantic_complete__` is set when rebuilding `dataclasses` by [@Viicos](https://github.com/Viicos) in [#10291](https://github.com/pydantic/pydantic/pull/10291)
+* Respect `schema_generator` config value in `TypeAdapter` by [@sydney-runkle](https://github.com/sydney-runkle) in [#10300](https://github.com/pydantic/pydantic/pull/10300)
+
+### New Contributors
+
+#### `pydantic`
+
+* [@kwint](https://github.com/kwint) made their first contribution in [#9787](https://github.com/pydantic/pydantic/pull/9787)
+* [@seekinginfiniteloop](https://github.com/seekinginfiniteloop) made their first contribution in [#9822](https://github.com/pydantic/pydantic/pull/9822)
+* [@a-alexander](https://github.com/a-alexander) made their first contribution in [#9848](https://github.com/pydantic/pydantic/pull/9848)
+* [@maximilianfellhuber](https://github.com/maximilianfellhuber) made their first contribution in [#9885](https://github.com/pydantic/pydantic/pull/9885)
+* [@karmaBonfire](https://github.com/karmaBonfire) made their first contribution in [#9945](https://github.com/pydantic/pydantic/pull/9945)
+* [@s-rigaud](https://github.com/s-rigaud) made their first contribution in [#9958](https://github.com/pydantic/pydantic/pull/9958)
+* [@msabramo](https://github.com/msabramo) made their first contribution in [#9964](https://github.com/pydantic/pydantic/pull/9964)
+* [@DimaCybr](https://github.com/DimaCybr) made their first contribution in [#9972](https://github.com/pydantic/pydantic/pull/9972)
+* [@kc0506](https://github.com/kc0506) made their first contribution in [#9971](https://github.com/pydantic/pydantic/pull/9971)
+* [@haoyun](https://github.com/haoyun) made their first contribution in [#9990](https://github.com/pydantic/pydantic/pull/9990)
+* [@radekwlsk](https://github.com/radekwlsk) made their first contribution in [#9938](https://github.com/pydantic/pydantic/pull/9938)
+* [@dpeachey](https://github.com/dpeachey) made their first contribution in [#10029](https://github.com/pydantic/pydantic/pull/10029)
+* [@BoxyUwU](https://github.com/BoxyUwU) made their first contribution in [#10085](https://github.com/pydantic/pydantic/pull/10085)
+* [@mochi22](https://github.com/mochi22) made their first contribution in [#10082](https://github.com/pydantic/pydantic/pull/10082)
+* [@aditkumar72](https://github.com/aditkumar72) made their first contribution in [#10128](https://github.com/pydantic/pydantic/pull/10128)
+* [@changhc](https://github.com/changhc) made their first contribution in [#9654](https://github.com/pydantic/pydantic/pull/9654)
+* [@insumanth](https://github.com/insumanth) made their first contribution in [#10229](https://github.com/pydantic/pydantic/pull/10229)
+* [@AdolfoVillalobos](https://github.com/AdolfoVillalobos) made their first contribution in [#10240](https://github.com/pydantic/pydantic/pull/10240)
+* [@bllchmbrs](https://github.com/bllchmbrs) made their first contribution in [#10270](https://github.com/pydantic/pydantic/pull/10270)
+
+#### `pydantic-core`
+
+* [@kfreezen](https://github.com/kfreezen) made their first contribution in [pydantic/pydantic-core#1286](https://github.com/pydantic/pydantic-core/pull/1286)
+* [@tinez](https://github.com/tinez) made their first contribution in [pydantic/pydantic-core#1368](https://github.com/pydantic/pydantic-core/pull/1368)
+* [@fft001](https://github.com/fft001) made their first contribution in [pydantic/pydantic-core#1362](https://github.com/pydantic/pydantic-core/pull/1362)
+* [@nix010](https://github.com/nix010) made their first contribution in [pydantic/pydantic-core#1349](https://github.com/pydantic/pydantic-core/pull/1349)
+* [@BoxyUwU](https://github.com/BoxyUwU) made their first contribution in [pydantic/pydantic-core#1379](https://github.com/pydantic/pydantic-core/pull/1379)
+* [@candleindark](https://github.com/candleindark) made their first contribution in [pydantic/pydantic-core#1404](https://github.com/pydantic/pydantic-core/pull/1404)
+* [@changhc](https://github.com/changhc) made their first contribution in [pydantic/pydantic-core#1331](https://github.com/pydantic/pydantic-core/pull/1331)
+
+## v2.9.0b2 (2024-08-30)
+
+Pre-release, see [the GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.9.0b2) for details.
+
+## v2.9.0b1 (2024-08-26)
+
+Pre-release, see [the GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.9.0b1) for details.
+
+## v2.8.2 (2024-07-03)
+
+[GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.8.2)
+
+### What's Changed
+
+#### Fixes
+
+* Fix issue with assertion caused by pluggable schema validator by [@dmontagu](https://github.com/dmontagu) in [#9838](https://github.com/pydantic/pydantic/pull/9838)
+
+## v2.8.1 (2024-07-03)
+
+[GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.8.1)
+
+### What's Changed
+
+#### Packaging
+* Bump `ruff` to `v0.5.0` and `pyright` to `v1.1.369` by [@sydney-runkle](https://github.com/sydney-runkle) in [#9801](https://github.com/pydantic/pydantic/pull/9801)
+* Bump `pydantic-core` to `v2.20.1`, `pydantic-extra-types` to `v2.9.0` by [@sydney-runkle](https://github.com/sydney-runkle) in [#9832](https://github.com/pydantic/pydantic/pull/9832)
+
+#### Fixes
+* Fix breaking change in `to_snake` from v2.7 -> v2.8 by [@sydney-runkle](https://github.com/sydney-runkle) in [#9812](https://github.com/pydantic/pydantic/pull/9812)
+* Fix list constraint json schema application by [@sydney-runkle](https://github.com/sydney-runkle) in [#9818](https://github.com/pydantic/pydantic/pull/9818)
+* Support time duration more than 23 by [@nix010](https://github.com/nix010) in [pydantic/speedate#64](https://github.com/pydantic/speedate/pull/64)
+* Fix millisecond fraction being handled with the wrong scale by [@davidhewitt](https://github.com/davidhewitt) in [pydantic/speedate#65](https://github.com/pydantic/speedate/pull/65)
+* Handle negative fractional durations correctly by [@sydney-runkle](https://github.com/sydney-runkle) in [pydantic/speedate#71](https://github.com/pydantic/speedate/pull/71)
+
+## v2.8.0 (2024-07-01)
+
+[GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.8.0)
+
+The code released in v2.8.0 is functionally identical to that of v2.8.0b1.
+
+### What's Changed
+
+#### Packaging
+
+* Update citation version automatically with new releases by [@sydney-runkle](https://github.com/sydney-runkle) in [#9673](https://github.com/pydantic/pydantic/pull/9673)
+* Bump pyright to `v1.1.367` and add type checking tests for pipeline API by [@adriangb](https://github.com/adriangb) in [#9674](https://github.com/pydantic/pydantic/pull/9674)
+* Update `pydantic.v1` stub to `v1.10.17` by [@sydney-runkle](https://github.com/sydney-runkle) in [#9707](https://github.com/pydantic/pydantic/pull/9707)
+* General package updates to prep for `v2.8.0b1` by [@sydney-runkle](https://github.com/sydney-runkle) in [#9741](https://github.com/pydantic/pydantic/pull/9741)
+* Bump `pydantic-core` to `v2.20.0` by [@sydney-runkle](https://github.com/sydney-runkle) in [#9745](https://github.com/pydantic/pydantic/pull/9745)
+* Add support for Python 3.13 by [@sydney-runkle](https://github.com/sydney-runkle) in [#9743](https://github.com/pydantic/pydantic/pull/9743)
+* Update `pdm` version used for `pdm.lock` to v2.16.1 by [@sydney-runkle](https://github.com/sydney-runkle) in [#9761](https://github.com/pydantic/pydantic/pull/9761)
+* Update to `ruff` `v0.4.8` by [@Viicos](https://github.com/Viicos) in [#9585](https://github.com/pydantic/pydantic/pull/9585)
+
+#### New Features
+
+* Experimental: support `defer_build` for `TypeAdapter` by [@MarkusSintonen](https://github.com/MarkusSintonen) in [#8939](https://github.com/pydantic/pydantic/pull/8939)
+* Implement `deprecated` field in json schema by [@NeevCohen](https://github.com/NeevCohen) in [#9298](https://github.com/pydantic/pydantic/pull/9298)
+* Experimental: Add pipeline API by [@adriangb](https://github.com/adriangb) in [#9459](https://github.com/pydantic/pydantic/pull/9459)
+* Add support for programmatic title generation by [@NeevCohen](https://github.com/NeevCohen) in [#9183](https://github.com/pydantic/pydantic/pull/9183)
+* Implement `fail_fast` feature by [@uriyyo](https://github.com/uriyyo) in [#9708](https://github.com/pydantic/pydantic/pull/9708)
+* Add `ser_json_inf_nan='strings'` mode to produce valid JSON by [@josh-newman](https://github.com/josh-newman) in [pydantic/pydantic-core#1307](https://github.com/pydantic/pydantic-core/pull/1307)
+
+#### Changes
+
+* Add warning when "alias" is set in ignored `Annotated` field by [@nix010](https://github.com/nix010) in [#9170](https://github.com/pydantic/pydantic/pull/9170)
+* Support serialization of some serializable defaults in JSON schema by [@sydney-runkle](https://github.com/sydney-runkle) in [#9624](https://github.com/pydantic/pydantic/pull/9624)
+* Relax type specification for `__validators__` values in `create_model` by [@sydney-runkle](https://github.com/sydney-runkle) in [#9697](https://github.com/pydantic/pydantic/pull/9697)
+* **Breaking Change:** Improve `smart` union matching logic by [@sydney-runkle](https://github.com/sydney-runkle) in [pydantic/pydantic-core#1322](https://github.com/pydantic/pydantic-core/pull/1322)
+You can read more about our `smart` union matching logic [here](https://docs.pydantic.dev/dev/concepts/unions/#smart-mode). In some cases, if the old behavior
+is desired, you can switch to `left-to-right` mode and change the order of your `Union` members.
+
+#### Performance
+
+##### Internal Improvements
+
+* ⚡️ Speed up `_display_error_loc()` by 25% in `pydantic/v1/error_wrappers.py` by [@misrasaurabh1](https://github.com/misrasaurabh1) in [#9653](https://github.com/pydantic/pydantic/pull/9653)
+* ⚡️ Speed up `_get_all_json_refs()` by 34% in `pydantic/json_schema.py` by [@misrasaurabh1](https://github.com/misrasaurabh1) in [#9650](https://github.com/pydantic/pydantic/pull/9650)
+* ⚡️ Speed up `is_pydantic_dataclass()` by 41% in `pydantic/dataclasses.py` by [@misrasaurabh1](https://github.com/misrasaurabh1) in [#9652](https://github.com/pydantic/pydantic/pull/9652)
+* ⚡️ Speed up `to_snake()` by 27% in `pydantic/alias_generators.py` by [@misrasaurabh1](https://github.com/misrasaurabh1) in [#9747](https://github.com/pydantic/pydantic/pull/9747)
+* ⚡️ Speed up `unwrap_wrapped_function()` by 93% in `pydantic/_internal/_decorators.py` by [@misrasaurabh1](https://github.com/misrasaurabh1) in [#9727](https://github.com/pydantic/pydantic/pull/9727)
+
+#### Fixes
+
+* Replace `__spec__.parent` with `__package__` by [@hramezani](https://github.com/hramezani) in [#9331](https://github.com/pydantic/pydantic/pull/9331)
+* Fix Outputted Model JSON Schema for `Sequence` type by [@anesmemisevic](https://github.com/anesmemisevic) in [#9303](https://github.com/pydantic/pydantic/pull/9303)
+* Fix typing of `_frame_depth` by [@Viicos](https://github.com/Viicos) in [#9353](https://github.com/pydantic/pydantic/pull/9353)
+* Make `ImportString` json schema compatible by [@amitschang](https://github.com/amitschang) in [#9344](https://github.com/pydantic/pydantic/pull/9344)
+* Hide private attributes (`PrivateAttr`) from `__init__` signature in type checkers by [@idan22moral](https://github.com/idan22moral) in [#9293](https://github.com/pydantic/pydantic/pull/9293)
+* Make detection of `TypeVar` defaults robust to the CPython `PEP-696` implementation by [@AlexWaygood](https://github.com/AlexWaygood) in [#9426](https://github.com/pydantic/pydantic/pull/9426)
+* Fix usage of `PlainSerializer` with builtin types by [@Viicos](https://github.com/Viicos) in [#9450](https://github.com/pydantic/pydantic/pull/9450)
+* Add more robust custom validation examples by [@ChrisPappalardo](https://github.com/ChrisPappalardo) in [#9468](https://github.com/pydantic/pydantic/pull/9468)
+* Fix ignored `strict` specification for `StringConstraint(strict=False)` by [@vbmendes](https://github.com/vbmendes) in [#9476](https://github.com/pydantic/pydantic/pull/9476)
+* **Breaking Change:** Use PEP 570 syntax by [@Viicos](https://github.com/Viicos) in [#9479](https://github.com/pydantic/pydantic/pull/9479)
+* Use `Self` where possible by [@Viicos](https://github.com/Viicos) in [#9479](https://github.com/pydantic/pydantic/pull/9479)
+* Do not alter `RootModel.model_construct` signature in the `mypy` plugin by [@Viicos](https://github.com/Viicos) in [#9480](https://github.com/pydantic/pydantic/pull/9480)
+* Fixed type hint of `validation_context` by [@OhioDschungel6](https://github.com/OhioDschungel6) in [#9508](https://github.com/pydantic/pydantic/pull/9508)
+* Support context being passed to TypeAdapter's `dump_json`/`dump_python` by [@alexcouper](https://github.com/alexcouper) in [#9495](https://github.com/pydantic/pydantic/pull/9495)
+* Updates type signature for `Field()` constructor by [@bjmc](https://github.com/bjmc) in [#9484](https://github.com/pydantic/pydantic/pull/9484)
+* Improve builtin alias generators by [@sydney-runkle](https://github.com/sydney-runkle) in [#9561](https://github.com/pydantic/pydantic/pull/9561)
+* Fix typing of `TypeAdapter` by [@Viicos](https://github.com/Viicos) in [#9570](https://github.com/pydantic/pydantic/pull/9570)
+* Add fallback default value for private fields in `__setstate__` of BaseModel by [@anhpham1509](https://github.com/anhpham1509) in [#9584](https://github.com/pydantic/pydantic/pull/9584)
+* Support `PEP 746` by [@adriangb](https://github.com/adriangb) in [#9587](https://github.com/pydantic/pydantic/pull/9587)
+* Allow validator and serializer functions to have default values by [@Viicos](https://github.com/Viicos) in [#9478](https://github.com/pydantic/pydantic/pull/9478)
+* Fix bug with mypy plugin's handling of covariant `TypeVar` fields by [@dmontagu](https://github.com/dmontagu) in [#9606](https://github.com/pydantic/pydantic/pull/9606)
+* Fix multiple annotation / constraint application logic by [@sydney-runkle](https://github.com/sydney-runkle) in [#9623](https://github.com/pydantic/pydantic/pull/9623)
+* Respect `regex` flags in validation and json schema by [@sydney-runkle](https://github.com/sydney-runkle) in [#9591](https://github.com/pydantic/pydantic/pull/9591)
+* Fix type hint on `IpvAnyAddress` by [@sydney-runkle](https://github.com/sydney-runkle) in [#9640](https://github.com/pydantic/pydantic/pull/9640)
+* Allow a field specifier on `__pydantic_extra__` by [@dmontagu](https://github.com/dmontagu) in [#9659](https://github.com/pydantic/pydantic/pull/9659)
+* Use normalized case for file path comparison by [@sydney-runkle](https://github.com/sydney-runkle) in [#9737](https://github.com/pydantic/pydantic/pull/9737)
+* Modify constraint application logic to allow field constraints on `Optional[Decimal]` by [@lazyhope](https://github.com/lazyhope) in [#9754](https://github.com/pydantic/pydantic/pull/9754)
+* `validate_call` type params fix by [@sydney-runkle](https://github.com/sydney-runkle) in [#9760](https://github.com/pydantic/pydantic/pull/9760)
+* Check all warnings returned by pytest.warns() by [@s-t-e-v-e-n-k](https://github.com/s-t-e-v-e-n-k) in [#9702](https://github.com/pydantic/pydantic/pull/9702)
+* Reuse `re.Pattern` object in regex patterns to allow for regex flags by [@sydney-runkle](https://github.com/sydney-runkle) in [pydantic/pydantic-core#1318](https://github.com/pydantic/pydantic-core/pull/1318)
+
+### New Contributors
+
+* [@idan22moral](https://github.com/idan22moral) made their first contribution in [#9294](https://github.com/pydantic/pydantic/pull/9294)
+* [@anesmemisevic](https://github.com/anesmemisevic) made their first contribution in [#9303](https://github.com/pydantic/pydantic/pull/9303)
+* [@max-muoto](https://github.com/max-muoto) made their first contribution in [#9338](https://github.com/pydantic/pydantic/pull/9338)
+* [@amitschang](https://github.com/amitschang) made their first contribution in [#9344](https://github.com/pydantic/pydantic/pull/9344)
+* [@paulmartin91](https://github.com/paulmartin91) made their first contribution in [#9410](https://github.com/pydantic/pydantic/pull/9410)
+* [@OhioDschungel6](https://github.com/OhioDschungel6) made their first contribution in [#9405](https://github.com/pydantic/pydantic/pull/9405)
+* [@AlexWaygood](https://github.com/AlexWaygood) made their first contribution in [#9426](https://github.com/pydantic/pydantic/pull/9426)
+* [@kinuax](https://github.com/kinuax) made their first contribution in [#9433](https://github.com/pydantic/pydantic/pull/9433)
+* [@antoni-jamiolkowski](https://github.com/antoni-jamiolkowski) made their first contribution in [#9431](https://github.com/pydantic/pydantic/pull/9431)
+* [@candleindark](https://github.com/candleindark) made their first contribution in [#9448](https://github.com/pydantic/pydantic/pull/9448)
+* [@nix010](https://github.com/nix010) made their first contribution in [#9170](https://github.com/pydantic/pydantic/pull/9170)
+* [@tomy0000000](https://github.com/tomy0000000) made their first contribution in [#9457](https://github.com/pydantic/pydantic/pull/9457)
+* [@vbmendes](https://github.com/vbmendes) made their first contribution in [#9470](https://github.com/pydantic/pydantic/pull/9470)
+* [@micheleAlberto](https://github.com/micheleAlberto) made their first contribution in [#9471](https://github.com/pydantic/pydantic/pull/9471)
+* [@ChrisPappalardo](https://github.com/ChrisPappalardo) made their first contribution in [#9468](https://github.com/pydantic/pydantic/pull/9468)
+* [@blueTurtz](https://github.com/blueTurtz) made their first contribution in [#9475](https://github.com/pydantic/pydantic/pull/9475)
+* [@WinterBlue16](https://github.com/WinterBlue16) made their first contribution in [#9477](https://github.com/pydantic/pydantic/pull/9477)
+* [@bittner](https://github.com/bittner) made their first contribution in [#9500](https://github.com/pydantic/pydantic/pull/9500)
+* [@alexcouper](https://github.com/alexcouper) made their first contribution in [#9495](https://github.com/pydantic/pydantic/pull/9495)
+* [@bjmc](https://github.com/bjmc) made their first contribution in [#9484](https://github.com/pydantic/pydantic/pull/9484)
+* [@pjvv](https://github.com/pjvv) made their first contribution in [#9529](https://github.com/pydantic/pydantic/pull/9529)
+* [@nedbat](https://github.com/nedbat) made their first contribution in [#9530](https://github.com/pydantic/pydantic/pull/9530)
+* [@gunnellEvan](https://github.com/gunnellEvan) made their first contribution in [#9469](https://github.com/pydantic/pydantic/pull/9469)
+* [@jaymbans](https://github.com/jaymbans) made their first contribution in [#9531](https://github.com/pydantic/pydantic/pull/9531)
+* [@MarcBresson](https://github.com/MarcBresson) made their first contribution in [#9534](https://github.com/pydantic/pydantic/pull/9534)
+* [@anhpham1509](https://github.com/anhpham1509) made their first contribution in [#9584](https://github.com/pydantic/pydantic/pull/9584)
+* [@K-dash](https://github.com/K-dash) made their first contribution in [#9595](https://github.com/pydantic/pydantic/pull/9595)
+* [@s-t-e-v-e-n-k](https://github.com/s-t-e-v-e-n-k) made their first contribution in [#9527](https://github.com/pydantic/pydantic/pull/9527)
+* [@airwoodix](https://github.com/airwoodix) made their first contribution in [#9506](https://github.com/pydantic/pydantic/pull/9506)
+* [@misrasaurabh1](https://github.com/misrasaurabh1) made their first contribution in [#9653](https://github.com/pydantic/pydantic/pull/9653)
+* [@AlessandroMiola](https://github.com/AlessandroMiola) made their first contribution in [#9740](https://github.com/pydantic/pydantic/pull/9740)
+* [@mylapallilavanyaa](https://github.com/mylapallilavanyaa) made their first contribution in [#9746](https://github.com/pydantic/pydantic/pull/9746)
+* [@lazyhope](https://github.com/lazyhope) made their first contribution in [#9754](https://github.com/pydantic/pydantic/pull/9754)
+* [@YassinNouh21](https://github.com/YassinNouh21) made their first contribution in [#9759](https://github.com/pydantic/pydantic/pull/9759)
+
+## v2.8.0b1 (2024-06-27)
+
+Pre-release, see [the GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.8.0b1) for details.
+
+## v2.7.4 (2024-06-12)
+
+[Github release](https://github.com/pydantic/pydantic/releases/tag/v2.7.4)
+
+### What's Changed
+
+#### Packaging
+
+* Bump `pydantic.v1` to `v1.10.16` reference by [@sydney-runkle](https://github.com/sydney-runkle) in [#9639](https://github.com/pydantic/pydantic/pull/9639)
+
+#### Fixes
+
+* Specify `recursive_guard` as kwarg in `FutureRef._evaluate` by [@vfazio](https://github.com/vfazio) in [#9612](https://github.com/pydantic/pydantic/pull/9612)
+
+## v2.7.3 (2024-06-03)
+
+[GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.7.3)
+
+### What's Changed
+
+#### Packaging
+
+* Bump `pydantic-core` to `v2.18.4` by [@sydney-runkle](https://github.com/sydney-runkle) in [#9550](https://github.com/pydantic/pydantic/pull/9550)
+
+#### Fixes
+
+* Fix u style unicode strings in python [@samuelcolvin](https://github.com/samuelcolvin) in [pydantic/jiter#110](https://github.com/pydantic/jiter/pull/110)
+
+## v2.7.2 (2024-05-28)
+
+[GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.7.2)
+
+### What's Changed
+
+#### Packaging
+
+* Bump `pydantic-core` to `v2.18.3` by [@sydney-runkle](https://github.com/sydney-runkle) in [#9515](https://github.com/pydantic/pydantic/pull/9515)
+
+#### Fixes
+
+* Replace `__spec__.parent` with `__package__` by [@hramezani](https://github.com/hramezani) in [#9331](https://github.com/pydantic/pydantic/pull/9331)
+* Fix validation of `int`s with leading unary minus by [@RajatRajdeep](https://github.com/RajatRajdeep) in [pydantic/pydantic-core#1291](https://github.com/pydantic/pydantic-core/pull/1291)
+* Fix `str` subclass validation for enums by [@sydney-runkle](https://github.com/sydney-runkle) in [pydantic/pydantic-core#1273](https://github.com/pydantic/pydantic-core/pull/1273)
+* Support `BigInt`s in `Literal`s and `Enum`s by [@samuelcolvin](https://github.com/samuelcolvin) in [pydantic/pydantic-core#1297](https://github.com/pydantic/pydantic-core/pull/1297)
+* Fix: uuid - allow `str` subclass as input by [@davidhewitt](https://github.com/davidhewitt) in [pydantic/pydantic-core#1296](https://github.com/pydantic/pydantic-core/pull/1296)
+
+## v2.7.1 (2024-04-23)
+
+[GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.7.1)
+
+### What's Changed
+
+#### Packaging
+
+* Bump `pydantic-core` to `v2.18.2` by [@sydney-runkle](https://github.com/sydney-runkle) in [#9307](https://github.com/pydantic/pydantic/pull/9307)
+
+#### New Features
+
+* Ftp and Websocket connection strings support by [@CherrySuryp](https://github.com/CherrySuryp) in [#9205](https://github.com/pydantic/pydantic/pull/9205)
+
+#### Changes
+
+* Use field description for RootModel schema description when there is `…` by [@LouisGobert](https://github.com/LouisGobert) in [#9214](https://github.com/pydantic/pydantic/pull/9214)
+
+#### Fixes
+
+* Fix `validation_alias` behavior with `model_construct` for `AliasChoices` and `AliasPath` by [@sydney-runkle](https://github.com/sydney-runkle) in [#9223](https://github.com/pydantic/pydantic/pull/9223)
+* Revert `typing.Literal` and import it outside the TYPE_CHECKING block by [@frost-nzcr4](https://github.com/frost-nzcr4) in [#9232](https://github.com/pydantic/pydantic/pull/9232)
+* Fix `Secret` serialization schema, applicable for unions by [@sydney-runkle](https://github.com/sydney-runkle) in [#9240](https://github.com/pydantic/pydantic/pull/9240)
+* Fix `strict` application to `function-after` with `use_enum_values` by [@sydney-runkle](https://github.com/sydney-runkle) in [#9279](https://github.com/pydantic/pydantic/pull/9279)
+* Address case where `model_construct` on a class which defines `model_post_init` fails with `AttributeError` by [@babygrimes](https://github.com/babygrimes) in [#9168](https://github.com/pydantic/pydantic/pull/9168)
+* Fix `model_json_schema` with config types by [@NeevCohen](https://github.com/NeevCohen) in [#9287](https://github.com/pydantic/pydantic/pull/9287)
+* Support multiple zeros as an `int` by [@samuelcolvin](https://github.com/samuelcolvin) in [pydantic/pydantic-core#1269](https://github.com/pydantic/pydantic-core/pull/1269)
+* Fix validation of `int`s with leading unary plus by [@cknv](https://github.com/cknv) in [pydantic/pydantic-core#1272](https://github.com/pydantic/pydantic-core/pull/1272)
+* Fix interaction between `extra != 'ignore'` and `from_attributes=True` by [@davidhewitt](https://github.com/davidhewitt) in [pydantic/pydantic-core#1276](https://github.com/pydantic/pydantic-core/pull/1276)
+* Handle error from `Enum`'s `missing` function as `ValidationError` by [@sydney-runkle](https://github.com/sydney-runkle) in [pydantic/pydantic-core#1274](https://github.com/pydantic/pydantic-core/pull/1754)
+* Fix memory leak with `Iterable` validation by [@davidhewitt](https://github.com/davidhewitt) in [pydantic/pydantic-core#1271](https://github.com/pydantic/pydantic-core/pull/1751)
+
+### New Contributors
+
+* [@zzstoatzz](https://github.com/zzstoatzz) made their first contribution in [#9219](https://github.com/pydantic/pydantic/pull/9219)
+* [@frost-nzcr4](https://github.com/frost-nzcr4) made their first contribution in [#9232](https://github.com/pydantic/pydantic/pull/9232)
+* [@CherrySuryp](https://github.com/CherrySuryp) made their first contribution in [#9205](https://github.com/pydantic/pydantic/pull/9205)
+* [@vagenas](https://github.com/vagenas) made their first contribution in [#9268](https://github.com/pydantic/pydantic/pull/9268)
+* [@ollz272](https://github.com/ollz272) made their first contribution in [#9262](https://github.com/pydantic/pydantic/pull/9262)
+* [@babygrimes](https://github.com/babygrimes) made their first contribution in [#9168](https://github.com/pydantic/pydantic/pull/9168)
+* [@swelborn](https://github.com/swelborn) made their first contribution in [#9296](https://github.com/pydantic/pydantic/pull/9296)
+* [@kf-novi](https://github.com/kf-novi) made their first contribution in [#9236](https://github.com/pydantic/pydantic/pull/9236)
+* [@lgeiger](https://github.com/lgeiger) made their first contribution in [#9288](https://github.com/pydantic/pydantic/pull/9288)
+
+## v2.7.0 (2024-04-11)
+
+[GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.7.0)
+
+The code released in v2.7.0 is practically identical to that of v2.7.0b1.
+
+### What's Changed
+
+#### Packaging
+
+* Reorganize `pyproject.toml` sections by [@Viicos](https://github.com/Viicos) in [#8899](https://github.com/pydantic/pydantic/pull/8899)
+* Bump `pydantic-core` to `v2.18.1` by [@sydney-runkle](https://github.com/sydney-runkle) in [#9211](https://github.com/pydantic/pydantic/pull/9211)
+* Adopt `jiter` `v0.2.0` by [@samuelcolvin](https://github.com/samuelcolvin) in [pydantic/pydantic-core#1250](https://github.com/pydantic/pydantic-core/pull/1250)
+
+#### New Features
+
+* Extract attribute docstrings from `FieldInfo.description` by [@Viicos](https://github.com/Viicos) in [#6563](https://github.com/pydantic/pydantic/pull/6563)
+* Add a `with_config` decorator to comply with typing spec by [@Viicos](https://github.com/Viicos) in [#8611](https://github.com/pydantic/pydantic/pull/8611)
+* Allow an optional separator splitting the value and unit of the result of `ByteSize.human_readable` by [@jks15satoshi](https://github.com/jks15satoshi) in [#8706](https://github.com/pydantic/pydantic/pull/8706)
+* Add generic `Secret` base type by [@conradogarciaberrotaran](https://github.com/conradogarciaberrotaran) in [#8519](https://github.com/pydantic/pydantic/pull/8519)
+* Make use of `Sphinx` inventories for cross references in docs by [@Viicos](https://github.com/Viicos) in [#8682](https://github.com/pydantic/pydantic/pull/8682)
+* Add environment variable to disable plugins by [@geospackle](https://github.com/geospackle) in [#8767](https://github.com/pydantic/pydantic/pull/8767)
+* Add support for `deprecated` fields by [@Viicos](https://github.com/Viicos) in [#8237](https://github.com/pydantic/pydantic/pull/8237)
+* Allow `field_serializer('*')` by [@ornariece](https://github.com/ornariece) in [#9001](https://github.com/pydantic/pydantic/pull/9001)
+* Handle a case when `model_config` is defined as a model property by [@alexeyt101](https://github.com/alexeyt101) in [#9004](https://github.com/pydantic/pydantic/pull/9004)
+* Update `create_model()` to support `typing.Annotated` as input by [@wannieman98](https://github.com/wannieman98) in [#8947](https://github.com/pydantic/pydantic/pull/8947)
+* Add `ClickhouseDsn` support by [@solidguy7](https://github.com/solidguy7) in [#9062](https://github.com/pydantic/pydantic/pull/9062)
+* Add support for `re.Pattern[str]` to `pattern` field by [@jag-k](https://github.com/jag-k) in [#9053](https://github.com/pydantic/pydantic/pull/9053)
+* Support for `serialize_as_any` runtime setting by [@sydney-runkle](https://github.com/sydney-runkle) in [#8830](https://github.com/pydantic/pydantic/pull/8830)
+* Add support for `typing.Self` by [@Youssefares](https://github.com/Youssefares) in [#9023](https://github.com/pydantic/pydantic/pull/9023)
+* Ability to pass `context` to serialization by [@ornariece](https://github.com/ornariece) in [#8965](https://github.com/pydantic/pydantic/pull/8965)
+* Add feedback widget to docs with flarelytics integration by [@sydney-runkle](https://github.com/sydney-runkle) in [#9129](https://github.com/pydantic/pydantic/pull/9129)
+* Support for parsing partial JSON strings in Python by [@samuelcolvin](https://github.com/samuelcolvin) in [pydantic/jiter#66](https://github.com/pydantic/jiter/pull/66)
+
+**Finalized in v2.7.0, rather than v2.7.0b1:**
+* Add support for field level number to str coercion option by [@NeevCohen](https://github.com/NeevCohen) in [#9137](https://github.com/pydantic/pydantic/pull/9137)
+* Update `warnings` parameter for serialization utilities to allow raising a warning by [@Lance-Drane](https://github.com/Lance-Drane) in [#9166](https://github.com/pydantic/pydantic/pull/9166)
+
+#### Changes
+
+* Correct docs, logic for `model_construct` behavior with `extra` by [@sydney-runkle](https://github.com/sydney-runkle) in [#8807](https://github.com/pydantic/pydantic/pull/8807)
+* Improve error message for improper `RootModel` subclasses by [@sydney-runkle](https://github.com/sydney-runkle) in [#8857](https://github.com/pydantic/pydantic/pull/8857)
+* **Breaking Change:** Use `PEP570` syntax by [@Viicos](https://github.com/Viicos) in [#8940](https://github.com/pydantic/pydantic/pull/8940)
+* Add `enum` and `type` to the JSON schema for single item literals by [@dmontagu](https://github.com/dmontagu) in [#8944](https://github.com/pydantic/pydantic/pull/8944)
+* Deprecate `update_json_schema` internal function by [@sydney-runkle](https://github.com/sydney-runkle) in [#9125](https://github.com/pydantic/pydantic/pull/9125)
+* Serialize duration to hour minute second, instead of just seconds by [@kakilangit](https://github.com/kakilangit) in [pydantic/speedate#50](https://github.com/pydantic/speedate/pull/50)
+* Trimming str before parsing to int and float by [@hungtsetse](https://github.com/hungtsetse) in [pydantic/pydantic-core#1203](https://github.com/pydantic/pydantic-core/pull/1203)
+
+#### Performance
+
+* `enum` validator improvements by [@samuelcolvin](https://github.com/samuelcolvin) in [#9045](https://github.com/pydantic/pydantic/pull/9045)
+* Move `enum` validation and serialization to Rust by [@samuelcolvin](https://github.com/samuelcolvin) in [#9064](https://github.com/pydantic/pydantic/pull/9064)
+* Improve schema generation for nested dataclasses by [@sydney-runkle](https://github.com/sydney-runkle) in [#9114](https://github.com/pydantic/pydantic/pull/9114)
+* Fast path for ASCII python string creation in JSON by [@samuelcolvin](https://github.com/samuelcolvin) in in [pydantic/jiter#72](https://github.com/pydantic/jiter/pull/72)
+* SIMD integer and string JSON parsing on `aarch64`(**Note:** SIMD on x86 will be implemented in a future release) by [@samuelcolvin](https://github.com/samuelcolvin) in in [pydantic/jiter#65](https://github.com/pydantic/jiter/pull/65)
+* Support JSON `Cow<str>` from `jiter` by [@davidhewitt](https://github.com/davidhewitt) in [pydantic/pydantic-core#1231](https://github.com/pydantic/pydantic-core/pull/1231)
+* MAJOR performance improvement: update to PyO3 0.21 final by [@davidhewitt](https://github.com/davidhewitt) in [pydantic/pydantic-core#1248](https://github.com/pydantic/pydantic-core/pull/1248)
+* cache Python strings by [@samuelcolvin](https://github.com/samuelcolvin) in [pydantic/pydantic-core#1240](https://github.com/pydantic/pydantic-core/pull/1240)
+
+#### Fixes
+
+* Fix strict parsing for some `Sequence`s by [@sydney-runkle](https://github.com/sydney-runkle) in [#8614](https://github.com/pydantic/pydantic/pull/8614)
+* Add a check on the existence of `__qualname__` by [@anci3ntr0ck](https://github.com/anci3ntr0ck) in [#8642](https://github.com/pydantic/pydantic/pull/8642)
+* Handle `__pydantic_extra__` annotation being a string or inherited by [@alexmojaki](https://github.com/alexmojaki) in [#8659](https://github.com/pydantic/pydantic/pull/8659)
+* Fix json validation for `NameEmail` by [@Holi0317](https://github.com/Holi0317) in [#8650](https://github.com/pydantic/pydantic/pull/8650)
+* Fix type-safety of attribute access in `BaseModel` by [@bluenote10](https://github.com/bluenote10) in [#8651](https://github.com/pydantic/pydantic/pull/8651)
+* Fix bug with `mypy` plugin and `no_strict_optional = True` by [@dmontagu](https://github.com/dmontagu) in [#8666](https://github.com/pydantic/pydantic/pull/8666)
+* Fix `ByteSize` error `type` change by [@sydney-runkle](https://github.com/sydney-runkle) in [#8681](https://github.com/pydantic/pydantic/pull/8681)
+* Fix inheriting annotations in dataclasses by [@sydney-runkle](https://github.com/sydney-runkle) in [#8679](https://github.com/pydantic/pydantic/pull/8679)
+* Fix regression in core schema generation for indirect definition references by [@dmontagu](https://github.com/dmontagu) in [#8702](https://github.com/pydantic/pydantic/pull/8702)
+* Fix unsupported types bug with plain validator by [@sydney-runkle](https://github.com/sydney-runkle) in [#8710](https://github.com/pydantic/pydantic/pull/8710)
+* Reverting problematic fix from 2.6 release, fixing schema building bug by [@sydney-runkle](https://github.com/sydney-runkle) in [#8718](https://github.com/pydantic/pydantic/pull/8718)
+* fixes `__pydantic_config__` ignored for TypeDict by [@13sin](https://github.com/13sin) in [#8734](https://github.com/pydantic/pydantic/pull/8734)
+* Fix test failures with `pytest v8.0.0` due to `pytest.warns()` starting to work inside `pytest.raises()` by [@mgorny](https://github.com/mgorny) in [#8678](https://github.com/pydantic/pydantic/pull/8678)
+* Use `is_valid_field` from 1.x for `mypy` plugin by [@DanielNoord](https://github.com/DanielNoord) in [#8738](https://github.com/pydantic/pydantic/pull/8738)
+* Better-support `mypy` strict equality flag by [@dmontagu](https://github.com/dmontagu) in [#8799](https://github.com/pydantic/pydantic/pull/8799)
+* model_json_schema export with Annotated types misses 'required' parameters by [@LouisGobert](https://github.com/LouisGobert) in [#8793](https://github.com/pydantic/pydantic/pull/8793)
+* Fix default inclusion in `FieldInfo.__repr_args__` by [@sydney-runkle](https://github.com/sydney-runkle) in [#8801](https://github.com/pydantic/pydantic/pull/8801)
+* Fix resolution of forward refs in dataclass base classes that are not present in the subclass module namespace by [@matsjoyce-refeyn](https://github.com/matsjoyce-refeyn) in [#8751](https://github.com/pydantic/pydantic/pull/8751)
+* Fix `BaseModel` type annotations to be resolvable by `typing.get_type_hints` by [@devmonkey22](https://github.com/devmonkey22) in [#7680](https://github.com/pydantic/pydantic/pull/7680)
+* Fix: allow empty string aliases with `AliasGenerator` by [@sydney-runkle](https://github.com/sydney-runkle) in [#8810](https://github.com/pydantic/pydantic/pull/8810)
+* Fix test along with `date` -> `datetime` timezone assumption fix by [@sydney-runkle](https://github.com/sydney-runkle) in [#8823](https://github.com/pydantic/pydantic/pull/8823)
+* Fix deprecation warning with usage of `ast.Str` by [@Viicos](https://github.com/Viicos) in [#8837](https://github.com/pydantic/pydantic/pull/8837)
+* Add missing `deprecated` decorators by [@Viicos](https://github.com/Viicos) in [#8877](https://github.com/pydantic/pydantic/pull/8877)
+* Fix serialization of `NameEmail` if name includes an email address by [@NeevCohen](https://github.com/NeevCohen) in [#8860](https://github.com/pydantic/pydantic/pull/8860)
+* Add information about class in error message of schema generation by [@Czaki](https://github.com/Czaki) in [#8917](https://github.com/pydantic/pydantic/pull/8917)
+* Make `TypeAdapter`'s typing compatible with special forms by [@adriangb](https://github.com/adriangb) in [#8923](https://github.com/pydantic/pydantic/pull/8923)
+* Fix issue with config behavior being baked into the ref schema for `enum`s by [@dmontagu](https://github.com/dmontagu) in [#8920](https://github.com/pydantic/pydantic/pull/8920)
+* More helpful error re wrong `model_json_schema` usage by [@sydney-runkle](https://github.com/sydney-runkle) in [#8928](https://github.com/pydantic/pydantic/pull/8928)
+* Fix nested discriminated union schema gen, pt 2 by [@sydney-runkle](https://github.com/sydney-runkle) in [#8932](https://github.com/pydantic/pydantic/pull/8932)
+* Fix schema build for nested dataclasses / TypedDicts with discriminators by [@sydney-runkle](https://github.com/sydney-runkle) in [#8950](https://github.com/pydantic/pydantic/pull/8950)
+* Remove unnecessary logic for definitions schema gen with discriminated unions by [@sydney-runkle](https://github.com/sydney-runkle) in [#8951](https://github.com/pydantic/pydantic/pull/8951)
+* Fix handling of optionals in `mypy` plugin by [@dmontagu](https://github.com/dmontagu) in [#9008](https://github.com/pydantic/pydantic/pull/9008)
+* Fix `PlainSerializer` usage with std type constructor by [@sydney-runkle](https://github.com/sydney-runkle) in [#9031](https://github.com/pydantic/pydantic/pull/9031)
+* Remove unnecessary warning for config in plugin by [@dmontagu](https://github.com/dmontagu) in [#9039](https://github.com/pydantic/pydantic/pull/9039)
+* Fix default value serializing by [@NeevCohen](https://github.com/NeevCohen) in [#9066](https://github.com/pydantic/pydantic/pull/9066)
+* Fix extra fields check in `Model.__getattr__()` by [@NeevCohen](https://github.com/NeevCohen) in [#9082](https://github.com/pydantic/pydantic/pull/9082)
+* Fix `ClassVar` forward ref inherited from parent class by [@alexmojaki](https://github.com/alexmojaki) in [#9097](https://github.com/pydantic/pydantic/pull/9097)
+* fix sequence like validator with strict `True` by [@andresliszt](https://github.com/andresliszt) in [#8977](https://github.com/pydantic/pydantic/pull/8977)
+* Improve warning message when a field name shadows a field in a parent model by [@chan-vince](https://github.com/chan-vince) in [#9105](https://github.com/pydantic/pydantic/pull/9105)
+* Do not warn about shadowed fields if they are not redefined in a child class by [@chan-vince](https://github.com/chan-vince) in [#9111](https://github.com/pydantic/pydantic/pull/9111)
+* Fix discriminated union bug with unsubstituted type var by [@sydney-runkle](https://github.com/sydney-runkle) in [#9124](https://github.com/pydantic/pydantic/pull/9124)
+* Support serialization of `deque` when passed to `Sequence[blah blah blah]` by [@sydney-runkle](https://github.com/sydney-runkle) in [#9128](https://github.com/pydantic/pydantic/pull/9128)
+* Init private attributes from super-types in `model_post_init` by [@Viicos](https://github.com/Viicos) in [#9134](https://github.com/pydantic/pydantic/pull/9134)
+* fix `model_construct` with `validation_alias` by [@ornariece](https://github.com/ornariece) in [#9144](https://github.com/pydantic/pydantic/pull/9144)
+* Ensure json-schema generator handles `Literal` `null` types by [@bruno-f-cruz](https://github.com/bruno-f-cruz) in [#9135](https://github.com/pydantic/pydantic/pull/9135)
+* **Fixed in v2.7.0**: Fix allow extra generic by [@dmontagu](https://github.com/dmontagu) in [#9193](https://github.com/pydantic/pydantic/pull/9193)
+
+### New Contributors
+
+* [@hungtsetse](https://github.com/hungtsetse) made their first contribution in [#8546](https://github.com/pydantic/pydantic/pull/8546)
+* [@StrawHatDrag0n](https://github.com/StrawHatDrag0n) made their first contribution in [#8583](https://github.com/pydantic/pydantic/pull/8583)
+* [@anci3ntr0ck](https://github.com/anci3ntr0ck) made their first contribution in [#8642](https://github.com/pydantic/pydantic/pull/8642)
+* [@Holi0317](https://github.com/Holi0317) made their first contribution in [#8650](https://github.com/pydantic/pydantic/pull/8650)
+* [@bluenote10](https://github.com/bluenote10) made their first contribution in [#8651](https://github.com/pydantic/pydantic/pull/8651)
+* [@ADSteele916](https://github.com/ADSteele916) made their first contribution in [#8703](https://github.com/pydantic/pydantic/pull/8703)
+* [@musicinmybrain](https://github.com/musicinmybrain) made their first contribution in [#8731](https://github.com/pydantic/pydantic/pull/8731)
+* [@jks15satoshi](https://github.com/jks15satoshi) made their first contribution in [#8706](https://github.com/pydantic/pydantic/pull/8706)
+* [@13sin](https://github.com/13sin) made their first contribution in [#8734](https://github.com/pydantic/pydantic/pull/8734)
+* [@DanielNoord](https://github.com/DanielNoord) made their first contribution in [#8738](https://github.com/pydantic/pydantic/pull/8738)
+* [@conradogarciaberrotaran](https://github.com/conradogarciaberrotaran) made their first contribution in [#8519](https://github.com/pydantic/pydantic/pull/8519)
+* [@chris-griffin](https://github.com/chris-griffin) made their first contribution in [#8775](https://github.com/pydantic/pydantic/pull/8775)
+* [@LouisGobert](https://github.com/LouisGobert) made their first contribution in [#8793](https://github.com/pydantic/pydantic/pull/8793)
+* [@matsjoyce-refeyn](https://github.com/matsjoyce-refeyn) made their first contribution in [#8751](https://github.com/pydantic/pydantic/pull/8751)
+* [@devmonkey22](https://github.com/devmonkey22) made their first contribution in [#7680](https://github.com/pydantic/pydantic/pull/7680)
+* [@adamency](https://github.com/adamency) made their first contribution in [#8847](https://github.com/pydantic/pydantic/pull/8847)
+* [@MamfTheKramf](https://github.com/MamfTheKramf) made their first contribution in [#8851](https://github.com/pydantic/pydantic/pull/8851)
+* [@ornariece](https://github.com/ornariece) made their first contribution in [#9001](https://github.com/pydantic/pydantic/pull/9001)
+* [@alexeyt101](https://github.com/alexeyt101) made their first contribution in [#9004](https://github.com/pydantic/pydantic/pull/9004)
+* [@wannieman98](https://github.com/wannieman98) made their first contribution in [#8947](https://github.com/pydantic/pydantic/pull/8947)
+* [@solidguy7](https://github.com/solidguy7) made their first contribution in [#9062](https://github.com/pydantic/pydantic/pull/9062)
+* [@kloczek](https://github.com/kloczek) made their first contribution in [#9047](https://github.com/pydantic/pydantic/pull/9047)
+* [@jag-k](https://github.com/jag-k) made their first contribution in [#9053](https://github.com/pydantic/pydantic/pull/9053)
+* [@priya-gitTest](https://github.com/priya-gitTest) made their first contribution in [#9088](https://github.com/pydantic/pydantic/pull/9088)
+* [@Youssefares](https://github.com/Youssefares) made their first contribution in [#9023](https://github.com/pydantic/pydantic/pull/9023)
+* [@chan-vince](https://github.com/chan-vince) made their first contribution in [#9105](https://github.com/pydantic/pydantic/pull/9105)
+* [@bruno-f-cruz](https://github.com/bruno-f-cruz) made their first contribution in [#9135](https://github.com/pydantic/pydantic/pull/9135)
+* [@Lance-Drane](https://github.com/Lance-Drane) made their first contribution in [#9166](https://github.com/pydantic/pydantic/pull/9166)
+
+## v2.7.0b1 (2024-04-03)
+
+Pre-release, see [the GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.7.0b1) for details.
+
+## v2.6.4 (2024-03-12)
+
+[GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.6.4)
+
+### What's Changed
+
+#### Fixes
+
+* Fix usage of `AliasGenerator` with `computed_field` decorator by [@sydney-runkle](https://github.com/sydney-runkle) in [#8806](https://github.com/pydantic/pydantic/pull/8806)
+* Fix nested discriminated union schema gen, pt 2 by [@sydney-runkle](https://github.com/sydney-runkle) in [#8932](https://github.com/pydantic/pydantic/pull/8932)
+* Fix bug with no_strict_optional=True caused by API deferral by [@dmontagu](https://github.com/dmontagu) in [#8826](https://github.com/pydantic/pydantic/pull/8826)
+
+
+## v2.6.3 (2024-02-27)
+
+[GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.6.3)
+
+### What's Changed
+
+#### Packaging
+
+* Update `pydantic-settings` version in the docs by [@hramezani](https://github.com/hramezani) in [#8906](https://github.com/pydantic/pydantic/pull/8906)
+
+#### Fixes
+
+* Fix discriminated union schema gen bug by [@sydney-runkle](https://github.com/sydney-runkle) in [#8904](https://github.com/pydantic/pydantic/pull/8904)
+
+
+## v2.6.2 (2024-02-23)
+
+[GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.6.2)
+
+### What's Changed
+
+#### Packaging
+
+* Upgrade to `pydantic-core` 2.16.3 by [@sydney-runkle](https://github.com/sydney-runkle) in [#8879](https://github.com/pydantic/pydantic/pull/8879)
+
+#### Fixes
+
+* 'YYYY-MM-DD' date string coerced to datetime shouldn't infer timezone by [@sydney-runkle](https://github.com/sydney-runkle) in [pydantic/pydantic-core#1193](https://github.com/pydantic/pydantic-core/pull/1193)
+
+
+## v2.6.1 (2024-02-05)
+
+[GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.6.1)
+
+### What's Changed
+
+#### Packaging
+
+* Upgrade to `pydantic-core` 2.16.2 by [@sydney-runkle](https://github.com/sydney-runkle) in [#8717](https://github.com/pydantic/pydantic/pull/8717)
+
+#### Fixes
+
+* Fix bug with `mypy` plugin and `no_strict_optional = True` by [@dmontagu](https://github.com/dmontagu) in [#8666](https://github.com/pydantic/pydantic/pull/8666)
+* Fix `ByteSize` error `type` change by [@sydney-runkle](https://github.com/sydney-runkle) in [#8681](https://github.com/pydantic/pydantic/pull/8681)
+* Fix inheriting `Field` annotations in dataclasses by [@sydney-runkle](https://github.com/sydney-runkle) in [#8679](https://github.com/pydantic/pydantic/pull/8679)
+* Fix regression in core schema generation for indirect definition references by [@dmontagu](https://github.com/dmontagu) in [#8702](https://github.com/pydantic/pydantic/pull/8702)
+* Fix unsupported types bug with `PlainValidator` by [@sydney-runkle](https://github.com/sydney-runkle) in [#8710](https://github.com/pydantic/pydantic/pull/8710)
+* Reverting problematic fix from 2.6 release, fixing schema building bug by [@sydney-runkle](https://github.com/sydney-runkle) in [#8718](https://github.com/pydantic/pydantic/pull/8718)
+* Fix warning for tuple of wrong size in `Union` by [@davidhewitt](https://github.com/davidhewitt) in [pydantic/pydantic-core#1174](https://github.com/pydantic/pydantic-core/pull/1174)
+* Fix `computed_field` JSON serializer `exclude_none` behavior by [@sydney-runkle](https://github.com/sydney-runkle) in [pydantic/pydantic-core#1187](https://github.com/pydantic/pydantic-core/pull/1187)
+
+
+## v2.6.0 (2024-01-23)
+
+[GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.6.0)
+
+The code released in v2.6.0 is practically identical to that of v2.6.0b1.
+
+### What's Changed
+
+#### Packaging
+
+* Check for `email-validator` version >= 2.0 by [@commonism](https://github.com/commonism) in [#6033](https://github.com/pydantic/pydantic/pull/6033)
+* Upgrade `ruff`` target version to Python 3.8 by [@Elkiwa](https://github.com/Elkiwa) in [#8341](https://github.com/pydantic/pydantic/pull/8341)
+* Update to `pydantic-extra-types==2.4.1` by [@yezz123](https://github.com/yezz123) in [#8478](https://github.com/pydantic/pydantic/pull/8478)
+* Update to `pyright==1.1.345` by [@Viicos](https://github.com/Viicos) in [#8453](https://github.com/pydantic/pydantic/pull/8453)
+* Update pydantic-core from 2.14.6 to 2.16.1, significant changes from these updates are described below, full changelog [here](https://github.com/pydantic/pydantic-core/compare/v2.14.6...v2.16.1)
+
+#### New Features
+
+* Add `NatsDsn` by [@ekeew](https://github.com/ekeew) in [#6874](https://github.com/pydantic/pydantic/pull/6874)
+* Add `ConfigDict.ser_json_inf_nan` by [@davidhewitt](https://github.com/davidhewitt) in [#8159](https://github.com/pydantic/pydantic/pull/8159)
+* Add `types.OnErrorOmit` by [@adriangb](https://github.com/adriangb) in [#8222](https://github.com/pydantic/pydantic/pull/8222)
+* Support `AliasGenerator` usage by [@sydney-runkle](https://github.com/sydney-runkle) in [#8282](https://github.com/pydantic/pydantic/pull/8282)
+* Add Pydantic People Page to docs by [@sydney-runkle](https://github.com/sydney-runkle) in [#8345](https://github.com/pydantic/pydantic/pull/8345)
+* Support `yyyy-MM-DD` datetime parsing by [@sydney-runkle](https://github.com/sydney-runkle) in [#8404](https://github.com/pydantic/pydantic/pull/8404)
+* Added bits conversions to the `ByteSize` class [#8415](https://github.com/pydantic/pydantic/issues/8415) by [@luca-matei](https://github.com/luca-matei) in [#8507](https://github.com/pydantic/pydantic/pull/8507)
+* Enable json schema creation with type `ByteSize` by [@geospackle](https://github.com/geospackle) in [#8537](https://github.com/pydantic/pydantic/pull/8537)
+* Add `eval_type_backport` to handle union operator and builtin generic subscripting in older Pythons by [@alexmojaki](https://github.com/alexmojaki) in [#8209](https://github.com/pydantic/pydantic/pull/8209)
+* Add support for `dataclass` fields `init` by [@dmontagu](https://github.com/dmontagu) in [#8552](https://github.com/pydantic/pydantic/pull/8552)
+* Implement pickling for `ValidationError` by [@davidhewitt](https://github.com/davidhewitt) in [pydantic/pydantic-core#1119](https://github.com/pydantic/pydantic-core/pull/1119)
+* Add unified tuple validator that can handle "variadic" tuples via PEP-646 by [@dmontagu](https://github.com/dmontagu) in [pydantic/pydantic-core#865](https://github.com/pydantic/pydantic-core/pull/865)
+
+#### Changes
+
+* Drop Python3.7 support by [@hramezani](https://github.com/hramezani) in [#7188](https://github.com/pydantic/pydantic/pull/7188)
+* Drop Python 3.7, and PyPy 3.7 and 3.8 by [@davidhewitt](https://github.com/davidhewitt) in [pydantic/pydantic-core#1129](https://github.com/pydantic/pydantic-core/pull/1129)
+* Use positional-only `self` in `BaseModel` constructor, so no field name can ever conflict with it by [@ariebovenberg](https://github.com/ariebovenberg) in [#8072](https://github.com/pydantic/pydantic/pull/8072)
+* Make `@validate_call` return a function instead of a custom descriptor - fixes binding issue with inheritance and adds `self/cls` argument to validation errors by [@alexmojaki](https://github.com/alexmojaki) in [#8268](https://github.com/pydantic/pydantic/pull/8268)
+* Exclude `BaseModel` docstring from JSON schema description by [@sydney-runkle](https://github.com/sydney-runkle) in [#8352](https://github.com/pydantic/pydantic/pull/8352)
+* Introducing `classproperty` decorator for `model_computed_fields` by [@Jocelyn-Gas](https://github.com/Jocelyn-Gas) in [#8437](https://github.com/pydantic/pydantic/pull/8437)
+* Explicitly raise an error if field names clashes with types by [@Viicos](https://github.com/Viicos) in [#8243](https://github.com/pydantic/pydantic/pull/8243)
+* Use stricter serializer for unions of simple types by [@alexdrydew](https://github.com/alexdrydew) [pydantic/pydantic-core#1132](https://github.com/pydantic/pydantic-core/pull/1132)
+
+#### Performance
+
+* Add Codspeed profiling Actions workflow  by [@lambertsbennett](https://github.com/lambertsbennett) in [#8054](https://github.com/pydantic/pydantic/pull/8054)
+* Improve `int` extraction by [@samuelcolvin](https://github.com/samuelcolvin) in [pydantic/pydantic-core#1155](https://github.com/pydantic/pydantic-core/pull/1155)
+* Improve performance of recursion guard by [@samuelcolvin](https://github.com/samuelcolvin) in [pydantic/pydantic-core#1156](https://github.com/pydantic/pydantic-core/pull/1156)
+* `dataclass` serialization speedups by [@samuelcolvin](https://github.com/samuelcolvin) in [pydantic/pydantic-core#1162](https://github.com/pydantic/pydantic-core/pull/1162)
+* Avoid `HashMap` creation when looking up small JSON objects in `LazyIndexMaps` by [@samuelcolvin](https://github.com/samuelcolvin) in [pydantic/jiter#55](https://github.com/pydantic/jiter/pull/55)
+* use hashbrown to speedup python string caching by [@davidhewitt](https://github.com/davidhewitt) in [pydantic/jiter#51](https://github.com/pydantic/jiter/pull/51)
+* Replace `Peak` with more efficient `Peek` by [@davidhewitt](https://github.com/davidhewitt) in [pydantic/jiter#48](https://github.com/pydantic/jiter/pull/48)
+
+#### Fixes
+
+* Move `getattr` warning in deprecated `BaseConfig` by [@tlambert03](https://github.com/tlambert03) in [#7183](https://github.com/pydantic/pydantic/pull/7183)
+* Only hash `model_fields`, not whole `__dict__` by [@alexmojaki](https://github.com/alexmojaki) in [#7786](https://github.com/pydantic/pydantic/pull/7786)
+* Fix mishandling of unions while freezing types in the `mypy` plugin by [@dmontagu](https://github.com/dmontagu) in [#7411](https://github.com/pydantic/pydantic/pull/7411)
+* Fix `mypy` error on untyped `ClassVar` by [@vincent-hachin-wmx](https://github.com/vincent-hachin-wmx) in [#8138](https://github.com/pydantic/pydantic/pull/8138)
+* Only compare pydantic fields in `BaseModel.__eq__` instead of whole `__dict__` by [@QuentinSoubeyranAqemia](https://github.com/QuentinSoubeyranAqemia) in [#7825](https://github.com/pydantic/pydantic/pull/7825)
+* Update `strict` docstring in `model_validate` method. by [@LukeTonin](https://github.com/LukeTonin) in [#8223](https://github.com/pydantic/pydantic/pull/8223)
+* Fix overload position of `computed_field` by [@Viicos](https://github.com/Viicos) in [#8227](https://github.com/pydantic/pydantic/pull/8227)
+* Fix custom type type casting used in multiple attributes by [@ianhfc](https://github.com/ianhfc) in [#8066](https://github.com/pydantic/pydantic/pull/8066)
+* Fix issue not allowing `validate_call` decorator to be dynamically assigned to a class method by [@jusexton](https://github.com/jusexton) in [#8249](https://github.com/pydantic/pydantic/pull/8249)
+* Fix issue `unittest.mock` deprecation warnings  by [@ibleedicare](https://github.com/ibleedicare) in [#8262](https://github.com/pydantic/pydantic/pull/8262)
+* Added tests for the case `JsonValue` contains subclassed primitive values by [@jusexton](https://github.com/jusexton) in [#8286](https://github.com/pydantic/pydantic/pull/8286)
+* Fix `mypy` error on free before validator (classmethod) by [@sydney-runkle](https://github.com/sydney-runkle) in [#8285](https://github.com/pydantic/pydantic/pull/8285)
+* Fix `to_snake` conversion by [@jevins09](https://github.com/jevins09) in [#8316](https://github.com/pydantic/pydantic/pull/8316)
+* Fix type annotation of `ModelMetaclass.__prepare__` by [@slanzmich](https://github.com/slanzmich) in [#8305](https://github.com/pydantic/pydantic/pull/8305)
+* Disallow `config` specification when initializing a `TypeAdapter` when the annotated type has config already by [@sydney-runkle](https://github.com/sydney-runkle) in [#8365](https://github.com/pydantic/pydantic/pull/8365)
+* Fix a naming issue with JSON schema for generics parametrized by recursive type aliases by [@dmontagu](https://github.com/dmontagu) in [#8389](https://github.com/pydantic/pydantic/pull/8389)
+* Fix type annotation in pydantic people script by [@shenxiangzhuang](https://github.com/shenxiangzhuang) in [#8402](https://github.com/pydantic/pydantic/pull/8402)
+* Add support for field `alias` in `dataclass` signature by [@NeevCohen](https://github.com/NeevCohen) in [#8387](https://github.com/pydantic/pydantic/pull/8387)
+* Fix bug with schema generation with `Field(...)` in a forward ref by [@dmontagu](https://github.com/dmontagu) in [#8494](https://github.com/pydantic/pydantic/pull/8494)
+* Fix ordering of keys in `__dict__` with `model_construct` call by [@sydney-runkle](https://github.com/sydney-runkle) in [#8500](https://github.com/pydantic/pydantic/pull/8500)
+* Fix module `path_type` creation when globals does not contain `__name__` by [@hramezani](https://github.com/hramezani) in [#8470](https://github.com/pydantic/pydantic/pull/8470)
+* Fix for namespace issue with dataclasses with `from __future__ import annotations` by [@sydney-runkle](https://github.com/sydney-runkle) in [#8513](https://github.com/pydantic/pydantic/pull/8513)
+* Fix: make function validator types positional-only by [@pmmmwh](https://github.com/pmmmwh) in [#8479](https://github.com/pydantic/pydantic/pull/8479)
+* Fix usage of `@deprecated` by [@Viicos](https://github.com/Viicos) in [#8294](https://github.com/pydantic/pydantic/pull/8294)
+* Add more support for private attributes in `model_construct` call by [@sydney-runkle](https://github.com/sydney-runkle) in [#8525](https://github.com/pydantic/pydantic/pull/8525)
+* Use a stack for the types namespace by [@dmontagu](https://github.com/dmontagu) in [#8378](https://github.com/pydantic/pydantic/pull/8378)
+* Fix schema-building bug with `TypeAliasType` for types with refs by [@dmontagu](https://github.com/dmontagu) in [#8526](https://github.com/pydantic/pydantic/pull/8526)
+* Support `pydantic.Field(repr=False)` in dataclasses by [@tigeryy2](https://github.com/tigeryy2) in [#8511](https://github.com/pydantic/pydantic/pull/8511)
+* Override `dataclass_transform` behavior for `RootModel` by [@Viicos](https://github.com/Viicos) in [#8163](https://github.com/pydantic/pydantic/pull/8163)
+* Refactor signature generation for simplicity by [@sydney-runkle](https://github.com/sydney-runkle) in [#8572](https://github.com/pydantic/pydantic/pull/8572)
+* Fix ordering bug of PlainValidator annotation by [@Anvil](https://github.com/Anvil) in [#8567](https://github.com/pydantic/pydantic/pull/8567)
+* Fix `exclude_none` for json serialization of `computed_field`s by [@sydney-runkle](https://github.com/sydney-runkle) in [pydantic/pydantic-core#1098](https://github.com/pydantic/pydantic-core/pull/1098)
+* Support yyyy-MM-DD string for datetimes by [@sydney-runkle](https://github.com/sydney-runkle) in [pydantic/pydantic-core#1124](https://github.com/pydantic/pydantic-core/pull/1124)
+* Tweak ordering of definitions in generated schemas by [@StrawHatDrag0n](https://github.com/StrawHatDrag0n) in [#8583](https://github.com/pydantic/pydantic/pull/8583)
+
+
+### New Contributors
+
+#### `pydantic`
+* [@ekeew](https://github.com/ekeew) made their first contribution in [#6874](https://github.com/pydantic/pydantic/pull/6874)
+* [@lambertsbennett](https://github.com/lambertsbennett) made their first contribution in [#8054](https://github.com/pydantic/pydantic/pull/8054)
+* [@vincent-hachin-wmx](https://github.com/vincent-hachin-wmx) made their first contribution in [#8138](https://github.com/pydantic/pydantic/pull/8138)
+* [@QuentinSoubeyranAqemia](https://github.com/QuentinSoubeyranAqemia) made their first contribution in [#7825](https://github.com/pydantic/pydantic/pull/7825)
+* [@ariebovenberg](https://github.com/ariebovenberg) made their first contribution in [#8072](https://github.com/pydantic/pydantic/pull/8072)
+* [@LukeTonin](https://github.com/LukeTonin) made their first contribution in [#8223](https://github.com/pydantic/pydantic/pull/8223)
+* [@denisart](https://github.com/denisart) made their first contribution in [#8231](https://github.com/pydantic/pydantic/pull/8231)
+* [@ianhfc](https://github.com/ianhfc) made their first contribution in [#8066](https://github.com/pydantic/pydantic/pull/8066)
+* [@eonu](https://github.com/eonu) made their first contribution in [#8255](https://github.com/pydantic/pydantic/pull/8255)
+* [@amandahla](https://github.com/amandahla) made their first contribution in [#8263](https://github.com/pydantic/pydantic/pull/8263)
+* [@ibleedicare](https://github.com/ibleedicare) made their first contribution in [#8262](https://github.com/pydantic/pydantic/pull/8262)
+* [@jevins09](https://github.com/jevins09) made their first contribution in [#8316](https://github.com/pydantic/pydantic/pull/8316)
+* [@cuu508](https://github.com/cuu508) made their first contribution in [#8322](https://github.com/pydantic/pydantic/pull/8322)
+* [@slanzmich](https://github.com/slanzmich) made their first contribution in [#8305](https://github.com/pydantic/pydantic/pull/8305)
+* [@jensenbox](https://github.com/jensenbox) made their first contribution in [#8331](https://github.com/pydantic/pydantic/pull/8331)
+* [@szepeviktor](https://github.com/szepeviktor) made their first contribution in [#8356](https://github.com/pydantic/pydantic/pull/8356)
+* [@Elkiwa](https://github.com/Elkiwa) made their first contribution in [#8341](https://github.com/pydantic/pydantic/pull/8341)
+* [@parhamfh](https://github.com/parhamfh) made their first contribution in [#8395](https://github.com/pydantic/pydantic/pull/8395)
+* [@shenxiangzhuang](https://github.com/shenxiangzhuang) made their first contribution in [#8402](https://github.com/pydantic/pydantic/pull/8402)
+* [@NeevCohen](https://github.com/NeevCohen) made their first contribution in [#8387](https://github.com/pydantic/pydantic/pull/8387)
+* [@zby](https://github.com/zby) made their first contribution in [#8497](https://github.com/pydantic/pydantic/pull/8497)
+* [@patelnets](https://github.com/patelnets) made their first contribution in [#8491](https://github.com/pydantic/pydantic/pull/8491)
+* [@edwardwli](https://github.com/edwardwli) made their first contribution in [#8503](https://github.com/pydantic/pydantic/pull/8503)
+* [@luca-matei](https://github.com/luca-matei) made their first contribution in [#8507](https://github.com/pydantic/pydantic/pull/8507)
+* [@Jocelyn-Gas](https://github.com/Jocelyn-Gas) made their first contribution in [#8437](https://github.com/pydantic/pydantic/pull/8437)
+* [@bL34cHig0](https://github.com/bL34cHig0) made their first contribution in [#8501](https://github.com/pydantic/pydantic/pull/8501)
+* [@tigeryy2](https://github.com/tigeryy2) made their first contribution in [#8511](https://github.com/pydantic/pydantic/pull/8511)
+* [@geospackle](https://github.com/geospackle) made their first contribution in [#8537](https://github.com/pydantic/pydantic/pull/8537)
+* [@Anvil](https://github.com/Anvil) made their first contribution in [#8567](https://github.com/pydantic/pydantic/pull/8567)
+* [@hungtsetse](https://github.com/hungtsetse) made their first contribution in [#8546](https://github.com/pydantic/pydantic/pull/8546)
+* [@StrawHatDrag0n](https://github.com/StrawHatDrag0n) made their first contribution in [#8583](https://github.com/pydantic/pydantic/pull/8583)
+
+#### `pydantic-core`
+* [@mariuswinger](https://github.com/mariuswinger) made their first contribution in [pydantic/pydantic-core#1087](https://github.com/pydantic/pydantic-core/pull/1087)
+* [@adamchainz](https://github.com/adamchainz) made their first contribution in [pydantic/pydantic-core#1090](https://github.com/pydantic/pydantic-core/pull/1090)
+* [@akx](https://github.com/akx) made their first contribution in [pydantic/pydantic-core#1123](https://github.com/pydantic/pydantic-core/pull/1123)
+
+## v2.6.0b1 (2024-01-19)
+
+Pre-release, see [the GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.6.0b1) for details.
+
+## v2.5.3 (2023-12-22)
+
+[GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.5.3)
+
+### What's Changed
+
+#### Packaging
+
+* uprev `pydantic-core` to 2.14.6
+
+#### Fixes
+
+* Fix memory leak with recursive definitions creating reference cycles by [@davidhewitt](https://github.com/davidhewitt) in [pydantic/pydantic-core#1125](https://github.com/pydantic/pydantic-core/pull/1125)
+
+## v2.5.2 (2023-11-22)
+
+[GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.5.2)
+
+### What's Changed
+
+#### Packaging
+
+* uprev `pydantic-core` to 2.14.5
+
+#### New Features
+
+* Add `ConfigDict.ser_json_inf_nan` by [@davidhewitt](https://github.com/davidhewitt) in [#8159](https://github.com/pydantic/pydantic/pull/8159)
+
+#### Fixes
+
+* Fix validation of `Literal` from JSON keys when used as `dict` key by [@sydney-runkle](https://github.com/sydney-runkle) in [pydantic/pydantic-core#1075](https://github.com/pydantic/pydantic-core/pull/1075)
+* Fix bug re `custom_init` on members of `Union` by [@sydney-runkle](https://github.com/sydney-runkle) in [pydantic/pydantic-core#1076](https://github.com/pydantic/pydantic-core/pull/1076)
+* Fix `JsonValue` `bool` serialization by [@sydney-runkle](https://github.com/sydney-runkle) in [#8190](https://github.com/pydantic/pydantic/pull/8159)
+* Fix handling of unhashable inputs with `Literal` in `Union`s by [@sydney-runkle](https://github.com/sydney-runkle) in [pydantic/pydantic-core#1089](https://github.com/pydantic/pydantic-core/pull/1089)
+
+## v2.5.1 (2023-11-15)
+
+[GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.5.1)
+
+### What's Changed
+
+#### Packaging
+
+* uprev pydantic-core to 2.14.3 by [@samuelcolvin](https://github.com/samuelcolvin) in [#8120](https://github.com/pydantic/pydantic/pull/8120)
+
+#### Fixes
+
+* Fix package description limit by [@dmontagu](https://github.com/dmontagu) in [#8097](https://github.com/pydantic/pydantic/pull/8097)
+* Fix `ValidateCallWrapper` error when creating a model which has a [@validate_call](https://github.com/validate_call) wrapped field annotation by [@sydney-runkle](https://github.com/sydney-runkle) in [#8110](https://github.com/pydantic/pydantic/pull/8110)
+
+## v2.5.0 (2023-11-13)
+
+[GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.5.0)
+
+The code released in v2.5.0 is functionally identical to that of v2.5.0b1.
+
+### What's Changed
+
+#### Packaging
+
+* Update pydantic-core from 2.10.1 to 2.14.1, significant changes from these updates are described below, full changelog [here](https://github.com/pydantic/pydantic-core/compare/v2.10.1...v2.14.1)
+* Update to `pyright==1.1.335` by [@Viicos](https://github.com/Viicos) in [#8075](https://github.com/pydantic/pydantic/pull/8075)
+
+#### New Features
+
+* Allow plugins to catch non `ValidationError` errors by [@adriangb](https://github.com/adriangb) in [#7806](https://github.com/pydantic/pydantic/pull/7806)
+* Support `__doc__` argument in `create_model()` by [@chris-spann](https://github.com/chris-spann) in [#7863](https://github.com/pydantic/pydantic/pull/7863)
+* Expose `regex_engine` flag - meaning you can use with the Rust or Python regex libraries in constraints by [@utkini](https://github.com/utkini) in [#7768](https://github.com/pydantic/pydantic/pull/7768)
+* Save return type generated from type annotation in `ComputedFieldInfo` by [@alexmojaki](https://github.com/alexmojaki) in [#7889](https://github.com/pydantic/pydantic/pull/7889)
+* Adopting `ruff` formatter by [@Luca-Blight](https://github.com/Luca-Blight) in [#7930](https://github.com/pydantic/pydantic/pull/7930)
+* Added `validation_error_cause` to config by [@zakstucke](https://github.com/zakstucke) in [#7626](https://github.com/pydantic/pydantic/pull/7626)
+* Make path of the item to validate available in plugin by [@hramezani](https://github.com/hramezani) in [#7861](https://github.com/pydantic/pydantic/pull/7861)
+* Add `CallableDiscriminator` and `Tag` by [@dmontagu](https://github.com/dmontagu) in [#7983](https://github.com/pydantic/pydantic/pull/7983)
+  * `CallableDiscriminator` renamed to `Discriminator` by [@dmontagu](https://github.com/dmontagu) in [#8047](https://github.com/pydantic/pydantic/pull/8047)
+* Make union case tags affect union error messages by [@dmontagu](https://github.com/dmontagu) in [#8001](https://github.com/pydantic/pydantic/pull/8001)
+* Add `examples` and `json_schema_extra` to `@computed_field` by [@alexmojaki](https://github.com/alexmojaki) in [#8013](https://github.com/pydantic/pydantic/pull/8013)
+* Add `JsonValue` type by [@dmontagu](https://github.com/dmontagu) in [#7998](https://github.com/pydantic/pydantic/pull/7998)
+* Allow `str` as argument to `Discriminator` by [@dmontagu](https://github.com/dmontagu) in [#8047](https://github.com/pydantic/pydantic/pull/8047)
+* Add `SchemaSerializer.__reduce__` method to enable pickle serialization by [@edoakes](https://github.com/edoakes) in [pydantic/pydantic-core#1006](https://github.com/pydantic/pydantic-core/pull/1006)
+
+#### Changes
+
+* **Significant Change:** replace `ultra_strict` with new smart union implementation, the way unions are validated has changed significantly to improve performance and correctness, we have worked hard to absolutely minimise the number of cases where behaviour has changed, see the PR for details - by [@davidhewitt](https://github.com/davidhewitt) in [pydantic/pydantic-core#867](https://github.com/pydantic/pydantic-core/pull/867)
+* Add support for instance method reassignment when `extra='allow'` by [@sydney-runkle](https://github.com/sydney-runkle) in [#7683](https://github.com/pydantic/pydantic/pull/7683)
+* Support JSON schema generation for `Enum` types with no cases by [@sydney-runkle](https://github.com/sydney-runkle) in [#7927](https://github.com/pydantic/pydantic/pull/7927)
+* Warn if a class inherits from `Generic` before `BaseModel` by [@alexmojaki](https://github.com/alexmojaki) in [#7891](https://github.com/pydantic/pydantic/pull/7891)
+
+#### Performance
+
+* New custom JSON parser, `jiter` by [@samuelcolvin](https://github.com/samuelcolvin) in [pydantic/pydantic-core#974](https://github.com/pydantic/pydantic-core/pull/974)
+* PGO build for MacOS M1 by [@samuelcolvin](https://github.com/samuelcolvin) in [pydantic/pydantic-core#1063](https://github.com/pydantic/pydantic-core/pull/1063)
+* Use `__getattr__` for all package imports, improve import time by [@samuelcolvin](https://github.com/samuelcolvin) in [#7947](https://github.com/pydantic/pydantic/pull/7947)
+
+#### Fixes
+
+* Fix `mypy` issue with subclasses of `RootModel` by [@sydney-runkle](https://github.com/sydney-runkle) in [#7677](https://github.com/pydantic/pydantic/pull/7677)
+* Properly rebuild the `FieldInfo` when a forward ref gets evaluated by [@dmontagu](https://github.com/dmontagu) in [#7698](https://github.com/pydantic/pydantic/pull/7698)
+* Fix failure to load `SecretStr` from JSON (regression in v2.4) by [@sydney-runkle](https://github.com/sydney-runkle) in [#7729](https://github.com/pydantic/pydantic/pull/7729)
+* Fix `defer_build` behavior with `TypeAdapter` by [@sydney-runkle](https://github.com/sydney-runkle) in [#7736](https://github.com/pydantic/pydantic/pull/7736)
+* Improve compatibility with legacy `mypy` versions by [@dmontagu](https://github.com/dmontagu) in [#7742](https://github.com/pydantic/pydantic/pull/7742)
+* Fix: update `TypeVar` handling when default is not set by [@pmmmwh](https://github.com/pmmmwh) in [#7719](https://github.com/pydantic/pydantic/pull/7719)
+* Support specification of `strict` on `Enum` type fields by [@sydney-runkle](https://github.com/sydney-runkle) in [#7761](https://github.com/pydantic/pydantic/pull/7761)
+* Wrap `weakref.ref` instead of subclassing to fix `cloudpickle` serialization by [@edoakes](https://github.com/edoakes) in [#7780](https://github.com/pydantic/pydantic/pull/7780)
+* Keep values of private attributes set within `model_post_init` in subclasses by [@alexmojaki](https://github.com/alexmojaki) in [#7775](https://github.com/pydantic/pydantic/pull/7775)
+* Add more specific type for non-callable `json_schema_extra` by [@alexmojaki](https://github.com/alexmojaki) in [#7803](https://github.com/pydantic/pydantic/pull/7803)
+* Raise an error when deleting frozen (model) fields by [@alexmojaki](https://github.com/alexmojaki) in [#7800](https://github.com/pydantic/pydantic/pull/7800)
+* Fix schema sorting bug with default values by [@sydney-runkle](https://github.com/sydney-runkle) in [#7817](https://github.com/pydantic/pydantic/pull/7817)
+* Use generated alias for aliases that are not specified otherwise by [@alexmojaki](https://github.com/alexmojaki) in [#7802](https://github.com/pydantic/pydantic/pull/7802)
+* Support `strict` specification for `UUID` types by [@sydney-runkle](https://github.com/sydney-runkle) in [#7865](https://github.com/pydantic/pydantic/pull/7865)
+* JSON schema: fix extra parameter handling by [@me-and](https://github.com/me-and) in [#7810](https://github.com/pydantic/pydantic/pull/7810)
+* Fix: support `pydantic.Field(kw_only=True)` with inherited dataclasses by [@PrettyWood](https://github.com/PrettyWood) in [#7827](https://github.com/pydantic/pydantic/pull/7827)
+* Support `validate_call` decorator for methods in classes with `__slots__` by [@sydney-runkle](https://github.com/sydney-runkle) in [#7883](https://github.com/pydantic/pydantic/pull/7883)
+* Fix pydantic dataclass problem with `dataclasses.field` default by [@hramezani](https://github.com/hramezani) in [#7898](https://github.com/pydantic/pydantic/pull/7898)
+* Fix schema generation for generics with union type bounds by [@sydney-runkle](https://github.com/sydney-runkle) in [#7899](https://github.com/pydantic/pydantic/pull/7899)
+* Fix version for `importlib_metadata` on python 3.7 by [@sydney-runkle](https://github.com/sydney-runkle) in [#7904](https://github.com/pydantic/pydantic/pull/7904)
+* Support `|` operator (Union) in PydanticRecursiveRef by [@alexmojaki](https://github.com/alexmojaki) in [#7892](https://github.com/pydantic/pydantic/pull/7892)
+* Fix `display_as_type` for `TypeAliasType` in python 3.12 by [@dmontagu](https://github.com/dmontagu) in [#7929](https://github.com/pydantic/pydantic/pull/7929)
+* Add support for `NotRequired` generics in `TypedDict` by [@sydney-runkle](https://github.com/sydney-runkle) in [#7932](https://github.com/pydantic/pydantic/pull/7932)
+* Make generic `TypeAliasType` specifications produce different schema definitions by [@alexdrydew](https://github.com/alexdrydew) in [#7893](https://github.com/pydantic/pydantic/pull/7893)
+* Added fix for signature of inherited dataclass by [@howsunjow](https://github.com/howsunjow) in [#7925](https://github.com/pydantic/pydantic/pull/7925)
+* Make the model name generation more robust in JSON schema by [@joakimnordling](https://github.com/joakimnordling) in [#7881](https://github.com/pydantic/pydantic/pull/7881)
+* Fix plurals in validation error messages (in tests) by [@Iipin](https://github.com/Iipin) in [#7972](https://github.com/pydantic/pydantic/pull/7972)
+* `PrivateAttr` is passed from `Annotated` default position by [@tabassco](https://github.com/tabassco) in [#8004](https://github.com/pydantic/pydantic/pull/8004)
+* Don't decode bytes (which may not be UTF8) when displaying SecretBytes by [@alexmojaki](https://github.com/alexmojaki) in [#8012](https://github.com/pydantic/pydantic/pull/8012)
+* Use `classmethod` instead of `classmethod[Any, Any, Any]` by [@Mr-Pepe](https://github.com/Mr-Pepe) in [#7979](https://github.com/pydantic/pydantic/pull/7979)
+* Clearer error on invalid Plugin by [@samuelcolvin](https://github.com/samuelcolvin) in [#8023](https://github.com/pydantic/pydantic/pull/8023)
+* Correct pydantic dataclasses import by [@samuelcolvin](https://github.com/samuelcolvin) in [#8027](https://github.com/pydantic/pydantic/pull/8027)
+* Fix misbehavior for models referencing redefined type aliases by [@dmontagu](https://github.com/dmontagu) in [#8050](https://github.com/pydantic/pydantic/pull/8050)
+* Fix `Optional` field with `validate_default` only performing one field validation by [@sydney-runkle](https://github.com/sydney-runkle) in [pydantic/pydantic-core#1002](https://github.com/pydantic/pydantic-core/pull/1002)
+* Fix `definition-ref` bug with `Dict` keys by [@sydney-runkle](https://github.com/sydney-runkle) in [pydantic/pydantic-core#1014](https://github.com/pydantic/pydantic-core/pull/1014)
+* Fix bug allowing validation of `bool` types with `coerce_numbers_to_str=True` by [@sydney-runkle](https://github.com/sydney-runkle) in [pydantic/pydantic-core#1017](https://github.com/pydantic/pydantic-core/pull/1017)
+* Don't accept `NaN` in float and decimal constraints by [@davidhewitt](https://github.com/davidhewitt) in [pydantic/pydantic-core#1037](https://github.com/pydantic/pydantic-core/pull/1037)
+* Add `lax_str` and `lax_int` support for enum values not inherited from str/int by [@michaelhly](https://github.com/michaelhly) in [pydantic/pydantic-core#1015](https://github.com/pydantic/pydantic-core/pull/1015)
+* Support subclasses in lists in `Union` of `List` types by [@sydney-runkle](https://github.com/sydney-runkle) in [pydantic/pydantic-core#1039](https://github.com/pydantic/pydantic-core/pull/1039)
+* Allow validation against `max_digits` and `decimals` to pass if normalized or non-normalized input is valid by [@sydney-runkle](https://github.com/sydney-runkle) in [pydantic/pydantic-core#1049](https://github.com/pydantic/pydantic-core/pull/1049)
+* Fix: proper pluralization in `ValidationError` messages by [@Iipin](https://github.com/Iipin) in [pydantic/pydantic-core#1050](https://github.com/pydantic/pydantic-core/pull/1050)
+* Disallow the string `'-'` as `datetime` input by [@davidhewitt](https://github.com/davidhewitt) in [pydantic/speedate#52](https://github.com/pydantic/speedate/pull/52) & [pydantic/pydantic-core#1060](https://github.com/pydantic/pydantic-core/pull/1060)
+* Fix: NaN and Inf float serialization by [@davidhewitt](https://github.com/davidhewitt) in [pydantic/pydantic-core#1062](https://github.com/pydantic/pydantic-core/pull/1062)
+* Restore manylinux-compatible PGO builds by [@davidhewitt](https://github.com/davidhewitt) in [pydantic/pydantic-core#1068](https://github.com/pydantic/pydantic-core/pull/1068)
+
+### New Contributors
+
+#### `pydantic`
+* [@schneebuzz](https://github.com/schneebuzz) made their first contribution in [#7699](https://github.com/pydantic/pydantic/pull/7699)
+* [@edoakes](https://github.com/edoakes) made their first contribution in [#7780](https://github.com/pydantic/pydantic/pull/7780)
+* [@alexmojaki](https://github.com/alexmojaki) made their first contribution in [#7775](https://github.com/pydantic/pydantic/pull/7775)
+* [@NickG123](https://github.com/NickG123) made their first contribution in [#7751](https://github.com/pydantic/pydantic/pull/7751)
+* [@gowthamgts](https://github.com/gowthamgts) made their first contribution in [#7830](https://github.com/pydantic/pydantic/pull/7830)
+* [@jamesbraza](https://github.com/jamesbraza) made their first contribution in [#7848](https://github.com/pydantic/pydantic/pull/7848)
+* [@laundmo](https://github.com/laundmo) made their first contribution in [#7850](https://github.com/pydantic/pydantic/pull/7850)
+* [@rahmatnazali](https://github.com/rahmatnazali) made their first contribution in [#7870](https://github.com/pydantic/pydantic/pull/7870)
+* [@waterfountain1996](https://github.com/waterfountain1996) made their first contribution in [#7878](https://github.com/pydantic/pydantic/pull/7878)
+* [@chris-spann](https://github.com/chris-spann) made their first contribution in [#7863](https://github.com/pydantic/pydantic/pull/7863)
+* [@me-and](https://github.com/me-and) made their first contribution in [#7810](https://github.com/pydantic/pydantic/pull/7810)
+* [@utkini](https://github.com/utkini) made their first contribution in [#7768](https://github.com/pydantic/pydantic/pull/7768)
+* [@bn-l](https://github.com/bn-l) made their first contribution in [#7744](https://github.com/pydantic/pydantic/pull/7744)
+* [@alexdrydew](https://github.com/alexdrydew) made their first contribution in [#7893](https://github.com/pydantic/pydantic/pull/7893)
+* [@Luca-Blight](https://github.com/Luca-Blight) made their first contribution in [#7930](https://github.com/pydantic/pydantic/pull/7930)
+* [@howsunjow](https://github.com/howsunjow) made their first contribution in [#7925](https://github.com/pydantic/pydantic/pull/7925)
+* [@joakimnordling](https://github.com/joakimnordling) made their first contribution in [#7881](https://github.com/pydantic/pydantic/pull/7881)
+* [@icfly2](https://github.com/icfly2) made their first contribution in [#7976](https://github.com/pydantic/pydantic/pull/7976)
+* [@Yummy-Yums](https://github.com/Yummy-Yums) made their first contribution in [#8003](https://github.com/pydantic/pydantic/pull/8003)
+* [@Iipin](https://github.com/Iipin) made their first contribution in [#7972](https://github.com/pydantic/pydantic/pull/7972)
+* [@tabassco](https://github.com/tabassco) made their first contribution in [#8004](https://github.com/pydantic/pydantic/pull/8004)
+* [@Mr-Pepe](https://github.com/Mr-Pepe) made their first contribution in [#7979](https://github.com/pydantic/pydantic/pull/7979)
+* [@0x00cl](https://github.com/0x00cl) made their first contribution in [#8010](https://github.com/pydantic/pydantic/pull/8010)
+* [@barraponto](https://github.com/barraponto) made their first contribution in [#8032](https://github.com/pydantic/pydantic/pull/8032)
+
+#### `pydantic-core`
+* [@sisp](https://github.com/sisp) made their first contribution in [pydantic/pydantic-core#995](https://github.com/pydantic/pydantic-core/pull/995)
+* [@michaelhly](https://github.com/michaelhly) made their first contribution in [pydantic/pydantic-core#1015](https://github.com/pydantic/pydantic-core/pull/1015)
+
+## v2.5.0b1 (2023-11-09)
+
+Pre-release, see [the GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.5.0b1) for details.
+
+## v2.4.2 (2023-09-27)
+
+[GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.4.2)
+
+### What's Changed
+
+#### Fixes
+
+* Fix bug with JSON schema for sequence of discriminated union by [@dmontagu](https://github.com/dmontagu) in [#7647](https://github.com/pydantic/pydantic/pull/7647)
+* Fix schema references in discriminated unions by [@adriangb](https://github.com/adriangb) in [#7646](https://github.com/pydantic/pydantic/pull/7646)
+* Fix json schema generation for recursive models by [@adriangb](https://github.com/adriangb) in [#7653](https://github.com/pydantic/pydantic/pull/7653)
+* Fix `models_json_schema` for generic models by [@adriangb](https://github.com/adriangb) in [#7654](https://github.com/pydantic/pydantic/pull/7654)
+* Fix xfailed test for generic model signatures by [@adriangb](https://github.com/adriangb) in [#7658](https://github.com/pydantic/pydantic/pull/7658)
+
+### New Contributors
+
+* [@austinorr](https://github.com/austinorr) made their first contribution in [#7657](https://github.com/pydantic/pydantic/pull/7657)
+* [@peterHoburg](https://github.com/peterHoburg) made their first contribution in [#7670](https://github.com/pydantic/pydantic/pull/7670)
+
+## v2.4.1 (2023-09-26)
+
+[GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.4.1)
+
+### What's Changed
+
+#### Packaging
+
+* Update pydantic-core to 2.10.1 by [@davidhewitt](https://github.com/davidhewitt) in [#7633](https://github.com/pydantic/pydantic/pull/7633)
+
+#### Fixes
+
+* Serialize unsubstituted type vars as `Any` by [@adriangb](https://github.com/adriangb) in [#7606](https://github.com/pydantic/pydantic/pull/7606)
+* Remove schema building caches by [@adriangb](https://github.com/adriangb) in [#7624](https://github.com/pydantic/pydantic/pull/7624)
+* Fix an issue where JSON schema extras weren't JSON encoded by [@dmontagu](https://github.com/dmontagu) in [#7625](https://github.com/pydantic/pydantic/pull/7625)
+
+## v2.4.0 (2023-09-22)
+
+[GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.4.0)
+
+### What's Changed
+
+#### Packaging
+
+* Update pydantic-core to 2.10.0 by [@samuelcolvin](https://github.com/samuelcolvin) in [#7542](https://github.com/pydantic/pydantic/pull/7542)
+
+#### New Features
+
+* Add `Base64Url` types by [@dmontagu](https://github.com/dmontagu) in [#7286](https://github.com/pydantic/pydantic/pull/7286)
+* Implement optional `number` to `str` coercion by [@lig](https://github.com/lig) in [#7508](https://github.com/pydantic/pydantic/pull/7508)
+* Allow access to `field_name` and `data` in all validators if there is data and a field name by [@samuelcolvin](https://github.com/samuelcolvin) in [#7542](https://github.com/pydantic/pydantic/pull/7542)
+* Add `BaseModel.model_validate_strings` and `TypeAdapter.validate_strings` by [@hramezani](https://github.com/hramezani) in [#7552](https://github.com/pydantic/pydantic/pull/7552)
+* Add Pydantic `plugins` experimental implementation by [@lig](https://github.com/lig) [@samuelcolvin](https://github.com/samuelcolvin) and [@Kludex](https://github.com/Kludex) in [#6820](https://github.com/pydantic/pydantic/pull/6820)
+
+#### Changes
+
+* Do not override `model_post_init` in subclass with private attrs by [@Viicos](https://github.com/Viicos) in [#7302](https://github.com/pydantic/pydantic/pull/7302)
+* Make fields with defaults not required in the serialization schema by default by [@dmontagu](https://github.com/dmontagu) in [#7275](https://github.com/pydantic/pydantic/pull/7275)
+* Mark `Extra` as deprecated by [@disrupted](https://github.com/disrupted) in [#7299](https://github.com/pydantic/pydantic/pull/7299)
+* Make `EncodedStr` a dataclass by [@Kludex](https://github.com/Kludex) in [#7396](https://github.com/pydantic/pydantic/pull/7396)
+* Move `annotated_handlers` to be public by [@samuelcolvin](https://github.com/samuelcolvin) in [#7569](https://github.com/pydantic/pydantic/pull/7569)
+
+#### Performance
+
+* Simplify flattening and inlining of `CoreSchema` by [@adriangb](https://github.com/adriangb) in [#7523](https://github.com/pydantic/pydantic/pull/7523)
+* Remove unused copies in `CoreSchema` walking by [@adriangb](https://github.com/adriangb) in [#7528](https://github.com/pydantic/pydantic/pull/7528)
+* Add caches for collecting definitions and invalid schemas from a CoreSchema by [@adriangb](https://github.com/adriangb) in [#7527](https://github.com/pydantic/pydantic/pull/7527)
+* Eagerly resolve discriminated unions and cache cases where we can't by [@adriangb](https://github.com/adriangb) in [#7529](https://github.com/pydantic/pydantic/pull/7529)
+* Replace `dict.get` and `dict.setdefault` with more verbose versions in `CoreSchema` building hot paths by [@adriangb](https://github.com/adriangb) in [#7536](https://github.com/pydantic/pydantic/pull/7536)
+* Cache invalid `CoreSchema` discovery by [@adriangb](https://github.com/adriangb) in [#7535](https://github.com/pydantic/pydantic/pull/7535)
+* Allow disabling `CoreSchema` validation for faster startup times by [@adriangb](https://github.com/adriangb) in [#7565](https://github.com/pydantic/pydantic/pull/7565)
+
+#### Fixes
+
+* Fix config detection for `TypedDict` from grandparent classes by [@dmontagu](https://github.com/dmontagu) in [#7272](https://github.com/pydantic/pydantic/pull/7272)
+* Fix hash function generation for frozen models with unusual MRO by [@dmontagu](https://github.com/dmontagu) in [#7274](https://github.com/pydantic/pydantic/pull/7274)
+* Make `strict` config overridable in field for Path by [@hramezani](https://github.com/hramezani) in [#7281](https://github.com/pydantic/pydantic/pull/7281)
+* Use `ser_json_<timedelta|bytes>` on default in `GenerateJsonSchema` by [@Kludex](https://github.com/Kludex) in [#7269](https://github.com/pydantic/pydantic/pull/7269)
+* Adding a check that alias is validated as an identifier for Python by [@andree0](https://github.com/andree0) in [#7319](https://github.com/pydantic/pydantic/pull/7319)
+* Raise an error when computed field overrides field by [@sydney-runkle](https://github.com/sydney-runkle) in [#7346](https://github.com/pydantic/pydantic/pull/7346)
+* Fix applying `SkipValidation` to referenced schemas by [@adriangb](https://github.com/adriangb) in [#7381](https://github.com/pydantic/pydantic/pull/7381)
+* Enforce behavior of private attributes having double leading underscore by [@lig](https://github.com/lig) in [#7265](https://github.com/pydantic/pydantic/pull/7265)
+* Standardize `__get_pydantic_core_schema__` signature by [@hramezani](https://github.com/hramezani) in [#7415](https://github.com/pydantic/pydantic/pull/7415)
+* Fix generic dataclass fields mutation bug (when using `TypeAdapter`) by [@sydney-runkle](https://github.com/sydney-runkle) in [#7435](https://github.com/pydantic/pydantic/pull/7435)
+* Fix `TypeError` on `model_validator` in `wrap` mode by [@pmmmwh](https://github.com/pmmmwh) in [#7496](https://github.com/pydantic/pydantic/pull/7496)
+* Improve enum error message by [@hramezani](https://github.com/hramezani) in [#7506](https://github.com/pydantic/pydantic/pull/7506)
+* Make `repr` work for instances that failed initialization when handling `ValidationError`s by [@dmontagu](https://github.com/dmontagu) in [#7439](https://github.com/pydantic/pydantic/pull/7439)
+* Fixed a regular expression denial of service issue by limiting whitespaces by [@prodigysml](https://github.com/prodigysml) in [#7360](https://github.com/pydantic/pydantic/pull/7360)
+* Fix handling of `UUID` values having `UUID.version=None` by [@lig](https://github.com/lig) in [#7566](https://github.com/pydantic/pydantic/pull/7566)
+* Fix `__iter__` returning private `cached_property` info by [@sydney-runkle](https://github.com/sydney-runkle) in [#7570](https://github.com/pydantic/pydantic/pull/7570)
+* Improvements to version info message by [@samuelcolvin](https://github.com/samuelcolvin) in [#7594](https://github.com/pydantic/pydantic/pull/7594)
+
+### New Contributors
+* [@15498th](https://github.com/15498th) made their first contribution in [#7238](https://github.com/pydantic/pydantic/pull/7238)
+* [@GabrielCappelli](https://github.com/GabrielCappelli) made their first contribution in [#7213](https://github.com/pydantic/pydantic/pull/7213)
+* [@tobni](https://github.com/tobni) made their first contribution in [#7184](https://github.com/pydantic/pydantic/pull/7184)
+* [@redruin1](https://github.com/redruin1) made their first contribution in [#7282](https://github.com/pydantic/pydantic/pull/7282)
+* [@FacerAin](https://github.com/FacerAin) made their first contribution in [#7288](https://github.com/pydantic/pydantic/pull/7288)
+* [@acdha](https://github.com/acdha) made their first contribution in [#7297](https://github.com/pydantic/pydantic/pull/7297)
+* [@andree0](https://github.com/andree0) made their first contribution in [#7319](https://github.com/pydantic/pydantic/pull/7319)
+* [@gordonhart](https://github.com/gordonhart) made their first contribution in [#7375](https://github.com/pydantic/pydantic/pull/7375)
+* [@pmmmwh](https://github.com/pmmmwh) made their first contribution in [#7496](https://github.com/pydantic/pydantic/pull/7496)
+* [@disrupted](https://github.com/disrupted) made their first contribution in [#7299](https://github.com/pydantic/pydantic/pull/7299)
+* [@prodigysml](https://github.com/prodigysml) made their first contribution in [#7360](https://github.com/pydantic/pydantic/pull/7360)
+
+## v2.3.0 (2023-08-23)
+
+[GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.3.0)
+
+* 🔥 Remove orphaned changes file from repo by [@lig](https://github.com/lig) in [#7168](https://github.com/pydantic/pydantic/pull/7168)
+* Add copy button on documentation by [@Kludex](https://github.com/Kludex) in [#7190](https://github.com/pydantic/pydantic/pull/7190)
+* Fix docs on JSON type by [@Kludex](https://github.com/Kludex) in [#7189](https://github.com/pydantic/pydantic/pull/7189)
+* Update mypy 1.5.0 to 1.5.1 in CI by [@hramezani](https://github.com/hramezani) in [#7191](https://github.com/pydantic/pydantic/pull/7191)
+* fix download links badge by [@samuelcolvin](https://github.com/samuelcolvin) in [#7200](https://github.com/pydantic/pydantic/pull/7200)
+* add 2.2.1 to changelog by [@samuelcolvin](https://github.com/samuelcolvin) in [#7212](https://github.com/pydantic/pydantic/pull/7212)
+* Make ModelWrapValidator protocols generic by [@dmontagu](https://github.com/dmontagu) in [#7154](https://github.com/pydantic/pydantic/pull/7154)
+* Correct `Field(..., exclude: bool)` docs by [@samuelcolvin](https://github.com/samuelcolvin) in [#7214](https://github.com/pydantic/pydantic/pull/7214)
+* Make shadowing attributes a warning instead of an error by [@adriangb](https://github.com/adriangb) in [#7193](https://github.com/pydantic/pydantic/pull/7193)
+* Document `Base64Str` and `Base64Bytes` by [@Kludex](https://github.com/Kludex) in [#7192](https://github.com/pydantic/pydantic/pull/7192)
+* Fix `config.defer_build` for serialization first cases by [@samuelcolvin](https://github.com/samuelcolvin) in [#7024](https://github.com/pydantic/pydantic/pull/7024)
+* clean Model docstrings in JSON Schema by [@samuelcolvin](https://github.com/samuelcolvin) in [#7210](https://github.com/pydantic/pydantic/pull/7210)
+* fix [#7228](https://github.com/pydantic/pydantic/pull/7228) (typo): docs in `validators.md` to correct `validate_default` kwarg by [@lmmx](https://github.com/lmmx) in [#7229](https://github.com/pydantic/pydantic/pull/7229)
+* ✅ Implement `tzinfo.fromutc` method for `TzInfo` in `pydantic-core` by [@lig](https://github.com/lig) in [#7019](https://github.com/pydantic/pydantic/pull/7019)
+* Support `__get_validators__` by [@hramezani](https://github.com/hramezani) in [#7197](https://github.com/pydantic/pydantic/pull/7197)
+
+## v2.2.1 (2023-08-18)
+
+[GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.2.1)
+
+* Make `xfail`ing test for root model extra stop `xfail`ing by [@dmontagu](https://github.com/dmontagu) in [#6937](https://github.com/pydantic/pydantic/pull/6937)
+* Optimize recursion detection by stopping on the second visit for the same object by [@mciucu](https://github.com/mciucu) in [#7160](https://github.com/pydantic/pydantic/pull/7160)
+* fix link in docs by [@tlambert03](https://github.com/tlambert03) in [#7166](https://github.com/pydantic/pydantic/pull/7166)
+* Replace MiMalloc w/ default allocator by [@adriangb](https://github.com/adriangb) in [pydantic/pydantic-core#900](https://github.com/pydantic/pydantic-core/pull/900)
+* Bump pydantic-core to 2.6.1 and prepare 2.2.1 release by [@adriangb](https://github.com/adriangb) in [#7176](https://github.com/pydantic/pydantic/pull/7176)
+
+## v2.2.0 (2023-08-17)
+
+[GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.2.0)
+
+* Split "pipx install" setup command into two commands on the documentation site by [@nomadmtb](https://github.com/nomadmtb) in [#6869](https://github.com/pydantic/pydantic/pull/6869)
+* Deprecate `Field.include` by [@hramezani](https://github.com/hramezani) in [#6852](https://github.com/pydantic/pydantic/pull/6852)
+* Fix typo in default factory error msg by [@hramezani](https://github.com/hramezani) in [#6880](https://github.com/pydantic/pydantic/pull/6880)
+* Simplify handling of typing.Annotated in GenerateSchema by [@dmontagu](https://github.com/dmontagu) in [#6887](https://github.com/pydantic/pydantic/pull/6887)
+* Re-enable fastapi tests in CI by [@dmontagu](https://github.com/dmontagu) in [#6883](https://github.com/pydantic/pydantic/pull/6883)
+* Make it harder to hit collisions with json schema defrefs by [@dmontagu](https://github.com/dmontagu) in [#6566](https://github.com/pydantic/pydantic/pull/6566)
+* Cleaner error for invalid input to `Path` fields by [@samuelcolvin](https://github.com/samuelcolvin) in [#6903](https://github.com/pydantic/pydantic/pull/6903)
+* :memo: support Coordinate Type by [@yezz123](https://github.com/yezz123) in [#6906](https://github.com/pydantic/pydantic/pull/6906)
+* Fix `ForwardRef` wrapper for py 3.10.0 (shim until bpo-45166) by [@randomir](https://github.com/randomir) in [#6919](https://github.com/pydantic/pydantic/pull/6919)
+* Fix misbehavior related to copying of RootModel by [@dmontagu](https://github.com/dmontagu) in [#6918](https://github.com/pydantic/pydantic/pull/6918)
+* Fix issue with recursion error caused by ParamSpec by [@dmontagu](https://github.com/dmontagu) in [#6923](https://github.com/pydantic/pydantic/pull/6923)
+* Add section about Constrained classes to the Migration Guide by [@Kludex](https://github.com/Kludex) in [#6924](https://github.com/pydantic/pydantic/pull/6924)
+* Use `main` branch for badge links by [@Viicos](https://github.com/Viicos) in [#6925](https://github.com/pydantic/pydantic/pull/6925)
+* Add test for v1/v2 Annotated discrepancy by [@carlbordum](https://github.com/carlbordum) in [#6926](https://github.com/pydantic/pydantic/pull/6926)
+* Make the v1 mypy plugin work with both v1 and v2 by [@dmontagu](https://github.com/dmontagu) in [#6921](https://github.com/pydantic/pydantic/pull/6921)
+* Fix issue where generic models couldn't be parametrized with BaseModel by [@dmontagu](https://github.com/dmontagu) in [#6933](https://github.com/pydantic/pydantic/pull/6933)
+* Remove xfail for discriminated union with alias by [@dmontagu](https://github.com/dmontagu) in [#6938](https://github.com/pydantic/pydantic/pull/6938)
+* add field_serializer to computed_field by [@andresliszt](https://github.com/andresliszt) in [#6965](https://github.com/pydantic/pydantic/pull/6965)
+* Use union_schema with Type[Union[...]] by [@JeanArhancet](https://github.com/JeanArhancet) in [#6952](https://github.com/pydantic/pydantic/pull/6952)
+* Fix inherited typeddict attributes / config by [@adriangb](https://github.com/adriangb) in [#6981](https://github.com/pydantic/pydantic/pull/6981)
+* fix dataclass annotated before validator called twice by [@davidhewitt](https://github.com/davidhewitt) in [#6998](https://github.com/pydantic/pydantic/pull/6998)
+* Update test-fastapi deselected tests by [@hramezani](https://github.com/hramezani) in [#7014](https://github.com/pydantic/pydantic/pull/7014)
+* Fix validator doc format by [@hramezani](https://github.com/hramezani) in [#7015](https://github.com/pydantic/pydantic/pull/7015)
+* Fix typo in docstring of model_json_schema by [@AdamVinch-Federated](https://github.com/AdamVinch-Federated) in [#7032](https://github.com/pydantic/pydantic/pull/7032)
+* remove unused "type ignores" with pyright by [@samuelcolvin](https://github.com/samuelcolvin) in [#7026](https://github.com/pydantic/pydantic/pull/7026)
+* Add benchmark representing FastAPI startup time by [@adriangb](https://github.com/adriangb) in [#7030](https://github.com/pydantic/pydantic/pull/7030)
+* Fix json_encoders for Enum subclasses by [@adriangb](https://github.com/adriangb) in [#7029](https://github.com/pydantic/pydantic/pull/7029)
+* Update docstring of `ser_json_bytes` regarding base64 encoding by [@Viicos](https://github.com/Viicos) in [#7052](https://github.com/pydantic/pydantic/pull/7052)
+* Allow `@validate_call` to work on async methods by [@adriangb](https://github.com/adriangb) in [#7046](https://github.com/pydantic/pydantic/pull/7046)
+* Fix: mypy error with `Settings` and `SettingsConfigDict` by [@JeanArhancet](https://github.com/JeanArhancet) in [#7002](https://github.com/pydantic/pydantic/pull/7002)
+* Fix some typos (repeated words and it's/its) by [@eumiro](https://github.com/eumiro) in [#7063](https://github.com/pydantic/pydantic/pull/7063)
+* Fix the typo in docstring by [@harunyasar](https://github.com/harunyasar) in [#7062](https://github.com/pydantic/pydantic/pull/7062)
+* Docs: Fix broken URL in the pydantic-settings package recommendation by [@swetjen](https://github.com/swetjen) in [#6995](https://github.com/pydantic/pydantic/pull/6995)
+* Handle constraints being applied to schemas that don't accept it by [@adriangb](https://github.com/adriangb) in [#6951](https://github.com/pydantic/pydantic/pull/6951)
+* Replace almost_equal_floats with math.isclose by [@eumiro](https://github.com/eumiro) in [#7082](https://github.com/pydantic/pydantic/pull/7082)
+* bump pydantic-core to 2.5.0 by [@davidhewitt](https://github.com/davidhewitt) in [#7077](https://github.com/pydantic/pydantic/pull/7077)
+* Add `short_version` and use it in links by [@hramezani](https://github.com/hramezani) in [#7115](https://github.com/pydantic/pydantic/pull/7115)
+* 📝 Add usage link to `RootModel` by [@Kludex](https://github.com/Kludex) in [#7113](https://github.com/pydantic/pydantic/pull/7113)
+* Revert "Fix default port for mongosrv DSNs (#6827)" by [@Kludex](https://github.com/Kludex) in [#7116](https://github.com/pydantic/pydantic/pull/7116)
+* Clarify validate_default and _Unset handling in usage docs and migration guide by [@benbenbang](https://github.com/benbenbang) in [#6950](https://github.com/pydantic/pydantic/pull/6950)
+* Tweak documentation of `Field.exclude` by [@Viicos](https://github.com/Viicos) in [#7086](https://github.com/pydantic/pydantic/pull/7086)
+* Do not require `validate_assignment` to use `Field.frozen` by [@Viicos](https://github.com/Viicos) in [#7103](https://github.com/pydantic/pydantic/pull/7103)
+* tweaks to `_core_utils` by [@samuelcolvin](https://github.com/samuelcolvin) in [#7040](https://github.com/pydantic/pydantic/pull/7040)
+* Make DefaultDict working with set by [@hramezani](https://github.com/hramezani) in [#7126](https://github.com/pydantic/pydantic/pull/7126)
+* Don't always require typing.Generic as a base for partially parametrized models by [@dmontagu](https://github.com/dmontagu) in [#7119](https://github.com/pydantic/pydantic/pull/7119)
+* Fix issue with JSON schema incorrectly using parent class core schema by [@dmontagu](https://github.com/dmontagu) in [#7020](https://github.com/pydantic/pydantic/pull/7020)
+* Fix xfailed test related to TypedDict and alias_generator by [@dmontagu](https://github.com/dmontagu) in [#6940](https://github.com/pydantic/pydantic/pull/6940)
+* Improve error message for NameEmail by [@dmontagu](https://github.com/dmontagu) in [#6939](https://github.com/pydantic/pydantic/pull/6939)
+* Fix generic computed fields by [@dmontagu](https://github.com/dmontagu) in [#6988](https://github.com/pydantic/pydantic/pull/6988)
+* Reflect namedtuple default values during validation by [@dmontagu](https://github.com/dmontagu) in [#7144](https://github.com/pydantic/pydantic/pull/7144)
+* Update dependencies, fix pydantic-core usage, fix CI issues by [@dmontagu](https://github.com/dmontagu) in [#7150](https://github.com/pydantic/pydantic/pull/7150)
+* Add mypy 1.5.0 by [@hramezani](https://github.com/hramezani) in [#7118](https://github.com/pydantic/pydantic/pull/7118)
+* Handle non-json native enum values by [@adriangb](https://github.com/adriangb) in [#7056](https://github.com/pydantic/pydantic/pull/7056)
+* document `round_trip` in Json type documentation  by [@jc-louis](https://github.com/jc-louis) in [#7137](https://github.com/pydantic/pydantic/pull/7137)
+* Relax signature checks to better support builtins and C extension functions as validators by [@adriangb](https://github.com/adriangb) in [#7101](https://github.com/pydantic/pydantic/pull/7101)
+* add union_mode='left_to_right' by [@davidhewitt](https://github.com/davidhewitt) in [#7151](https://github.com/pydantic/pydantic/pull/7151)
+* Include an error message hint for inherited ordering by [@yvalencia91](https://github.com/yvalencia91) in [#7124](https://github.com/pydantic/pydantic/pull/7124)
+* Fix one docs link and resolve some warnings for two others by [@dmontagu](https://github.com/dmontagu) in [#7153](https://github.com/pydantic/pydantic/pull/7153)
+* Include Field extra keys name in warning by [@hramezani](https://github.com/hramezani) in [#7136](https://github.com/pydantic/pydantic/pull/7136)
+
+## v2.1.1 (2023-07-25)
+
+[GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.1.1)
+
+* Skip FieldInfo merging when unnecessary by [@dmontagu](https://github.com/dmontagu) in [#6862](https://github.com/pydantic/pydantic/pull/6862)
+
+## v2.1.0 (2023-07-25)
+
+[GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.1.0)
+
+* Add `StringConstraints` for use as Annotated metadata by [@adriangb](https://github.com/adriangb) in [#6605](https://github.com/pydantic/pydantic/pull/6605)
+* Try to fix intermittently failing CI by [@adriangb](https://github.com/adriangb) in [#6683](https://github.com/pydantic/pydantic/pull/6683)
+* Remove redundant example of optional vs default. by [@ehiggs-deliverect](https://github.com/ehiggs-deliverect) in [#6676](https://github.com/pydantic/pydantic/pull/6676)
+* Docs update by [@samuelcolvin](https://github.com/samuelcolvin) in [#6692](https://github.com/pydantic/pydantic/pull/6692)
+* Remove the Validate always section in validator docs by [@adriangb](https://github.com/adriangb) in [#6679](https://github.com/pydantic/pydantic/pull/6679)
+* Fix recursion error in json schema generation by [@adriangb](https://github.com/adriangb) in [#6720](https://github.com/pydantic/pydantic/pull/6720)
+* Fix incorrect subclass check for secretstr by [@AlexVndnblcke](https://github.com/AlexVndnblcke) in [#6730](https://github.com/pydantic/pydantic/pull/6730)
+* update pdm / pdm lockfile to 2.8.0 by [@davidhewitt](https://github.com/davidhewitt) in [#6714](https://github.com/pydantic/pydantic/pull/6714)
+* unpin pdm on more CI jobs by [@davidhewitt](https://github.com/davidhewitt) in [#6755](https://github.com/pydantic/pydantic/pull/6755)
+* improve source locations for auxiliary packages in docs by [@davidhewitt](https://github.com/davidhewitt) in [#6749](https://github.com/pydantic/pydantic/pull/6749)
+* Assume builtins don't accept an info argument by [@adriangb](https://github.com/adriangb) in [#6754](https://github.com/pydantic/pydantic/pull/6754)
+* Fix bug where calling `help(BaseModelSubclass)` raises errors by [@hramezani](https://github.com/hramezani) in [#6758](https://github.com/pydantic/pydantic/pull/6758)
+* Fix mypy plugin handling of `@model_validator(mode="after")` by [@ljodal](https://github.com/ljodal) in [#6753](https://github.com/pydantic/pydantic/pull/6753)
+* update pydantic-core to 2.3.1 by [@davidhewitt](https://github.com/davidhewitt) in [#6756](https://github.com/pydantic/pydantic/pull/6756)
+* Mypy plugin for settings by [@hramezani](https://github.com/hramezani) in [#6760](https://github.com/pydantic/pydantic/pull/6760)
+* Use `contentSchema` keyword for JSON schema by [@dmontagu](https://github.com/dmontagu) in [#6715](https://github.com/pydantic/pydantic/pull/6715)
+* fast-path checking finite decimals by [@davidhewitt](https://github.com/davidhewitt) in [#6769](https://github.com/pydantic/pydantic/pull/6769)
+* Docs update by [@samuelcolvin](https://github.com/samuelcolvin) in [#6771](https://github.com/pydantic/pydantic/pull/6771)
+* Improve json schema doc by [@hramezani](https://github.com/hramezani) in [#6772](https://github.com/pydantic/pydantic/pull/6772)
+* Update validator docs by [@adriangb](https://github.com/adriangb) in [#6695](https://github.com/pydantic/pydantic/pull/6695)
+* Fix typehint for wrap validator by [@dmontagu](https://github.com/dmontagu) in [#6788](https://github.com/pydantic/pydantic/pull/6788)
+* 🐛 Fix validation warning for unions of Literal and other type by [@lig](https://github.com/lig) in [#6628](https://github.com/pydantic/pydantic/pull/6628)
+* Update documentation for generics support in V2 by [@tpdorsey](https://github.com/tpdorsey) in [#6685](https://github.com/pydantic/pydantic/pull/6685)
+* add pydantic-core build info to `version_info()` by [@samuelcolvin](https://github.com/samuelcolvin) in [#6785](https://github.com/pydantic/pydantic/pull/6785)
+* Fix pydantic dataclasses that use slots with default values by [@dmontagu](https://github.com/dmontagu) in [#6796](https://github.com/pydantic/pydantic/pull/6796)
+* Fix inheritance of hash function for frozen models by [@dmontagu](https://github.com/dmontagu) in [#6789](https://github.com/pydantic/pydantic/pull/6789)
+* ✨ Add `SkipJsonSchema` annotation by [@Kludex](https://github.com/Kludex) in [#6653](https://github.com/pydantic/pydantic/pull/6653)
+* Error if an invalid field name is used with Field by [@dmontagu](https://github.com/dmontagu) in [#6797](https://github.com/pydantic/pydantic/pull/6797)
+* Add `GenericModel` to `MOVED_IN_V2` by [@adriangb](https://github.com/adriangb) in [#6776](https://github.com/pydantic/pydantic/pull/6776)
+* Remove unused code from `docs/usage/types/custom.md` by [@hramezani](https://github.com/hramezani) in [#6803](https://github.com/pydantic/pydantic/pull/6803)
+* Fix `float` -> `Decimal` coercion precision loss by [@adriangb](https://github.com/adriangb) in [#6810](https://github.com/pydantic/pydantic/pull/6810)
+* remove email validation from the north star benchmark by [@davidhewitt](https://github.com/davidhewitt) in [#6816](https://github.com/pydantic/pydantic/pull/6816)
+* Fix link to mypy by [@progsmile](https://github.com/progsmile) in [#6824](https://github.com/pydantic/pydantic/pull/6824)
+* Improve initialization hooks example by [@hramezani](https://github.com/hramezani) in [#6822](https://github.com/pydantic/pydantic/pull/6822)
+* Fix default port for mongosrv DSNs by [@dmontagu](https://github.com/dmontagu) in [#6827](https://github.com/pydantic/pydantic/pull/6827)
+* Improve API documentation, in particular more links between usage and API docs by [@samuelcolvin](https://github.com/samuelcolvin) in [#6780](https://github.com/pydantic/pydantic/pull/6780)
+* update pydantic-core to 2.4.0 by [@davidhewitt](https://github.com/davidhewitt) in [#6831](https://github.com/pydantic/pydantic/pull/6831)
+* Fix `annotated_types.MaxLen` validator for custom sequence types by [@ImogenBits](https://github.com/ImogenBits) in [#6809](https://github.com/pydantic/pydantic/pull/6809)
+* Update V1 by [@hramezani](https://github.com/hramezani) in [#6833](https://github.com/pydantic/pydantic/pull/6833)
+* Make it so callable JSON schema extra works by [@dmontagu](https://github.com/dmontagu) in [#6798](https://github.com/pydantic/pydantic/pull/6798)
+* Fix serialization issue with `InstanceOf` by [@dmontagu](https://github.com/dmontagu) in [#6829](https://github.com/pydantic/pydantic/pull/6829)
+* Add back support for `json_encoders` by [@adriangb](https://github.com/adriangb) in [#6811](https://github.com/pydantic/pydantic/pull/6811)
+* Update field annotations when building the schema by [@dmontagu](https://github.com/dmontagu) in [#6838](https://github.com/pydantic/pydantic/pull/6838)
+* Use `WeakValueDictionary` to fix generic memory leak by [@dmontagu](https://github.com/dmontagu) in [#6681](https://github.com/pydantic/pydantic/pull/6681)
+* Add `config.defer_build` to optionally make model building lazy by [@samuelcolvin](https://github.com/samuelcolvin) in [#6823](https://github.com/pydantic/pydantic/pull/6823)
+* delegate `UUID` serialization to pydantic-core by [@davidhewitt](https://github.com/davidhewitt) in [#6850](https://github.com/pydantic/pydantic/pull/6850)
+* Update `json_encoders` docs by [@adriangb](https://github.com/adriangb) in [#6848](https://github.com/pydantic/pydantic/pull/6848)
+* Fix error message for `staticmethod`/`classmethod` order with validate_call by [@dmontagu](https://github.com/dmontagu) in [#6686](https://github.com/pydantic/pydantic/pull/6686)
+* Improve documentation for `Config` by [@samuelcolvin](https://github.com/samuelcolvin) in [#6847](https://github.com/pydantic/pydantic/pull/6847)
+* Update serialization doc to mention `Field.exclude` takes priority over call-time `include/exclude` by [@hramezani](https://github.com/hramezani) in [#6851](https://github.com/pydantic/pydantic/pull/6851)
+* Allow customizing core schema generation by making `GenerateSchema` public by [@adriangb](https://github.com/adriangb) in [#6737](https://github.com/pydantic/pydantic/pull/6737)
+
+## v2.0.3 (2023-07-05)
+
+[GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.0.3)
+
+* Mention PyObject (v1) moving to ImportString (v2) in migration doc by [@slafs](https://github.com/slafs) in [#6456](https://github.com/pydantic/pydantic/pull/6456)
+* Fix release-tweet CI by [@Kludex](https://github.com/Kludex) in [#6461](https://github.com/pydantic/pydantic/pull/6461)
+* Revise the section on required / optional / nullable fields. by [@ybressler](https://github.com/ybressler) in [#6468](https://github.com/pydantic/pydantic/pull/6468)
+* Warn if a type hint is not in fact a type by [@adriangb](https://github.com/adriangb) in [#6479](https://github.com/pydantic/pydantic/pull/6479)
+* Replace TransformSchema with GetPydanticSchema by [@dmontagu](https://github.com/dmontagu) in [#6484](https://github.com/pydantic/pydantic/pull/6484)
+* Fix the un-hashability of various annotation types, for use in caching generic containers by [@dmontagu](https://github.com/dmontagu) in [#6480](https://github.com/pydantic/pydantic/pull/6480)
+* PYD-164: Rework custom types docs by [@adriangb](https://github.com/adriangb) in [#6490](https://github.com/pydantic/pydantic/pull/6490)
+* Fix ci by [@adriangb](https://github.com/adriangb) in [#6507](https://github.com/pydantic/pydantic/pull/6507)
+* Fix forward ref in generic by [@adriangb](https://github.com/adriangb) in [#6511](https://github.com/pydantic/pydantic/pull/6511)
+* Fix generation of serialization JSON schemas for core_schema.ChainSchema by [@dmontagu](https://github.com/dmontagu) in [#6515](https://github.com/pydantic/pydantic/pull/6515)
+* Document the change in `Field.alias` behavior in Pydantic V2 by [@hramezani](https://github.com/hramezani) in [#6508](https://github.com/pydantic/pydantic/pull/6508)
+* Give better error message attempting to compute the json schema of a model with undefined fields by [@dmontagu](https://github.com/dmontagu) in [#6519](https://github.com/pydantic/pydantic/pull/6519)
+* Document `alias_priority` by [@tpdorsey](https://github.com/tpdorsey) in [#6520](https://github.com/pydantic/pydantic/pull/6520)
+* Add redirect for types documentation by [@tpdorsey](https://github.com/tpdorsey) in [#6513](https://github.com/pydantic/pydantic/pull/6513)
+* Allow updating docs without release by [@samuelcolvin](https://github.com/samuelcolvin) in [#6551](https://github.com/pydantic/pydantic/pull/6551)
+* Ensure docs tests always run in the right folder by [@dmontagu](https://github.com/dmontagu) in [#6487](https://github.com/pydantic/pydantic/pull/6487)
+* Defer evaluation of return type hints for serializer functions by [@dmontagu](https://github.com/dmontagu) in [#6516](https://github.com/pydantic/pydantic/pull/6516)
+* Disable E501 from Ruff and rely on just Black by [@adriangb](https://github.com/adriangb) in [#6552](https://github.com/pydantic/pydantic/pull/6552)
+* Update JSON Schema documentation for V2 by [@tpdorsey](https://github.com/tpdorsey) in [#6492](https://github.com/pydantic/pydantic/pull/6492)
+* Add documentation of cyclic reference handling by [@dmontagu](https://github.com/dmontagu) in [#6493](https://github.com/pydantic/pydantic/pull/6493)
+* Remove the need for change files by [@samuelcolvin](https://github.com/samuelcolvin) in [#6556](https://github.com/pydantic/pydantic/pull/6556)
+* add "north star" benchmark by [@davidhewitt](https://github.com/davidhewitt) in [#6547](https://github.com/pydantic/pydantic/pull/6547)
+* Update Dataclasses docs by [@tpdorsey](https://github.com/tpdorsey) in [#6470](https://github.com/pydantic/pydantic/pull/6470)
+* ♻️ Use different error message on v1 redirects by [@Kludex](https://github.com/Kludex) in [#6595](https://github.com/pydantic/pydantic/pull/6595)
+* ⬆ Upgrade `pydantic-core` to v2.2.0 by [@lig](https://github.com/lig) in [#6589](https://github.com/pydantic/pydantic/pull/6589)
+* Fix serialization for IPvAny by [@dmontagu](https://github.com/dmontagu) in [#6572](https://github.com/pydantic/pydantic/pull/6572)
+* Improve CI by using PDM instead of pip to install typing-extensions by [@adriangb](https://github.com/adriangb) in [#6602](https://github.com/pydantic/pydantic/pull/6602)
+* Add `enum` error type docs  by [@lig](https://github.com/lig) in [#6603](https://github.com/pydantic/pydantic/pull/6603)
+* 🐛 Fix `max_length` for unicode strings by [@lig](https://github.com/lig) in [#6559](https://github.com/pydantic/pydantic/pull/6559)
+* Add documentation for accessing features via `pydantic.v1` by [@tpdorsey](https://github.com/tpdorsey) in [#6604](https://github.com/pydantic/pydantic/pull/6604)
+* Include extra when iterating over a model by [@adriangb](https://github.com/adriangb) in [#6562](https://github.com/pydantic/pydantic/pull/6562)
+* Fix typing of model_validator by [@adriangb](https://github.com/adriangb) in [#6514](https://github.com/pydantic/pydantic/pull/6514)
+* Touch up Decimal validator by [@adriangb](https://github.com/adriangb) in [#6327](https://github.com/pydantic/pydantic/pull/6327)
+* Fix various docstrings using fixed pytest-examples by [@dmontagu](https://github.com/dmontagu) in [#6607](https://github.com/pydantic/pydantic/pull/6607)
+* Handle function validators in a discriminated union by [@dmontagu](https://github.com/dmontagu) in [#6570](https://github.com/pydantic/pydantic/pull/6570)
+* Review json_schema.md by [@tpdorsey](https://github.com/tpdorsey) in [#6608](https://github.com/pydantic/pydantic/pull/6608)
+* Make validate_call work on basemodel methods by [@dmontagu](https://github.com/dmontagu) in [#6569](https://github.com/pydantic/pydantic/pull/6569)
+* add test for big int json serde by [@davidhewitt](https://github.com/davidhewitt) in [#6614](https://github.com/pydantic/pydantic/pull/6614)
+* Fix pydantic dataclass problem with dataclasses.field default_factory by [@hramezani](https://github.com/hramezani) in [#6616](https://github.com/pydantic/pydantic/pull/6616)
+* Fixed mypy type inference for TypeAdapter by [@zakstucke](https://github.com/zakstucke) in [#6617](https://github.com/pydantic/pydantic/pull/6617)
+* Make it work to use None as a generic parameter by [@dmontagu](https://github.com/dmontagu) in [#6609](https://github.com/pydantic/pydantic/pull/6609)
+* Make it work to use `$ref` as an alias by [@dmontagu](https://github.com/dmontagu) in [#6568](https://github.com/pydantic/pydantic/pull/6568)
+* add note to migration guide about changes to `AnyUrl` etc by [@davidhewitt](https://github.com/davidhewitt) in [#6618](https://github.com/pydantic/pydantic/pull/6618)
+* 🐛 Support defining `json_schema_extra` on `RootModel` using `Field` by [@lig](https://github.com/lig) in [#6622](https://github.com/pydantic/pydantic/pull/6622)
+* Update pre-commit to prevent commits to main branch on accident by [@dmontagu](https://github.com/dmontagu) in [#6636](https://github.com/pydantic/pydantic/pull/6636)
+* Fix PDM CI for python 3.7 on MacOS/windows by [@dmontagu](https://github.com/dmontagu) in [#6627](https://github.com/pydantic/pydantic/pull/6627)
+* Produce more accurate signatures for pydantic dataclasses by [@dmontagu](https://github.com/dmontagu) in [#6633](https://github.com/pydantic/pydantic/pull/6633)
+* Updates to Url types for Pydantic V2 by [@tpdorsey](https://github.com/tpdorsey) in [#6638](https://github.com/pydantic/pydantic/pull/6638)
+* Fix list markdown in `transform` docstring by [@StefanBRas](https://github.com/StefanBRas) in [#6649](https://github.com/pydantic/pydantic/pull/6649)
+* simplify slots_dataclass construction to appease mypy by [@davidhewitt](https://github.com/davidhewitt) in [#6639](https://github.com/pydantic/pydantic/pull/6639)
+* Update TypedDict schema generation docstring by [@adriangb](https://github.com/adriangb) in [#6651](https://github.com/pydantic/pydantic/pull/6651)
+* Detect and lint-error for prints by [@dmontagu](https://github.com/dmontagu) in [#6655](https://github.com/pydantic/pydantic/pull/6655)
+* Add xfailing test for pydantic-core PR 766 by [@dmontagu](https://github.com/dmontagu) in [#6641](https://github.com/pydantic/pydantic/pull/6641)
+* Ignore unrecognized fields from dataclasses metadata by [@dmontagu](https://github.com/dmontagu) in [#6634](https://github.com/pydantic/pydantic/pull/6634)
+* Make non-existent class getattr a mypy error by [@dmontagu](https://github.com/dmontagu) in [#6658](https://github.com/pydantic/pydantic/pull/6658)
+* Update pydantic-core to 2.3.0 by [@hramezani](https://github.com/hramezani) in [#6648](https://github.com/pydantic/pydantic/pull/6648)
+* Use OrderedDict from typing_extensions by [@dmontagu](https://github.com/dmontagu) in [#6664](https://github.com/pydantic/pydantic/pull/6664)
+* Fix typehint for JSON schema extra callable by [@dmontagu](https://github.com/dmontagu) in [#6659](https://github.com/pydantic/pydantic/pull/6659)
+
+## v2.0.2 (2023-07-05)
+
+[GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.0.2)
+
+* Fix bug where round-trip pickling/unpickling a `RootModel` would change the value of `__dict__`, [#6457](https://github.com/pydantic/pydantic/pull/6457) by [@dmontagu](https://github.com/dmontagu)
+* Allow single-item discriminated unions, [#6405](https://github.com/pydantic/pydantic/pull/6405) by [@dmontagu](https://github.com/dmontagu)
+* Fix issue with union parsing of enums, [#6440](https://github.com/pydantic/pydantic/pull/6440) by [@dmontagu](https://github.com/dmontagu)
+* Docs: Fixed `constr` documentation, renamed old `regex` to new `pattern`, [#6452](https://github.com/pydantic/pydantic/pull/6452) by [@miili](https://github.com/miili)
+* Change `GenerateJsonSchema.generate_definitions` signature, [#6436](https://github.com/pydantic/pydantic/pull/6436) by [@dmontagu](https://github.com/dmontagu)
+
+See the full changelog [here](https://github.com/pydantic/pydantic/releases/tag/v2.0.2)
+
+## v2.0.1 (2023-07-04)
+
+[GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.0.1)
+
+First patch release of Pydantic V2
+
+* Extra fields added via `setattr` (i.e. `m.some_extra_field = 'extra_value'`)
+  are added to `.model_extra` if `model_config` `extra='allowed'`. Fixed [#6333](https://github.com/pydantic/pydantic/pull/6333), [#6365](https://github.com/pydantic/pydantic/pull/6365) by [@aaraney](https://github.com/aaraney)
+* Automatically unpack JSON schema '$ref' for custom types, [#6343](https://github.com/pydantic/pydantic/pull/6343) by [@adriangb](https://github.com/adriangb)
+* Fix tagged unions multiple processing in submodels, [#6340](https://github.com/pydantic/pydantic/pull/6340) by [@suharnikov](https://github.com/suharnikov)
+
+See the full changelog [here](https://github.com/pydantic/pydantic/releases/tag/v2.0.1)
+
+## v2.0 (2023-06-30)
+
+[GitHub release](https://github.com/pydantic/pydantic/releases/tag/v2.0)
+
+Pydantic V2 is here! :tada:
+
+See [this post](https://docs.pydantic.dev/2.0/blog/pydantic-v2-final/) for more details.
+
+## v2.0b3 (2023-06-16)
+
+Third beta pre-release of Pydantic V2
+
+See the full changelog [here](https://github.com/pydantic/pydantic/releases/tag/v2.0b3)
+
+## v2.0b2 (2023-06-03)
+
+Add `from_attributes` runtime flag to `TypeAdapter.validate_python` and `BaseModel.model_validate`.
+
+See the full changelog [here](https://github.com/pydantic/pydantic/releases/tag/v2.0b2)
+
+## v2.0b1 (2023-06-01)
+
+First beta pre-release of Pydantic V2
+
+See the full changelog [here](https://github.com/pydantic/pydantic/releases/tag/v2.0b1)
+
+## v2.0a4 (2023-05-05)
+
+Fourth pre-release of Pydantic V2
+
+See the full changelog [here](https://github.com/pydantic/pydantic/releases/tag/v2.0a4)
+
+## v2.0a3 (2023-04-20)
+
+Third pre-release of Pydantic V2
+
+See the full changelog [here](https://github.com/pydantic/pydantic/releases/tag/v2.0a3)
+
+## v2.0a2 (2023-04-12)
+
+Second pre-release of Pydantic V2
+
+See the full changelog [here](https://github.com/pydantic/pydantic/releases/tag/v2.0a2)
+
+## v2.0a1 (2023-04-03)
+
+First pre-release of Pydantic V2!
+
+See [this post](https://docs.pydantic.dev/blog/pydantic-v2-alpha/) for more details.
+
+
+... see [here](https://docs.pydantic.dev/changelog/#v0322-2019-08-17) for earlier changes.
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@@ -0,0 +1,4 @@
+Wheel-Version: 1.0
+Generator: hatchling 1.25.0
+Root-Is-Purelib: true
+Tag: py3-none-any
diff --git a/llava_next/lib/python3.10/site-packages/pydantic-2.9.2.dist-info/licenses/LICENSE b/llava_next/lib/python3.10/site-packages/pydantic-2.9.2.dist-info/licenses/LICENSE
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index 0000000000000000000000000000000000000000..488c6260c10f2e88fa1fae58a63fccec8d600cd1
--- /dev/null
+++ b/llava_next/lib/python3.10/site-packages/pydantic-2.9.2.dist-info/licenses/LICENSE
@@ -0,0 +1,21 @@
+The MIT License (MIT)
+
+Copyright (c) 2017 to present Pydantic Services Inc. and individual contributors.
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
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+size 35123345
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diff --git a/parrot/lib/python3.10/site-packages/sympy/physics/continuum_mechanics/cable.py b/parrot/lib/python3.10/site-packages/sympy/physics/continuum_mechanics/cable.py
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--- /dev/null
+++ b/parrot/lib/python3.10/site-packages/sympy/physics/continuum_mechanics/cable.py
@@ -0,0 +1,587 @@
+"""
+This module can be used to solve problems related
+to 2D Cables.
+"""
+
+from sympy.core.sympify import sympify
+from sympy.core.symbol import Symbol
+from sympy import sin, cos, pi, atan, diff
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.solvers.solveset import linsolve
+from sympy.matrices import Matrix
+
+
+class Cable:
+    """
+    Cables are structures in engineering that support
+    the applied transverse loads through the tensile
+    resistance developed in its members.
+
+    Cables are widely used in suspension bridges, tension
+    leg offshore platforms, transmission lines, and find
+    use in several other engineering applications.
+
+    Examples
+    ========
+    A cable is supported at (0, 10) and (10, 10). Two point loads
+    acting vertically downwards act on the cable, one with magnitude 3 kN
+    and acting 2 meters from the left support and 3 meters below it, while
+    the other with magnitude 2 kN is 6 meters from the left support and
+    6 meters below it.
+
+    >>> from sympy.physics.continuum_mechanics.cable import Cable
+    >>> c = Cable(('A', 0, 10), ('B', 10, 10))
+    >>> c.apply_load(-1, ('P', 2, 7, 3, 270))
+    >>> c.apply_load(-1, ('Q', 6, 4, 2, 270))
+    >>> c.loads
+    {'distributed': {}, 'point_load': {'P': [3, 270], 'Q': [2, 270]}}
+    >>> c.loads_position
+    {'P': [2, 7], 'Q': [6, 4]}
+    """
+    def __init__(self, support_1, support_2):
+        """
+        Initializes the class.
+
+        Parameters
+        ==========
+
+        support_1 and support_2 are tuples of the form
+        (label, x, y), where
+
+        label : String or symbol
+            The label of the support
+
+        x : Sympifyable
+            The x coordinate of the position of the support
+
+        y : Sympifyable
+            The y coordinate of the position of the support
+        """
+        self._left_support = []
+        self._right_support = []
+        self._supports = {}
+        self._support_labels = []
+        self._loads = {"distributed": {}, "point_load": {}}
+        self._loads_position = {}
+        self._length = 0
+        self._reaction_loads = {}
+        self._tension = {}
+        self._lowest_x_global = sympify(0)
+
+        if support_1[0] == support_2[0]:
+            raise ValueError("Supports can not have the same label")
+
+        elif support_1[1] == support_2[1]:
+            raise ValueError("Supports can not be at the same location")
+
+        x1 = sympify(support_1[1])
+        y1 = sympify(support_1[2])
+        self._supports[support_1[0]] = [x1, y1]
+
+        x2 = sympify(support_2[1])
+        y2 = sympify(support_2[2])
+        self._supports[support_2[0]] = [x2, y2]
+
+        if support_1[1] < support_2[1]:
+            self._left_support.append(x1)
+            self._left_support.append(y1)
+            self._right_support.append(x2)
+            self._right_support.append(y2)
+            self._support_labels.append(support_1[0])
+            self._support_labels.append(support_2[0])
+
+        else:
+            self._left_support.append(x2)
+            self._left_support.append(y2)
+            self._right_support.append(x1)
+            self._right_support.append(y1)
+            self._support_labels.append(support_2[0])
+            self._support_labels.append(support_1[0])
+
+        for i in self._support_labels:
+            self._reaction_loads[Symbol("R_"+ i +"_x")] = 0
+            self._reaction_loads[Symbol("R_"+ i +"_y")] = 0
+
+    @property
+    def supports(self):
+        """
+        Returns the supports of the cable along with their
+        positions.
+        """
+        return self._supports
+
+    @property
+    def left_support(self):
+        """
+        Returns the position of the left support.
+        """
+        return self._left_support
+
+    @property
+    def right_support(self):
+        """
+        Returns the position of the right support.
+        """
+        return self._right_support
+
+    @property
+    def loads(self):
+        """
+        Returns the magnitude and direction of the loads
+        acting on the cable.
+        """
+        return self._loads
+
+    @property
+    def loads_position(self):
+        """
+        Returns the position of the point loads acting on the
+        cable.
+        """
+        return self._loads_position
+
+    @property
+    def length(self):
+        """
+        Returns the length of the cable.
+        """
+        return self._length
+
+    @property
+    def reaction_loads(self):
+        """
+        Returns the reaction forces at the supports, which are
+        initialized to 0.
+        """
+        return self._reaction_loads
+
+    @property
+    def tension(self):
+        """
+        Returns the tension developed in the cable due to the loads
+        applied.
+        """
+        return self._tension
+
+    def tension_at(self, x):
+        """
+        Returns the tension at a given value of x developed due to
+        distributed load.
+        """
+        if 'distributed' not in self._tension.keys():
+            raise ValueError("No distributed load added or solve method not called")
+
+        if x > self._right_support[0] or x < self._left_support[0]:
+            raise ValueError("The value of x should be between the two supports")
+
+        A = self._tension['distributed']
+        X = Symbol('X')
+
+        return A.subs({X:(x-self._lowest_x_global)})
+
+    def apply_length(self, length):
+        """
+        This method specifies the length of the cable
+
+        Parameters
+        ==========
+
+        length : Sympifyable
+            The length of the cable
+
+        Examples
+        ========
+
+        >>> from sympy.physics.continuum_mechanics.cable import Cable
+        >>> c = Cable(('A', 0, 10), ('B', 10, 10))
+        >>> c.apply_length(20)
+        >>> c.length
+        20
+        """
+        dist = ((self._left_support[0] - self._right_support[0])**2
+                - (self._left_support[1] - self._right_support[1])**2)**(1/2)
+
+        if length < dist:
+            raise ValueError("length should not be less than the distance between the supports")
+
+        self._length = length
+
+    def change_support(self, label, new_support):
+        """
+        This method changes the mentioned support with a new support.
+
+        Parameters
+        ==========
+        label: String or symbol
+            The label of the support to be changed
+
+        new_support: Tuple of the form (new_label, x, y)
+            new_label: String or symbol
+                The label of the new support
+
+            x: Sympifyable
+                The x-coordinate of the position of the new support.
+
+            y: Sympifyable
+                The y-coordinate of the position of the new support.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.continuum_mechanics.cable import Cable
+        >>> c = Cable(('A', 0, 10), ('B', 10, 10))
+        >>> c.supports
+        {'A': [0, 10], 'B': [10, 10]}
+        >>> c.change_support('B', ('C', 5, 6))
+        >>> c.supports
+        {'A': [0, 10], 'C': [5, 6]}
+        """
+        if label not in self._supports:
+            raise ValueError("No support exists with the given label")
+
+        i = self._support_labels.index(label)
+        rem_label = self._support_labels[(i+1)%2]
+        x1 = self._supports[rem_label][0]
+        y1 = self._supports[rem_label][1]
+
+        x = sympify(new_support[1])
+        y = sympify(new_support[2])
+
+        for l in self._loads_position:
+            if l[0] >= max(x, x1) or l[0] <= min(x, x1):
+                raise ValueError("The change in support will throw an existing load out of range")
+
+        self._supports.pop(label)
+        self._left_support.clear()
+        self._right_support.clear()
+        self._reaction_loads.clear()
+        self._support_labels.remove(label)
+
+        self._supports[new_support[0]] = [x, y]
+
+        if x1 < x:
+            self._left_support.append(x1)
+            self._left_support.append(y1)
+            self._right_support.append(x)
+            self._right_support.append(y)
+            self._support_labels.append(new_support[0])
+
+        else:
+            self._left_support.append(x)
+            self._left_support.append(y)
+            self._right_support.append(x1)
+            self._right_support.append(y1)
+            self._support_labels.insert(0, new_support[0])
+
+        for i in self._support_labels:
+            self._reaction_loads[Symbol("R_"+ i +"_x")] = 0
+            self._reaction_loads[Symbol("R_"+ i +"_y")] = 0
+
+    def apply_load(self, order, load):
+        """
+        This method adds load to the cable.
+
+        Parameters
+        ==========
+
+        order : Integer
+            The order of the applied load.
+
+                - For point loads, order = -1
+                - For distributed load, order = 0
+
+        load : tuple
+
+            * For point loads, load is of the form (label, x, y, magnitude, direction), where:
+
+            label : String or symbol
+                The label of the load
+
+            x : Sympifyable
+                The x coordinate of the position of the load
+
+            y : Sympifyable
+                The y coordinate of the position of the load
+
+            magnitude : Sympifyable
+                The magnitude of the load. It must always be positive
+
+            direction : Sympifyable
+                The angle, in degrees, that the load vector makes with the horizontal
+                in the counter-clockwise direction. It takes the values 0 to 360,
+                inclusive.
+
+
+            * For uniformly distributed load, load is of the form (label, magnitude)
+
+            label : String or symbol
+                The label of the load
+
+            magnitude : Sympifyable
+                The magnitude of the load. It must always be positive
+
+        Examples
+        ========
+
+        For a point load of magnitude 12 units inclined at 30 degrees with the horizontal:
+
+        >>> from sympy.physics.continuum_mechanics.cable import Cable
+        >>> c = Cable(('A', 0, 10), ('B', 10, 10))
+        >>> c.apply_load(-1, ('Z', 5, 5, 12, 30))
+        >>> c.loads
+        {'distributed': {}, 'point_load': {'Z': [12, 30]}}
+        >>> c.loads_position
+        {'Z': [5, 5]}
+
+
+        For a uniformly distributed load of magnitude 9 units:
+
+        >>> from sympy.physics.continuum_mechanics.cable import Cable
+        >>> c = Cable(('A', 0, 10), ('B', 10, 10))
+        >>> c.apply_load(0, ('X', 9))
+        >>> c.loads
+        {'distributed': {'X': 9}, 'point_load': {}}
+        """
+        if order == -1:
+            if len(self._loads["distributed"]) != 0:
+                raise ValueError("Distributed load already exists")
+
+            label = load[0]
+            if label in self._loads["point_load"]:
+                raise ValueError("Label already exists")
+
+            x = sympify(load[1])
+            y = sympify(load[2])
+
+            if x > self._right_support[0] or x < self._left_support[0]:
+                raise ValueError("The load should be positioned between the supports")
+
+            magnitude = sympify(load[3])
+            direction = sympify(load[4])
+
+            self._loads["point_load"][label] = [magnitude, direction]
+            self._loads_position[label] = [x, y]
+
+        elif order == 0:
+            if len(self._loads_position) != 0:
+                raise ValueError("Point load(s) already exist")
+
+            label = load[0]
+            if label in self._loads["distributed"]:
+                raise ValueError("Label already exists")
+
+            magnitude = sympify(load[1])
+
+            self._loads["distributed"][label] = magnitude
+
+        else:
+            raise ValueError("Order should be either -1 or 0")
+
+    def remove_loads(self, *args):
+        """
+        This methods removes the specified loads.
+
+        Parameters
+        ==========
+        This input takes multiple label(s) as input
+        label(s): String or symbol
+            The label(s) of the loads to be removed.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.continuum_mechanics.cable import Cable
+        >>> c = Cable(('A', 0, 10), ('B', 10, 10))
+        >>> c.apply_load(-1, ('Z', 5, 5, 12, 30))
+        >>> c.loads
+        {'distributed': {}, 'point_load': {'Z': [12, 30]}}
+        >>> c.remove_loads('Z')
+        >>> c.loads
+        {'distributed': {}, 'point_load': {}}
+        """
+        for i in args:
+            if len(self._loads_position) == 0:
+                if i not in self._loads['distributed']:
+                    raise ValueError("Error removing load " + i + ": no such load exists")
+
+                else:
+                    self._loads['disrtibuted'].pop(i)
+
+            else:
+                if i not in self._loads['point_load']:
+                    raise ValueError("Error removing load " + i + ": no such load exists")
+
+                else:
+                    self._loads['point_load'].pop(i)
+                    self._loads_position.pop(i)
+
+    def solve(self, *args):
+        """
+        This method solves for the reaction forces at the supports, the tension developed in
+        the cable, and updates the length of the cable.
+
+        Parameters
+        ==========
+        This method requires no input when solving for point loads
+        For distributed load, the x and y coordinates of the lowest point of the cable are
+        required as
+
+        x: Sympifyable
+            The x coordinate of the lowest point
+
+        y: Sympifyable
+            The y coordinate of the lowest point
+
+        Examples
+        ========
+        For point loads,
+
+        >>> from sympy.physics.continuum_mechanics.cable import Cable
+        >>> c = Cable(("A", 0, 10), ("B", 10, 10))
+        >>> c.apply_load(-1, ('Z', 2, 7.26, 3, 270))
+        >>> c.apply_load(-1, ('X', 4, 6, 8, 270))
+        >>> c.solve()
+        >>> c.tension
+        {A_Z: 8.91403453669861, X_B: 19*sqrt(13)/10, Z_X: 4.79150773600774}
+        >>> c.reaction_loads
+        {R_A_x: -5.25547445255474, R_A_y: 7.2, R_B_x: 5.25547445255474, R_B_y: 3.8}
+        >>> c.length
+        5.7560958484519 + 2*sqrt(13)
+
+        For distributed load,
+
+        >>> from sympy.physics.continuum_mechanics.cable import Cable
+        >>> c=Cable(("A", 0, 40),("B", 100, 20))
+        >>> c.apply_load(0, ("X", 850))
+        >>> c.solve(58.58, 0)
+        >>> c.tension
+        {'distributed': 36456.8485*sqrt(0.000543529004799705*(X + 0.00135624381275735)**2 + 1)}
+        >>> c.tension_at(0)
+        61709.0363315913
+        >>> c.reaction_loads
+        {R_A_x: 36456.8485, R_A_y: -49788.5866682485, R_B_x: 44389.8401587246, R_B_y: 42866.621696333}
+        """
+
+        if len(self._loads_position) != 0:
+            sorted_position = sorted(self._loads_position.items(), key = lambda item : item[1][0])
+
+            sorted_position.append(self._support_labels[1])
+            sorted_position.insert(0, self._support_labels[0])
+
+            self._tension.clear()
+            moment_sum_from_left_support = 0
+            moment_sum_from_right_support = 0
+            F_x = 0
+            F_y = 0
+            self._length = 0
+
+            for i in range(1, len(sorted_position)-1):
+                if i == 1:
+                    self._length+=sqrt((self._left_support[0] - self._loads_position[sorted_position[i][0]][0])**2 + (self._left_support[1] - self._loads_position[sorted_position[i][0]][1])**2)
+
+                else:
+                    self._length+=sqrt((self._loads_position[sorted_position[i-1][0]][0] - self._loads_position[sorted_position[i][0]][0])**2 + (self._loads_position[sorted_position[i-1][0]][1] - self._loads_position[sorted_position[i][0]][1])**2)
+
+                if i == len(sorted_position)-2:
+                    self._length+=sqrt((self._right_support[0] - self._loads_position[sorted_position[i][0]][0])**2 + (self._right_support[1] - self._loads_position[sorted_position[i][0]][1])**2)
+
+                moment_sum_from_left_support += self._loads['point_load'][sorted_position[i][0]][0] * cos(pi * self._loads['point_load'][sorted_position[i][0]][1] / 180) * abs(self._left_support[1] - self._loads_position[sorted_position[i][0]][1])
+                moment_sum_from_left_support += self._loads['point_load'][sorted_position[i][0]][0] * sin(pi * self._loads['point_load'][sorted_position[i][0]][1] / 180) * abs(self._left_support[0] - self._loads_position[sorted_position[i][0]][0])
+
+                F_x += self._loads['point_load'][sorted_position[i][0]][0] * cos(pi * self._loads['point_load'][sorted_position[i][0]][1] / 180)
+                F_y += self._loads['point_load'][sorted_position[i][0]][0] * sin(pi * self._loads['point_load'][sorted_position[i][0]][1] / 180)
+
+                label = Symbol(sorted_position[i][0]+"_"+sorted_position[i+1][0])
+                y2 = self._loads_position[sorted_position[i][0]][1]
+                x2 = self._loads_position[sorted_position[i][0]][0]
+                y1 = 0
+                x1 = 0
+
+                if i == len(sorted_position)-2:
+                    x1 = self._right_support[0]
+                    y1 = self._right_support[1]
+
+                else:
+                    x1 = self._loads_position[sorted_position[i+1][0]][0]
+                    y1 = self._loads_position[sorted_position[i+1][0]][1]
+
+                angle_with_horizontal = atan((y1 - y2)/(x1 - x2))
+
+                tension = -(moment_sum_from_left_support)/(abs(self._left_support[1] - self._loads_position[sorted_position[i][0]][1])*cos(angle_with_horizontal) + abs(self._left_support[0] - self._loads_position[sorted_position[i][0]][0])*sin(angle_with_horizontal))
+                self._tension[label] = tension
+                moment_sum_from_right_support += self._loads['point_load'][sorted_position[i][0]][0] * cos(pi * self._loads['point_load'][sorted_position[i][0]][1] / 180) * abs(self._right_support[1] - self._loads_position[sorted_position[i][0]][1])
+                moment_sum_from_right_support += self._loads['point_load'][sorted_position[i][0]][0] * sin(pi * self._loads['point_load'][sorted_position[i][0]][1] / 180) * abs(self._right_support[0] - self._loads_position[sorted_position[i][0]][0])
+
+            label = Symbol(sorted_position[0][0]+"_"+sorted_position[1][0])
+            y2 = self._loads_position[sorted_position[1][0]][1]
+            x2 = self._loads_position[sorted_position[1][0]][0]
+            x1 = self._left_support[0]
+            y1 = self._left_support[1]
+
+            angle_with_horizontal = -atan((y2 - y1)/(x2 - x1))
+            tension = -(moment_sum_from_right_support)/(abs(self._right_support[1] - self._loads_position[sorted_position[1][0]][1])*cos(angle_with_horizontal) + abs(self._right_support[0] - self._loads_position[sorted_position[1][0]][0])*sin(angle_with_horizontal))
+            self._tension[label] = tension
+
+            angle_with_horizontal = pi/2 - angle_with_horizontal
+            label = self._support_labels[0]
+            self._reaction_loads[Symbol("R_"+label+"_x")] = -sin(angle_with_horizontal) * tension
+            F_x += -sin(angle_with_horizontal) * tension
+            self._reaction_loads[Symbol("R_"+label+"_y")] = cos(angle_with_horizontal) * tension
+            F_y += cos(angle_with_horizontal) * tension
+
+            label = self._support_labels[1]
+            self._reaction_loads[Symbol("R_"+label+"_x")] = -F_x
+            self._reaction_loads[Symbol("R_"+label+"_y")] = -F_y
+
+        elif len(self._loads['distributed']) != 0 :
+
+            if len(args) == 0:
+                raise ValueError("Provide the lowest point of the cable")
+
+            lowest_x = sympify(args[0])
+            lowest_y = sympify(args[1])
+            self._lowest_x_global = lowest_x
+
+            a = Symbol('a')
+            b = Symbol('b')
+            c = Symbol('c')
+            # augmented matrix form of linsolve
+
+            M = Matrix(
+                [[self._left_support[0]**2, self._left_support[0], 1, self._left_support[1]],
+                [self._right_support[0]**2, self._right_support[0], 1, self._right_support[1]],
+                [lowest_x**2, lowest_x, 1, lowest_y]  ]
+                       )
+
+            coefficient_solution = list(linsolve(M, (a, b, c)))
+
+            if len(coefficient_solution) == 0:
+                raise ValueError("The lowest point is inconsistent with the supports")
+
+            A = coefficient_solution[0][0]
+            B = coefficient_solution[0][1]
+            C = coefficient_solution[0][2]
+
+
+            # y = A*x**2 + B*x + C
+            # shifting origin to lowest point
+            X = Symbol('X')
+            Y = Symbol('Y')
+            Y = A*(X + lowest_x)**2 + B*(X + lowest_x) + C - lowest_y
+
+            temp_list = list(self._loads['distributed'].values())
+            applied_force = temp_list[0]
+
+            horizontal_force_constant = (applied_force * (self._right_support[0] - lowest_x)**2) / (2 * (self._right_support[1] - lowest_y))
+
+            self._tension.clear()
+            tangent_slope_to_curve = diff(Y, X)
+            self._tension['distributed'] = horizontal_force_constant / (cos(atan(tangent_slope_to_curve)))
+
+            label = self._support_labels[0]
+            self._reaction_loads[Symbol("R_"+label+"_x")] = self.tension_at(self._left_support[0]) * cos(atan(tangent_slope_to_curve.subs(X, self._left_support[0] - lowest_x)))
+            self._reaction_loads[Symbol("R_"+label+"_y")] = self.tension_at(self._left_support[0]) * sin(atan(tangent_slope_to_curve.subs(X, self._left_support[0] - lowest_x)))
+
+            label = self._support_labels[1]
+            self._reaction_loads[Symbol("R_"+label+"_x")] = self.tension_at(self._left_support[0]) * cos(atan(tangent_slope_to_curve.subs(X, self._right_support[0] - lowest_x)))
+            self._reaction_loads[Symbol("R_"+label+"_y")] = self.tension_at(self._left_support[0]) * sin(atan(tangent_slope_to_curve.subs(X, self._right_support[0] - lowest_x)))
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--- /dev/null
+++ b/parrot/lib/python3.10/site-packages/sympy/physics/continuum_mechanics/tests/test_beam.py
@@ -0,0 +1,802 @@
+from sympy.core.function import expand
+from sympy.core.numbers import (Rational, pi)
+from sympy.core.singleton import S
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.sets.sets import Interval
+from sympy.simplify.simplify import simplify
+from sympy.physics.continuum_mechanics.beam import Beam
+from sympy.functions import SingularityFunction, Piecewise, meijerg, Abs, log
+from sympy.testing.pytest import raises
+from sympy.physics.units import meter, newton, kilo, giga, milli
+from sympy.physics.continuum_mechanics.beam import Beam3D
+from sympy.geometry import Circle, Polygon, Point2D, Triangle
+from sympy.core.sympify import sympify
+
+x = Symbol('x')
+y = Symbol('y')
+R1, R2 = symbols('R1, R2')
+
+
+def test_Beam():
+    E = Symbol('E')
+    E_1 = Symbol('E_1')
+    I = Symbol('I')
+    I_1 = Symbol('I_1')
+    A = Symbol('A')
+
+    b = Beam(1, E, I)
+    assert b.length == 1
+    assert b.elastic_modulus == E
+    assert b.second_moment == I
+    assert b.variable == x
+
+    # Test the length setter
+    b.length = 4
+    assert b.length == 4
+
+    # Test the E setter
+    b.elastic_modulus = E_1
+    assert b.elastic_modulus == E_1
+
+    # Test the I setter
+    b.second_moment = I_1
+    assert b.second_moment is I_1
+
+    # Test the variable setter
+    b.variable = y
+    assert b.variable is y
+
+    # Test for all boundary conditions.
+    b.bc_deflection = [(0, 2)]
+    b.bc_slope = [(0, 1)]
+    assert b.boundary_conditions == {'deflection': [(0, 2)], 'slope': [(0, 1)]}
+
+    # Test for slope boundary condition method
+    b.bc_slope.extend([(4, 3), (5, 0)])
+    s_bcs = b.bc_slope
+    assert s_bcs == [(0, 1), (4, 3), (5, 0)]
+
+    # Test for deflection boundary condition method
+    b.bc_deflection.extend([(4, 3), (5, 0)])
+    d_bcs = b.bc_deflection
+    assert d_bcs == [(0, 2), (4, 3), (5, 0)]
+
+    # Test for updated boundary conditions
+    bcs_new = b.boundary_conditions
+    assert bcs_new == {
+        'deflection': [(0, 2), (4, 3), (5, 0)],
+        'slope': [(0, 1), (4, 3), (5, 0)]}
+
+    b1 = Beam(30, E, I)
+    b1.apply_load(-8, 0, -1)
+    b1.apply_load(R1, 10, -1)
+    b1.apply_load(R2, 30, -1)
+    b1.apply_load(120, 30, -2)
+    b1.bc_deflection = [(10, 0), (30, 0)]
+    b1.solve_for_reaction_loads(R1, R2)
+
+    # Test for finding reaction forces
+    p = b1.reaction_loads
+    q = {R1: 6, R2: 2}
+    assert p == q
+
+    # Test for load distribution function.
+    p = b1.load
+    q = -8*SingularityFunction(x, 0, -1) + 6*SingularityFunction(x, 10, -1) \
+    + 120*SingularityFunction(x, 30, -2) + 2*SingularityFunction(x, 30, -1)
+    assert p == q
+
+    # Test for shear force distribution function
+    p = b1.shear_force()
+    q = 8*SingularityFunction(x, 0, 0) - 6*SingularityFunction(x, 10, 0) \
+    - 120*SingularityFunction(x, 30, -1) - 2*SingularityFunction(x, 30, 0)
+    assert p == q
+
+    # Test for shear stress distribution function
+    p = b1.shear_stress()
+    q = (8*SingularityFunction(x, 0, 0) - 6*SingularityFunction(x, 10, 0) \
+    - 120*SingularityFunction(x, 30, -1) \
+    - 2*SingularityFunction(x, 30, 0))/A
+    assert p==q
+
+    # Test for bending moment distribution function
+    p = b1.bending_moment()
+    q = 8*SingularityFunction(x, 0, 1) - 6*SingularityFunction(x, 10, 1) \
+    - 120*SingularityFunction(x, 30, 0) - 2*SingularityFunction(x, 30, 1)
+    assert p == q
+
+    # Test for slope distribution function
+    p = b1.slope()
+    q = -4*SingularityFunction(x, 0, 2) + 3*SingularityFunction(x, 10, 2) \
+    + 120*SingularityFunction(x, 30, 1) + SingularityFunction(x, 30, 2) \
+    + Rational(4000, 3)
+    assert p == q/(E*I)
+
+    # Test for deflection distribution function
+    p = b1.deflection()
+    q = x*Rational(4000, 3) - 4*SingularityFunction(x, 0, 3)/3 \
+    + SingularityFunction(x, 10, 3) + 60*SingularityFunction(x, 30, 2) \
+    + SingularityFunction(x, 30, 3)/3 - 12000
+    assert p == q/(E*I)
+
+    # Test using symbols
+    l = Symbol('l')
+    w0 = Symbol('w0')
+    w2 = Symbol('w2')
+    a1 = Symbol('a1')
+    c = Symbol('c')
+    c1 = Symbol('c1')
+    d = Symbol('d')
+    e = Symbol('e')
+    f = Symbol('f')
+
+    b2 = Beam(l, E, I)
+
+    b2.apply_load(w0, a1, 1)
+    b2.apply_load(w2, c1, -1)
+
+    b2.bc_deflection = [(c, d)]
+    b2.bc_slope = [(e, f)]
+
+    # Test for load distribution function.
+    p = b2.load
+    q = w0*SingularityFunction(x, a1, 1) + w2*SingularityFunction(x, c1, -1)
+    assert p == q
+
+    # Test for shear force distribution function
+    p = b2.shear_force()
+    q = -w0*SingularityFunction(x, a1, 2)/2 \
+    - w2*SingularityFunction(x, c1, 0)
+    assert p == q
+
+    # Test for shear stress distribution function
+    p = b2.shear_stress()
+    q = (-w0*SingularityFunction(x, a1, 2)/2 \
+    - w2*SingularityFunction(x, c1, 0))/A
+    assert p == q
+
+    # Test for bending moment distribution function
+    p = b2.bending_moment()
+    q = -w0*SingularityFunction(x, a1, 3)/6 - w2*SingularityFunction(x, c1, 1)
+    assert p == q
+
+    # Test for slope distribution function
+    p = b2.slope()
+    q = (w0*SingularityFunction(x, a1, 4)/24 + w2*SingularityFunction(x, c1, 2)/2)/(E*I) + (E*I*f - w0*SingularityFunction(e, a1, 4)/24 - w2*SingularityFunction(e, c1, 2)/2)/(E*I)
+    assert expand(p) == expand(q)
+
+    # Test for deflection distribution function
+    p = b2.deflection()
+    q = x*(E*I*f - w0*SingularityFunction(e, a1, 4)/24 \
+    - w2*SingularityFunction(e, c1, 2)/2)/(E*I) \
+    + (w0*SingularityFunction(x, a1, 5)/120 \
+    + w2*SingularityFunction(x, c1, 3)/6)/(E*I) \
+    + (E*I*(-c*f + d) + c*w0*SingularityFunction(e, a1, 4)/24 \
+    + c*w2*SingularityFunction(e, c1, 2)/2 \
+    - w0*SingularityFunction(c, a1, 5)/120 \
+    - w2*SingularityFunction(c, c1, 3)/6)/(E*I)
+    assert simplify(p - q) == 0
+
+    b3 = Beam(9, E, I, 2)
+    b3.apply_load(value=-2, start=2, order=2, end=3)
+    b3.bc_slope.append((0, 2))
+    C3 = symbols('C3')
+    C4 = symbols('C4')
+
+    p = b3.load
+    q = -2*SingularityFunction(x, 2, 2) + 2*SingularityFunction(x, 3, 0) \
+    + 4*SingularityFunction(x, 3, 1) + 2*SingularityFunction(x, 3, 2)
+    assert p == q
+
+    p = b3.shear_force()
+    q = 2*SingularityFunction(x, 2, 3)/3 - 2*SingularityFunction(x, 3, 1) \
+    - 2*SingularityFunction(x, 3, 2) - 2*SingularityFunction(x, 3, 3)/3
+    assert p == q
+
+    p = b3.shear_stress()
+    q = SingularityFunction(x, 2, 3)/3 - 1*SingularityFunction(x, 3, 1) \
+    - 1*SingularityFunction(x, 3, 2) - 1*SingularityFunction(x, 3, 3)/3
+    assert p == q
+
+    p = b3.slope()
+    q = 2 - (SingularityFunction(x, 2, 5)/30 - SingularityFunction(x, 3, 3)/3 \
+    - SingularityFunction(x, 3, 4)/6 - SingularityFunction(x, 3, 5)/30)/(E*I)
+    assert p == q
+
+    p = b3.deflection()
+    q = 2*x - (SingularityFunction(x, 2, 6)/180 \
+    - SingularityFunction(x, 3, 4)/12 - SingularityFunction(x, 3, 5)/30 \
+    - SingularityFunction(x, 3, 6)/180)/(E*I)
+    assert p == q + C4
+
+    b4 = Beam(4, E, I, 3)
+    b4.apply_load(-3, 0, 0, end=3)
+
+    p = b4.load
+    q = -3*SingularityFunction(x, 0, 0) + 3*SingularityFunction(x, 3, 0)
+    assert p == q
+
+    p = b4.shear_force()
+    q = 3*SingularityFunction(x, 0, 1) \
+    - 3*SingularityFunction(x, 3, 1)
+    assert p == q
+
+    p = b4.shear_stress()
+    q = SingularityFunction(x, 0, 1) - SingularityFunction(x, 3, 1)
+    assert p == q
+
+    p = b4.slope()
+    q = -3*SingularityFunction(x, 0, 3)/6 + 3*SingularityFunction(x, 3, 3)/6
+    assert p == q/(E*I) + C3
+
+    p = b4.deflection()
+    q = -3*SingularityFunction(x, 0, 4)/24 + 3*SingularityFunction(x, 3, 4)/24
+    assert p == q/(E*I) + C3*x + C4
+
+    # can't use end with point loads
+    raises(ValueError, lambda: b4.apply_load(-3, 0, -1, end=3))
+    with raises(TypeError):
+        b4.variable = 1
+
+
+def test_insufficient_bconditions():
+    # Test cases when required number of boundary conditions
+    # are not provided to solve the integration constants.
+    L = symbols('L', positive=True)
+    E, I, P, a3, a4 = symbols('E I P a3 a4')
+
+    b = Beam(L, E, I, base_char='a')
+    b.apply_load(R2, L, -1)
+    b.apply_load(R1, 0, -1)
+    b.apply_load(-P, L/2, -1)
+    b.solve_for_reaction_loads(R1, R2)
+
+    p = b.slope()
+    q = P*SingularityFunction(x, 0, 2)/4 - P*SingularityFunction(x, L/2, 2)/2 + P*SingularityFunction(x, L, 2)/4
+    assert p == q/(E*I) + a3
+
+    p = b.deflection()
+    q = P*SingularityFunction(x, 0, 3)/12 - P*SingularityFunction(x, L/2, 3)/6 + P*SingularityFunction(x, L, 3)/12
+    assert p == q/(E*I) + a3*x + a4
+
+    b.bc_deflection = [(0, 0)]
+    p = b.deflection()
+    q = a3*x + P*SingularityFunction(x, 0, 3)/12 - P*SingularityFunction(x, L/2, 3)/6 + P*SingularityFunction(x, L, 3)/12
+    assert p == q/(E*I)
+
+    b.bc_deflection = [(0, 0), (L, 0)]
+    p = b.deflection()
+    q = -L**2*P*x/16 + P*SingularityFunction(x, 0, 3)/12 - P*SingularityFunction(x, L/2, 3)/6 + P*SingularityFunction(x, L, 3)/12
+    assert p == q/(E*I)
+
+
+def test_statically_indeterminate():
+    E = Symbol('E')
+    I = Symbol('I')
+    M1, M2 = symbols('M1, M2')
+    F = Symbol('F')
+    l = Symbol('l', positive=True)
+
+    b5 = Beam(l, E, I)
+    b5.bc_deflection = [(0, 0),(l, 0)]
+    b5.bc_slope = [(0, 0),(l, 0)]
+
+    b5.apply_load(R1, 0, -1)
+    b5.apply_load(M1, 0, -2)
+    b5.apply_load(R2, l, -1)
+    b5.apply_load(M2, l, -2)
+    b5.apply_load(-F, l/2, -1)
+
+    b5.solve_for_reaction_loads(R1, R2, M1, M2)
+    p = b5.reaction_loads
+    q = {R1: F/2, R2: F/2, M1: -F*l/8, M2: F*l/8}
+    assert p == q
+
+
+def test_beam_units():
+    E = Symbol('E')
+    I = Symbol('I')
+    R1, R2 = symbols('R1, R2')
+
+    kN = kilo*newton
+    gN = giga*newton
+
+    b = Beam(8*meter, 200*gN/meter**2, 400*1000000*(milli*meter)**4)
+    b.apply_load(5*kN, 2*meter, -1)
+    b.apply_load(R1, 0*meter, -1)
+    b.apply_load(R2, 8*meter, -1)
+    b.apply_load(10*kN/meter, 4*meter, 0, end=8*meter)
+    b.bc_deflection = [(0*meter, 0*meter), (8*meter, 0*meter)]
+    b.solve_for_reaction_loads(R1, R2)
+    assert b.reaction_loads == {R1: -13750*newton, R2: -31250*newton}
+
+    b = Beam(3*meter, E*newton/meter**2, I*meter**4)
+    b.apply_load(8*kN, 1*meter, -1)
+    b.apply_load(R1, 0*meter, -1)
+    b.apply_load(R2, 3*meter, -1)
+    b.apply_load(12*kN*meter, 2*meter, -2)
+    b.bc_deflection = [(0*meter, 0*meter), (3*meter, 0*meter)]
+    b.solve_for_reaction_loads(R1, R2)
+    assert b.reaction_loads == {R1: newton*Rational(-28000, 3), R2: newton*Rational(4000, 3)}
+    assert b.deflection().subs(x, 1*meter) == 62000*meter/(9*E*I)
+
+
+def test_variable_moment():
+    E = Symbol('E')
+    I = Symbol('I')
+
+    b = Beam(4, E, 2*(4 - x))
+    b.apply_load(20, 4, -1)
+    R, M = symbols('R, M')
+    b.apply_load(R, 0, -1)
+    b.apply_load(M, 0, -2)
+    b.bc_deflection = [(0, 0)]
+    b.bc_slope = [(0, 0)]
+    b.solve_for_reaction_loads(R, M)
+    assert b.slope().expand() == ((10*x*SingularityFunction(x, 0, 0)
+        - 10*(x - 4)*SingularityFunction(x, 4, 0))/E).expand()
+    assert b.deflection().expand() == ((5*x**2*SingularityFunction(x, 0, 0)
+        - 10*Piecewise((0, Abs(x)/4 < 1), (x**2*meijerg(((-1, 1), ()), ((), (-2, 0)), x/4), True))
+        + 40*SingularityFunction(x, 4, 1))/E).expand()
+
+    b = Beam(4, E - x, I)
+    b.apply_load(20, 4, -1)
+    R, M = symbols('R, M')
+    b.apply_load(R, 0, -1)
+    b.apply_load(M, 0, -2)
+    b.bc_deflection = [(0, 0)]
+    b.bc_slope = [(0, 0)]
+    b.solve_for_reaction_loads(R, M)
+    assert b.slope().expand() == ((-80*(-log(-E) + log(-E + x))*SingularityFunction(x, 0, 0)
+        + 80*(-log(-E + 4) + log(-E + x))*SingularityFunction(x, 4, 0) + 20*(-E*log(-E)
+        + E*log(-E + x) + x)*SingularityFunction(x, 0, 0) - 20*(-E*log(-E + 4) + E*log(-E + x)
+        + x - 4)*SingularityFunction(x, 4, 0))/I).expand()
+
+
+def test_composite_beam():
+    E = Symbol('E')
+    I = Symbol('I')
+    b1 = Beam(2, E, 1.5*I)
+    b2 = Beam(2, E, I)
+    b = b1.join(b2, "fixed")
+    b.apply_load(-20, 0, -1)
+    b.apply_load(80, 0, -2)
+    b.apply_load(20, 4, -1)
+    b.bc_slope = [(0, 0)]
+    b.bc_deflection = [(0, 0)]
+    assert b.length == 4
+    assert b.second_moment == Piecewise((1.5*I, x <= 2), (I, x <= 4))
+    assert b.slope().subs(x, 4) == 120.0/(E*I)
+    assert b.slope().subs(x, 2) == 80.0/(E*I)
+    assert int(b.deflection().subs(x, 4).args[0]) == -302  # Coefficient of 1/(E*I)
+
+    l = symbols('l', positive=True)
+    R1, M1, R2, R3, P = symbols('R1 M1 R2 R3 P')
+    b1 = Beam(2*l, E, I)
+    b2 = Beam(2*l, E, I)
+    b = b1.join(b2,"hinge")
+    b.apply_load(M1, 0, -2)
+    b.apply_load(R1, 0, -1)
+    b.apply_load(R2, l, -1)
+    b.apply_load(R3, 4*l, -1)
+    b.apply_load(P, 3*l, -1)
+    b.bc_slope = [(0, 0)]
+    b.bc_deflection = [(0, 0), (l, 0), (4*l, 0)]
+    b.solve_for_reaction_loads(M1, R1, R2, R3)
+    assert b.reaction_loads == {R3: -P/2, R2: P*Rational(-5, 4), M1: -P*l/4, R1: P*Rational(3, 4)}
+    assert b.slope().subs(x, 3*l) == -7*P*l**2/(48*E*I)
+    assert b.deflection().subs(x, 2*l) == 7*P*l**3/(24*E*I)
+    assert b.deflection().subs(x, 3*l) == 5*P*l**3/(16*E*I)
+
+    # When beams having same second moment are joined.
+    b1 = Beam(2, 500, 10)
+    b2 = Beam(2, 500, 10)
+    b = b1.join(b2, "fixed")
+    b.apply_load(M1, 0, -2)
+    b.apply_load(R1, 0, -1)
+    b.apply_load(R2, 1, -1)
+    b.apply_load(R3, 4, -1)
+    b.apply_load(10, 3, -1)
+    b.bc_slope = [(0, 0)]
+    b.bc_deflection = [(0, 0), (1, 0), (4, 0)]
+    b.solve_for_reaction_loads(M1, R1, R2, R3)
+    assert b.slope() == -2*SingularityFunction(x, 0, 1)/5625 + SingularityFunction(x, 0, 2)/1875\
+                - 133*SingularityFunction(x, 1, 2)/135000 + SingularityFunction(x, 3, 2)/1000\
+                - 37*SingularityFunction(x, 4, 2)/67500
+    assert b.deflection() == -SingularityFunction(x, 0, 2)/5625 + SingularityFunction(x, 0, 3)/5625\
+                    - 133*SingularityFunction(x, 1, 3)/405000 + SingularityFunction(x, 3, 3)/3000\
+                    - 37*SingularityFunction(x, 4, 3)/202500
+
+
+def test_point_cflexure():
+    E = Symbol('E')
+    I = Symbol('I')
+    b = Beam(10, E, I)
+    b.apply_load(-4, 0, -1)
+    b.apply_load(-46, 6, -1)
+    b.apply_load(10, 2, -1)
+    b.apply_load(20, 4, -1)
+    b.apply_load(3, 6, 0)
+    assert b.point_cflexure() == [Rational(10, 3)]
+
+
+def test_remove_load():
+    E = Symbol('E')
+    I = Symbol('I')
+    b = Beam(4, E, I)
+
+    try:
+        b.remove_load(2, 1, -1)
+    # As no load is applied on beam, ValueError should be returned.
+    except ValueError:
+        assert True
+    else:
+        assert False
+
+    b.apply_load(-3, 0, -2)
+    b.apply_load(4, 2, -1)
+    b.apply_load(-2, 2, 2, end = 3)
+    b.remove_load(-2, 2, 2, end = 3)
+    assert b.load == -3*SingularityFunction(x, 0, -2) + 4*SingularityFunction(x, 2, -1)
+    assert b.applied_loads == [(-3, 0, -2, None), (4, 2, -1, None)]
+
+    try:
+        b.remove_load(1, 2, -1)
+    # As load of this magnitude was never applied at
+    # this position, method should return a ValueError.
+    except ValueError:
+        assert True
+    else:
+        assert False
+
+    b.remove_load(-3, 0, -2)
+    b.remove_load(4, 2, -1)
+    assert b.load == 0
+    assert b.applied_loads == []
+
+
+def test_apply_support():
+    E = Symbol('E')
+    I = Symbol('I')
+
+    b = Beam(4, E, I)
+    b.apply_support(0, "cantilever")
+    b.apply_load(20, 4, -1)
+    M_0, R_0 = symbols('M_0, R_0')
+    b.solve_for_reaction_loads(R_0, M_0)
+    assert simplify(b.slope()) == simplify((80*SingularityFunction(x, 0, 1) - 10*SingularityFunction(x, 0, 2)
+                + 10*SingularityFunction(x, 4, 2))/(E*I))
+    assert simplify(b.deflection()) == simplify((40*SingularityFunction(x, 0, 2) - 10*SingularityFunction(x, 0, 3)/3
+                + 10*SingularityFunction(x, 4, 3)/3)/(E*I))
+
+    b = Beam(30, E, I)
+    p0 = b.apply_support(10, "pin")
+    p1 = b.apply_support(30, "roller")
+    b.apply_load(-8, 0, -1)
+    b.apply_load(120, 30, -2)
+    b.solve_for_reaction_loads(p0, p1)
+    assert b.slope() == (-4*SingularityFunction(x, 0, 2) + 3*SingularityFunction(x, 10, 2)
+            + 120*SingularityFunction(x, 30, 1) + SingularityFunction(x, 30, 2) + Rational(4000, 3))/(E*I)
+    assert b.deflection() == (x*Rational(4000, 3) - 4*SingularityFunction(x, 0, 3)/3 + SingularityFunction(x, 10, 3)
+            + 60*SingularityFunction(x, 30, 2) + SingularityFunction(x, 30, 3)/3 - 12000)/(E*I)
+    R_10 = Symbol('R_10')
+    R_30 = Symbol('R_30')
+    assert p0 == R_10
+    assert b.reaction_loads == {R_10: 6, R_30: 2}
+    assert b.reaction_loads[p0] == 6
+
+    b = Beam(8, E, I)
+    p0, m0 = b.apply_support(0, "fixed")
+    p1 = b.apply_support(8, "roller")
+    b.apply_load(-5, 0, 0, 8)
+    b.solve_for_reaction_loads(p0, m0, p1)
+    R_0 = Symbol('R_0')
+    M_0 = Symbol('M_0')
+    R_8 = Symbol('R_8')
+    assert p0 == R_0
+    assert m0 == M_0
+    assert p1 == R_8
+    assert b.reaction_loads == {R_0: 25, M_0: -40, R_8: 15}
+    assert b.reaction_loads[m0] == -40
+
+    P = Symbol('P', positive=True)
+    L = Symbol('L', positive=True)
+    b = Beam(L, E, I)
+    b.apply_support(0, type='fixed')
+    b.apply_support(L, type='fixed')
+    b.apply_load(-P, L/2, -1)
+    R_0, R_L, M_0, M_L = symbols('R_0, R_L, M_0, M_L')
+    b.solve_for_reaction_loads(R_0, R_L, M_0, M_L)
+    assert b.reaction_loads == {R_0: P/2, R_L: P/2, M_0: -L*P/8, M_L: L*P/8}
+
+
+def test_max_shear_force():
+    E = Symbol('E')
+    I = Symbol('I')
+
+    b = Beam(3, E, I)
+    R, M = symbols('R, M')
+    b.apply_load(R, 0, -1)
+    b.apply_load(M, 0, -2)
+    b.apply_load(2, 3, -1)
+    b.apply_load(4, 2, -1)
+    b.apply_load(2, 2, 0, end=3)
+    b.solve_for_reaction_loads(R, M)
+    assert b.max_shear_force() == (Interval(0, 2), 8)
+
+    l = symbols('l', positive=True)
+    P = Symbol('P')
+    b = Beam(l, E, I)
+    R1, R2 = symbols('R1, R2')
+    b.apply_load(R1, 0, -1)
+    b.apply_load(R2, l, -1)
+    b.apply_load(P, 0, 0, end=l)
+    b.solve_for_reaction_loads(R1, R2)
+    max_shear = b.max_shear_force()
+    assert max_shear[0] == 0
+    assert simplify(max_shear[1] - (l*Abs(P)/2)) == 0
+
+
+def test_max_bmoment():
+    E = Symbol('E')
+    I = Symbol('I')
+    l, P = symbols('l, P', positive=True)
+
+    b = Beam(l, E, I)
+    R1, R2 = symbols('R1, R2')
+    b.apply_load(R1, 0, -1)
+    b.apply_load(R2, l, -1)
+    b.apply_load(P, l/2, -1)
+    b.solve_for_reaction_loads(R1, R2)
+    b.reaction_loads
+    assert b.max_bmoment() == (l/2, P*l/4)
+
+    b = Beam(l, E, I)
+    R1, R2 = symbols('R1, R2')
+    b.apply_load(R1, 0, -1)
+    b.apply_load(R2, l, -1)
+    b.apply_load(P, 0, 0, end=l)
+    b.solve_for_reaction_loads(R1, R2)
+    assert b.max_bmoment() == (l/2, P*l**2/8)
+
+
+def test_max_deflection():
+    E, I, l, F = symbols('E, I, l, F', positive=True)
+    b = Beam(l, E, I)
+    b.bc_deflection = [(0, 0),(l, 0)]
+    b.bc_slope = [(0, 0),(l, 0)]
+    b.apply_load(F/2, 0, -1)
+    b.apply_load(-F*l/8, 0, -2)
+    b.apply_load(F/2, l, -1)
+    b.apply_load(F*l/8, l, -2)
+    b.apply_load(-F, l/2, -1)
+    assert b.max_deflection() == (l/2, F*l**3/(192*E*I))
+
+
+def test_Beam3D():
+    l, E, G, I, A = symbols('l, E, G, I, A')
+    R1, R2, R3, R4 = symbols('R1, R2, R3, R4')
+
+    b = Beam3D(l, E, G, I, A)
+    m, q = symbols('m, q')
+    b.apply_load(q, 0, 0, dir="y")
+    b.apply_moment_load(m, 0, 0, dir="z")
+    b.bc_slope = [(0, [0, 0, 0]), (l, [0, 0, 0])]
+    b.bc_deflection = [(0, [0, 0, 0]), (l, [0, 0, 0])]
+    b.solve_slope_deflection()
+
+    assert b.polar_moment() == 2*I
+    assert b.shear_force() == [0, -q*x, 0]
+    assert b.shear_stress() == [0, -q*x/A, 0]
+    assert b.axial_stress() == 0
+    assert b.bending_moment() == [0, 0, -m*x + q*x**2/2]
+    expected_deflection = (x*(A*G*q*x**3/4 + A*G*x**2*(-l*(A*G*l*(l*q - 2*m) +
+        12*E*I*q)/(A*G*l**2 + 12*E*I)/2 - m) + 3*E*I*l*(A*G*l*(l*q - 2*m) +
+        12*E*I*q)/(A*G*l**2 + 12*E*I) + x*(-A*G*l**2*q/2 +
+        3*A*G*l**2*(A*G*l*(l*q - 2*m) + 12*E*I*q)/(A*G*l**2 + 12*E*I)/4 +
+        A*G*l*m*Rational(3, 2) - 3*E*I*q))/(6*A*E*G*I))
+    dx, dy, dz = b.deflection()
+    assert dx == dz == 0
+    assert simplify(dy - expected_deflection) == 0
+
+    b2 = Beam3D(30, E, G, I, A, x)
+    b2.apply_load(50, start=0, order=0, dir="y")
+    b2.bc_deflection = [(0, [0, 0, 0]), (30, [0, 0, 0])]
+    b2.apply_load(R1, start=0, order=-1, dir="y")
+    b2.apply_load(R2, start=30, order=-1, dir="y")
+    b2.solve_for_reaction_loads(R1, R2)
+    assert b2.reaction_loads == {R1: -750, R2: -750}
+
+    b2.solve_slope_deflection()
+    assert b2.slope() == [0, 0, 25*x**3/(3*E*I) - 375*x**2/(E*I) + 3750*x/(E*I)]
+    expected_deflection = 25*x**4/(12*E*I) - 125*x**3/(E*I) + 1875*x**2/(E*I) - \
+        25*x**2/(A*G) + 750*x/(A*G)
+    dx, dy, dz = b2.deflection()
+    assert dx == dz == 0
+    assert dy == expected_deflection
+
+    # Test for solve_for_reaction_loads
+    b3 = Beam3D(30, E, G, I, A, x)
+    b3.apply_load(8, start=0, order=0, dir="y")
+    b3.apply_load(9*x, start=0, order=0, dir="z")
+    b3.apply_load(R1, start=0, order=-1, dir="y")
+    b3.apply_load(R2, start=30, order=-1, dir="y")
+    b3.apply_load(R3, start=0, order=-1, dir="z")
+    b3.apply_load(R4, start=30, order=-1, dir="z")
+    b3.solve_for_reaction_loads(R1, R2, R3, R4)
+    assert b3.reaction_loads == {R1: -120, R2: -120, R3: -1350, R4: -2700}
+
+
+def test_polar_moment_Beam3D():
+    l, E, G, A, I1, I2 = symbols('l, E, G, A, I1, I2')
+    I = [I1, I2]
+
+    b = Beam3D(l, E, G, I, A)
+    assert b.polar_moment() == I1 + I2
+
+
+def test_parabolic_loads():
+
+    E, I, L = symbols('E, I, L', positive=True, real=True)
+    R, M, P = symbols('R, M, P', real=True)
+
+    # cantilever beam fixed at x=0 and parabolic distributed loading across
+    # length of beam
+    beam = Beam(L, E, I)
+
+    beam.bc_deflection.append((0, 0))
+    beam.bc_slope.append((0, 0))
+    beam.apply_load(R, 0, -1)
+    beam.apply_load(M, 0, -2)
+
+    # parabolic load
+    beam.apply_load(1, 0, 2)
+
+    beam.solve_for_reaction_loads(R, M)
+
+    assert beam.reaction_loads[R] == -L**3/3
+
+    # cantilever beam fixed at x=0 and parabolic distributed loading across
+    # first half of beam
+    beam = Beam(2*L, E, I)
+
+    beam.bc_deflection.append((0, 0))
+    beam.bc_slope.append((0, 0))
+    beam.apply_load(R, 0, -1)
+    beam.apply_load(M, 0, -2)
+
+    # parabolic load from x=0 to x=L
+    beam.apply_load(1, 0, 2, end=L)
+
+    beam.solve_for_reaction_loads(R, M)
+
+    # result should be the same as the prior example
+    assert beam.reaction_loads[R] == -L**3/3
+
+    # check constant load
+    beam = Beam(2*L, E, I)
+    beam.apply_load(P, 0, 0, end=L)
+    loading = beam.load.xreplace({L: 10, E: 20, I: 30, P: 40})
+    assert loading.xreplace({x: 5}) == 40
+    assert loading.xreplace({x: 15}) == 0
+
+    # check ramp load
+    beam = Beam(2*L, E, I)
+    beam.apply_load(P, 0, 1, end=L)
+    assert beam.load == (P*SingularityFunction(x, 0, 1) -
+                         P*SingularityFunction(x, L, 1) -
+                         P*L*SingularityFunction(x, L, 0))
+
+    # check higher order load: x**8 load from x=0 to x=L
+    beam = Beam(2*L, E, I)
+    beam.apply_load(P, 0, 8, end=L)
+    loading = beam.load.xreplace({L: 10, E: 20, I: 30, P: 40})
+    assert loading.xreplace({x: 5}) == 40*5**8
+    assert loading.xreplace({x: 15}) == 0
+
+
+def test_cross_section():
+    I = Symbol('I')
+    l = Symbol('l')
+    E = Symbol('E')
+    C3, C4 = symbols('C3, C4')
+    a, c, g, h, r, n = symbols('a, c, g, h, r, n')
+
+    # test for second_moment and cross_section setter
+    b0 = Beam(l, E, I)
+    assert b0.second_moment == I
+    assert b0.cross_section == None
+    b0.cross_section = Circle((0, 0), 5)
+    assert b0.second_moment == pi*Rational(625, 4)
+    assert b0.cross_section == Circle((0, 0), 5)
+    b0.second_moment = 2*n - 6
+    assert b0.second_moment == 2*n-6
+    assert b0.cross_section == None
+    with raises(ValueError):
+        b0.second_moment = Circle((0, 0), 5)
+
+    # beam with a circular cross-section
+    b1 = Beam(50, E, Circle((0, 0), r))
+    assert b1.cross_section == Circle((0, 0), r)
+    assert b1.second_moment == pi*r*Abs(r)**3/4
+
+    b1.apply_load(-10, 0, -1)
+    b1.apply_load(R1, 5, -1)
+    b1.apply_load(R2, 50, -1)
+    b1.apply_load(90, 45, -2)
+    b1.solve_for_reaction_loads(R1, R2)
+    assert b1.load == (-10*SingularityFunction(x, 0, -1) + 82*SingularityFunction(x, 5, -1)/S(9)
+                         + 90*SingularityFunction(x, 45, -2) + 8*SingularityFunction(x, 50, -1)/9)
+    assert b1.bending_moment() == (10*SingularityFunction(x, 0, 1) - 82*SingularityFunction(x, 5, 1)/9
+                                     - 90*SingularityFunction(x, 45, 0) - 8*SingularityFunction(x, 50, 1)/9)
+    q = (-5*SingularityFunction(x, 0, 2) + 41*SingularityFunction(x, 5, 2)/S(9)
+           + 90*SingularityFunction(x, 45, 1) + 4*SingularityFunction(x, 50, 2)/S(9))/(pi*E*r*Abs(r)**3)
+    assert b1.slope() == C3 + 4*q
+    q = (-5*SingularityFunction(x, 0, 3)/3 + 41*SingularityFunction(x, 5, 3)/27 + 45*SingularityFunction(x, 45, 2)
+           + 4*SingularityFunction(x, 50, 3)/27)/(pi*E*r*Abs(r)**3)
+    assert b1.deflection() == C3*x + C4 + 4*q
+
+    # beam with a recatangular cross-section
+    b2 = Beam(20, E, Polygon((0, 0), (a, 0), (a, c), (0, c)))
+    assert b2.cross_section == Polygon((0, 0), (a, 0), (a, c), (0, c))
+    assert b2.second_moment == a*c**3/12
+    # beam with a triangular cross-section
+    b3 = Beam(15, E, Triangle((0, 0), (g, 0), (g/2, h)))
+    assert b3.cross_section == Triangle(Point2D(0, 0), Point2D(g, 0), Point2D(g/2, h))
+    assert b3.second_moment == g*h**3/36
+
+    # composite beam
+    b = b2.join(b3, "fixed")
+    b.apply_load(-30, 0, -1)
+    b.apply_load(65, 0, -2)
+    b.apply_load(40, 0, -1)
+    b.bc_slope = [(0, 0)]
+    b.bc_deflection = [(0, 0)]
+
+    assert b.second_moment == Piecewise((a*c**3/12, x <= 20), (g*h**3/36, x <= 35))
+    assert b.cross_section == None
+    assert b.length == 35
+    assert b.slope().subs(x, 7) == 8400/(E*a*c**3)
+    assert b.slope().subs(x, 25) == 52200/(E*g*h**3) + 39600/(E*a*c**3)
+    assert b.deflection().subs(x, 30) == -537000/(E*g*h**3) - 712000/(E*a*c**3)
+
+def test_max_shear_force_Beam3D():
+    x = symbols('x')
+    b = Beam3D(20, 40, 21, 100, 25)
+    b.apply_load(15, start=0, order=0, dir="z")
+    b.apply_load(12*x, start=0, order=0, dir="y")
+    b.bc_deflection = [(0, [0, 0, 0]), (20, [0, 0, 0])]
+    assert b.max_shear_force() == [(0, 0), (20, 2400), (20, 300)]
+
+def test_max_bending_moment_Beam3D():
+    x = symbols('x')
+    b = Beam3D(20, 40, 21, 100, 25)
+    b.apply_load(15, start=0, order=0, dir="z")
+    b.apply_load(12*x, start=0, order=0, dir="y")
+    b.bc_deflection = [(0, [0, 0, 0]), (20, [0, 0, 0])]
+    assert b.max_bmoment() == [(0, 0), (20, 3000), (20, 16000)]
+
+def test_max_deflection_Beam3D():
+    x = symbols('x')
+    b = Beam3D(20, 40, 21, 100, 25)
+    b.apply_load(15, start=0, order=0, dir="z")
+    b.apply_load(12*x, start=0, order=0, dir="y")
+    b.bc_deflection = [(0, [0, 0, 0]), (20, [0, 0, 0])]
+    b.solve_slope_deflection()
+    c = sympify("495/14")
+    p = sympify("-10 + 10*sqrt(10793)/43")
+    q = sympify("(10 - 10*sqrt(10793)/43)**3/160 - 20/7 + (10 - 10*sqrt(10793)/43)**4/6400 + 20*sqrt(10793)/301 + 27*(10 - 10*sqrt(10793)/43)**2/560")
+    assert b.max_deflection() == [(0, 0), (10, c), (p, q)]
+
+def test_torsion_Beam3D():
+    x = symbols('x')
+    b = Beam3D(20, 40, 21, 100, 25)
+    b.apply_moment_load(15, 5, -2, dir='x')
+    b.apply_moment_load(25, 10, -2, dir='x')
+    b.apply_moment_load(-5, 20, -2, dir='x')
+    b.solve_for_torsion()
+    assert b.angular_deflection().subs(x, 3) == sympify("1/40")
+    assert b.angular_deflection().subs(x, 9) == sympify("17/280")
+    assert b.angular_deflection().subs(x, 12) == sympify("53/840")
+    assert b.angular_deflection().subs(x, 17) == sympify("2/35")
+    assert b.angular_deflection().subs(x, 20) == sympify("3/56")
diff --git a/parrot/lib/python3.10/site-packages/sympy/physics/continuum_mechanics/tests/test_cable.py b/parrot/lib/python3.10/site-packages/sympy/physics/continuum_mechanics/tests/test_cable.py
new file mode 100644
index 0000000000000000000000000000000000000000..58c5d6e07164293c8b351333fb624f3fc01a30b7
--- /dev/null
+++ b/parrot/lib/python3.10/site-packages/sympy/physics/continuum_mechanics/tests/test_cable.py
@@ -0,0 +1,83 @@
+from sympy.physics.continuum_mechanics.cable import Cable
+from sympy.core.symbol import Symbol
+
+
+def test_cable():
+    c = Cable(('A', 0, 10), ('B', 10, 10))
+    assert c.supports == {'A': [0, 10], 'B': [10, 10]}
+    assert c.left_support == [0, 10]
+    assert c.right_support == [10, 10]
+    assert c.loads == {'distributed': {}, 'point_load': {}}
+    assert c.loads_position == {}
+    assert c.length == 0
+    assert c.reaction_loads == {Symbol("R_A_x"): 0, Symbol("R_A_y"): 0, Symbol("R_B_x"): 0, Symbol("R_B_y"): 0}
+
+    # tests for change_support method
+    c.change_support('A', ('C', 12, 3))
+    assert c.supports == {'B': [10, 10], 'C': [12, 3]}
+    assert c.left_support == [10, 10]
+    assert c.right_support == [12, 3]
+    assert c.reaction_loads == {Symbol("R_B_x"): 0, Symbol("R_B_y"): 0, Symbol("R_C_x"): 0, Symbol("R_C_y"): 0}
+
+    c.change_support('C', ('A', 0, 10))
+
+    # tests for apply_load method for point loads
+    c.apply_load(-1, ('X', 2, 5, 3, 30))
+    c.apply_load(-1, ('Y', 5, 8, 5, 60))
+    assert c.loads == {'distributed': {}, 'point_load': {'X': [3, 30], 'Y': [5, 60]}}
+    assert c.loads_position == {'X': [2, 5], 'Y': [5, 8]}
+    assert c.length == 0
+    assert c.reaction_loads == {Symbol("R_A_x"): 0, Symbol("R_A_y"): 0, Symbol("R_B_x"): 0, Symbol("R_B_y"): 0}
+
+    # tests for remove_loads method
+    c.remove_loads('X')
+    assert c.loads == {'distributed': {}, 'point_load': {'Y': [5, 60]}}
+    assert c.loads_position == {'Y': [5, 8]}
+    assert c.length == 0
+    assert c.reaction_loads == {Symbol("R_A_x"): 0, Symbol("R_A_y"): 0, Symbol("R_B_x"): 0, Symbol("R_B_y"): 0}
+
+    c.remove_loads('Y')
+
+    #tests for apply_load method for distributed load
+    c.apply_load(0, ('Z', 9))
+    assert c.loads == {'distributed': {'Z': 9}, 'point_load': {}}
+    assert c.loads_position == {}
+    assert c.length == 0
+    assert c.reaction_loads == {Symbol("R_A_x"): 0, Symbol("R_A_y"): 0, Symbol("R_B_x"): 0, Symbol("R_B_y"): 0}
+
+    # tests for apply_length method
+    c.apply_length(20)
+    assert c.length == 20
+
+    del c
+    # tests for solve method
+    # for point loads
+    c = Cable(("A", 0, 10), ("B", 5.5, 8))
+    c.apply_load(-1, ('Z', 2, 7.26, 3, 270))
+    c.apply_load(-1, ('X', 4, 6, 8, 270))
+    c.solve()
+    #assert c.tension == {Symbol("Z_X"): 4.79150773600774, Symbol("X_B"): 6.78571428571429, Symbol("A_Z"): 6.89488895397307}
+    assert abs(c.tension[Symbol("A_Z")] - 6.89488895397307) < 10e-12
+    assert abs(c.tension[Symbol("Z_X")] - 4.79150773600774) < 10e-12
+    assert abs(c.tension[Symbol("X_B")] - 6.78571428571429) < 10e-12
+    #assert c.reaction_loads == {Symbol("R_A_x"): -4.06504065040650, Symbol("R_A_y"): 5.56910569105691, Symbol("R_B_x"): 4.06504065040650, Symbol("R_B_y"): 5.43089430894309}
+    assert abs(c.reaction_loads[Symbol("R_A_x")] + 4.06504065040650) < 10e-12
+    assert abs(c.reaction_loads[Symbol("R_A_y")] - 5.56910569105691) < 10e-12
+    assert abs(c.reaction_loads[Symbol("R_B_x")] - 4.06504065040650) < 10e-12
+    assert abs(c.reaction_loads[Symbol("R_B_y")] - 5.43089430894309) < 10e-12
+    assert abs(c.length - 8.25609584845190) < 10e-12
+
+    del c
+    # tests for solve method
+    # for distributed loads
+    c=Cable(("A", 0, 40),("B", 100, 20))
+    c.apply_load(0, ("X", 850))
+    c.solve(58.58, 0)
+
+    # assert c.tension['distributed'] == 36456.8485*sqrt(0.000543529004799705*(X + 0.00135624381275735)**2 + 1)
+    assert abs(c.tension_at(0) - 61709.0363315913) < 10e-11
+    assert abs(c.tension_at(40) - 39729.7316969361) < 10e-11
+    assert abs(c.reaction_loads[Symbol("R_A_x")] - 36456.8485000000) < 10e-11
+    assert abs(c.reaction_loads[Symbol("R_A_y")] + 49788.5866682486) < 10e-11
+    assert abs(c.reaction_loads[Symbol("R_B_x")] - 44389.8401587246) < 10e-11
+    assert abs(c.reaction_loads[Symbol("R_B_y")] - 42866.6216963330) < 10e-11
diff --git a/parrot/lib/python3.10/site-packages/sympy/physics/continuum_mechanics/tests/test_truss.py b/parrot/lib/python3.10/site-packages/sympy/physics/continuum_mechanics/tests/test_truss.py
new file mode 100644
index 0000000000000000000000000000000000000000..61c89c9e09386257c7c69909dfdb0f37cda8627d
--- /dev/null
+++ b/parrot/lib/python3.10/site-packages/sympy/physics/continuum_mechanics/tests/test_truss.py
@@ -0,0 +1,100 @@
+from sympy.core.symbol import Symbol, symbols
+from sympy.physics.continuum_mechanics.truss import Truss
+from sympy import sqrt
+
+
+def test_truss():
+    A = Symbol('A')
+    B = Symbol('B')
+    C = Symbol('C')
+    AB, BC, AC = symbols('AB, BC, AC')
+    P = Symbol('P')
+
+    t = Truss()
+    assert t.nodes == []
+    assert t.node_labels == []
+    assert t.node_positions == []
+    assert t.members == {}
+    assert t.loads == {}
+    assert t.supports == {}
+    assert t.reaction_loads == {}
+    assert t.internal_forces == {}
+
+    # testing the add_node method
+    t.add_node((A, 0, 0), (B, 2, 2), (C, 3, 0))
+    assert t.nodes == [(A, 0, 0), (B, 2, 2), (C, 3, 0)]
+    assert t.node_labels == [A, B, C]
+    assert t.node_positions == [(0, 0), (2, 2), (3, 0)]
+    assert t.loads == {}
+    assert t.supports == {}
+    assert t.reaction_loads == {}
+
+    # testing the remove_node method
+    t.remove_node(C)
+    assert t.nodes == [(A, 0, 0), (B, 2, 2)]
+    assert t.node_labels == [A, B]
+    assert t.node_positions == [(0, 0), (2, 2)]
+    assert t.loads == {}
+    assert t.supports == {}
+
+    t.add_node((C, 3, 0))
+
+    # testing the add_member method
+    t.add_member((AB, A, B), (BC, B, C), (AC, A, C))
+    assert t.members == {AB: [A, B], BC: [B, C], AC: [A, C]}
+    assert t.internal_forces == {AB: 0, BC: 0, AC: 0}
+
+    # testing the remove_member method
+    t.remove_member(BC)
+    assert t.members == {AB: [A, B], AC: [A, C]}
+    assert t.internal_forces == {AB: 0, AC: 0}
+
+    t.add_member((BC, B, C))
+
+    D, CD = symbols('D, CD')
+
+    # testing the change_label methods
+    t.change_node_label((B, D))
+    assert t.nodes == [(A, 0, 0), (D, 2, 2), (C, 3, 0)]
+    assert t.node_labels == [A, D, C]
+    assert t.loads == {}
+    assert t.supports == {}
+    assert t.members == {AB: [A, D], BC: [D, C], AC: [A, C]}
+
+    t.change_member_label((BC, CD))
+    assert t.members == {AB: [A, D], CD: [D, C], AC: [A, C]}
+    assert t.internal_forces == {AB: 0, CD: 0, AC: 0}
+
+
+    # testing the apply_load method
+    t.apply_load((A, P, 90), (A, P/4, 90), (A, 2*P,45), (D, P/2, 90))
+    assert t.loads == {A: [[P, 90], [P/4, 90], [2*P, 45]], D: [[P/2, 90]]}
+    assert t.loads[A] == [[P, 90], [P/4, 90], [2*P, 45]]
+
+    # testing the remove_load method
+    t.remove_load((A, P/4, 90))
+    assert t.loads == {A: [[P, 90], [2*P, 45]], D: [[P/2, 90]]}
+    assert t.loads[A] == [[P, 90], [2*P, 45]]
+
+    # testing the apply_support method
+    t.apply_support((A, "pinned"), (D, "roller"))
+    assert t.supports == {A: 'pinned', D: 'roller'}
+    assert t.reaction_loads == {}
+    assert t.loads == {A: [[P, 90], [2*P, 45], [Symbol('R_A_x'), 0], [Symbol('R_A_y'), 90]],  D: [[P/2, 90], [Symbol('R_D_y'), 90]]}
+
+    # testing the remove_support method
+    t.remove_support(A)
+    assert t.supports == {D: 'roller'}
+    assert t.reaction_loads == {}
+    assert t.loads == {A: [[P, 90], [2*P, 45]], D: [[P/2, 90], [Symbol('R_D_y'), 90]]}
+
+    t.apply_support((A, "pinned"))
+
+    # testing the solve method
+    t.solve()
+    assert t.reaction_loads['R_A_x'] == -sqrt(2)*P
+    assert t.reaction_loads['R_A_y'] == -sqrt(2)*P - P
+    assert t.reaction_loads['R_D_y'] == -P/2
+    assert t.internal_forces[AB]/P == 0
+    assert t.internal_forces[CD] == 0
+    assert t.internal_forces[AC] == 0
diff --git a/parrot/lib/python3.10/site-packages/sympy/physics/continuum_mechanics/truss.py b/parrot/lib/python3.10/site-packages/sympy/physics/continuum_mechanics/truss.py
new file mode 100644
index 0000000000000000000000000000000000000000..f7fd0ea3f5e18574f21e2f656477c7af987d8eb6
--- /dev/null
+++ b/parrot/lib/python3.10/site-packages/sympy/physics/continuum_mechanics/truss.py
@@ -0,0 +1,1108 @@
+"""
+This module can be used to solve problems related
+to 2D Trusses.
+"""
+
+
+from cmath import atan, inf
+from sympy.core.add import Add
+from sympy.core.evalf import INF
+from sympy.core.mul import Mul
+from sympy.core.symbol import Symbol
+from sympy.core.sympify import sympify
+from sympy import Matrix, pi
+from sympy.external.importtools import import_module
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.matrices.dense import zeros
+import math
+from sympy.physics.units.quantities import Quantity
+from sympy.plotting import plot
+from sympy.utilities.decorator import doctest_depends_on
+from sympy import sin, cos
+
+
+__doctest_requires__ = {('Truss.draw'): ['matplotlib']}
+
+
+numpy = import_module('numpy', import_kwargs={'fromlist':['arange']})
+
+
+class Truss:
+    """
+    A Truss is an assembly of members such as beams,
+    connected by nodes, that create a rigid structure.
+    In engineering, a truss is a structure that
+    consists of two-force members only.
+
+    Trusses are extremely important in engineering applications
+    and can be seen in numerous real-world applications like bridges.
+
+    Examples
+    ========
+
+    There is a Truss consisting of four nodes and five
+    members connecting the nodes. A force P acts
+    downward on the node D and there also exist pinned
+    and roller joints on the nodes A and B respectively.
+
+    .. image:: truss_example.png
+
+    >>> from sympy.physics.continuum_mechanics.truss import Truss
+    >>> t = Truss()
+    >>> t.add_node(("node_1", 0, 0), ("node_2", 6, 0), ("node_3", 2, 2), ("node_4", 2, 0))
+    >>> t.add_member(("member_1", "node_1", "node_4"), ("member_2", "node_2", "node_4"), ("member_3", "node_1", "node_3"))
+    >>> t.add_member(("member_4", "node_2", "node_3"), ("member_5", "node_3", "node_4"))
+    >>> t.apply_load(("node_4", 10, 270))
+    >>> t.apply_support(("node_1", "pinned"), ("node_2", "roller"))
+    """
+
+    def __init__(self):
+        """
+        Initializes the class
+        """
+        self._nodes = []
+        self._members = {}
+        self._loads = {}
+        self._supports = {}
+        self._node_labels = []
+        self._node_positions = []
+        self._node_position_x = []
+        self._node_position_y = []
+        self._nodes_occupied = {}
+        self._member_lengths = {}
+        self._reaction_loads = {}
+        self._internal_forces = {}
+        self._node_coordinates = {}
+
+    @property
+    def nodes(self):
+        """
+        Returns the nodes of the truss along with their positions.
+        """
+        return self._nodes
+
+    @property
+    def node_labels(self):
+        """
+        Returns the node labels of the truss.
+        """
+        return self._node_labels
+
+    @property
+    def node_positions(self):
+        """
+        Returns the positions of the nodes of the truss.
+        """
+        return self._node_positions
+
+    @property
+    def members(self):
+        """
+        Returns the members of the truss along with the start and end points.
+        """
+        return self._members
+
+    @property
+    def member_lengths(self):
+        """
+        Returns the length of each member of the truss.
+        """
+        return self._member_lengths
+
+    @property
+    def supports(self):
+        """
+        Returns the nodes with provided supports along with the kind of support provided i.e.
+        pinned or roller.
+        """
+        return self._supports
+
+    @property
+    def loads(self):
+        """
+        Returns the loads acting on the truss.
+        """
+        return self._loads
+
+    @property
+    def reaction_loads(self):
+        """
+        Returns the reaction forces for all supports which are all initialized to 0.
+        """
+        return self._reaction_loads
+
+    @property
+    def internal_forces(self):
+        """
+        Returns the internal forces for all members which are all initialized to 0.
+        """
+        return self._internal_forces
+
+    def add_node(self, *args):
+        """
+        This method adds a node to the truss along with its name/label and its location.
+        Multiple nodes can be added at the same time.
+
+        Parameters
+        ==========
+        The input(s) for this method are tuples of the form (label, x, y).
+
+        label:  String or a Symbol
+            The label for a node. It is the only way to identify a particular node.
+
+        x: Sympifyable
+            The x-coordinate of the position of the node.
+
+        y: Sympifyable
+            The y-coordinate of the position of the node.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.continuum_mechanics.truss import Truss
+        >>> t = Truss()
+        >>> t.add_node(('A', 0, 0))
+        >>> t.nodes
+        [('A', 0, 0)]
+        >>> t.add_node(('B', 3, 0), ('C', 4, 1))
+        >>> t.nodes
+        [('A', 0, 0), ('B', 3, 0), ('C', 4, 1)]
+        """
+
+        for i in args:
+            label = i[0]
+            x = i[1]
+            x = sympify(x)
+            y=i[2]
+            y = sympify(y)
+            if label in self._node_coordinates:
+                raise ValueError("Node needs to have a unique label")
+
+            elif [x, y] in self._node_coordinates.values():
+                raise ValueError("A node already exists at the given position")
+
+            else :
+                self._nodes.append((label, x, y))
+                self._node_labels.append(label)
+                self._node_positions.append((x, y))
+                self._node_position_x.append(x)
+                self._node_position_y.append(y)
+                self._node_coordinates[label] = [x, y]
+
+
+
+    def remove_node(self, *args):
+        """
+        This method removes a node from the truss.
+        Multiple nodes can be removed at the same time.
+
+        Parameters
+        ==========
+        The input(s) for this method are the labels of the nodes to be removed.
+
+        label:  String or Symbol
+            The label of the node to be removed.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.continuum_mechanics.truss import Truss
+        >>> t = Truss()
+        >>> t.add_node(('A', 0, 0), ('B', 3, 0), ('C', 5, 0))
+        >>> t.nodes
+        [('A', 0, 0), ('B', 3, 0), ('C', 5, 0)]
+        >>> t.remove_node('A', 'C')
+        >>> t.nodes
+        [('B', 3, 0)]
+        """
+        for label in args:
+            for i in range(len(self.nodes)):
+                if self._node_labels[i] == label:
+                    x = self._node_position_x[i]
+                    y = self._node_position_y[i]
+
+            if label not in self._node_coordinates:
+                raise ValueError("No such node exists in the truss")
+
+            else:
+                members_duplicate = self._members.copy()
+                for member in members_duplicate:
+                    if label == self._members[member][0] or label == self._members[member][1]:
+                        raise ValueError("The given node already has member attached to it")
+                self._nodes.remove((label, x, y))
+                self._node_labels.remove(label)
+                self._node_positions.remove((x, y))
+                self._node_position_x.remove(x)
+                self._node_position_y.remove(y)
+                if label in self._loads:
+                    self._loads.pop(label)
+                if label in self._supports:
+                    self._supports.pop(label)
+                self._node_coordinates.pop(label)
+
+
+
+    def add_member(self, *args):
+        """
+        This method adds a member between any two nodes in the given truss.
+
+        Parameters
+        ==========
+        The input(s) of the method are tuple(s) of the form (label, start, end).
+
+        label: String or Symbol
+            The label for a member. It is the only way to identify a particular member.
+
+        start: String or Symbol
+            The label of the starting point/node of the member.
+
+        end: String or Symbol
+            The label of the ending point/node of the member.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.continuum_mechanics.truss import Truss
+        >>> t = Truss()
+        >>> t.add_node(('A', 0, 0), ('B', 3, 0), ('C', 2, 2))
+        >>> t.add_member(('AB', 'A', 'B'), ('BC', 'B', 'C'))
+        >>> t.members
+        {'AB': ['A', 'B'], 'BC': ['B', 'C']}
+        """
+        for i in args:
+            label = i[0]
+            start = i[1]
+            end = i[2]
+
+            if start not in self._node_coordinates or end not in self._node_coordinates or start==end:
+                raise ValueError("The start and end points of the member must be unique nodes")
+
+            elif label in self._members:
+                raise ValueError("A member with the same label already exists for the truss")
+
+            elif self._nodes_occupied.get((start, end)):
+                raise ValueError("A member already exists between the two nodes")
+
+            else:
+                self._members[label] = [start, end]
+                self._member_lengths[label] = sqrt((self._node_coordinates[end][0]-self._node_coordinates[start][0])**2 + (self._node_coordinates[end][1]-self._node_coordinates[start][1])**2)
+                self._nodes_occupied[start, end] = True
+                self._nodes_occupied[end, start] = True
+                self._internal_forces[label] = 0
+
+    def remove_member(self, *args):
+        """
+        This method removes members from the given truss.
+
+        Parameters
+        ==========
+        labels: String or Symbol
+            The label for the member to be removed.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.continuum_mechanics.truss import Truss
+        >>> t = Truss()
+        >>> t.add_node(('A', 0, 0), ('B', 3, 0), ('C', 2, 2))
+        >>> t.add_member(('AB', 'A', 'B'), ('AC', 'A', 'C'), ('BC', 'B', 'C'))
+        >>> t.members
+        {'AB': ['A', 'B'], 'AC': ['A', 'C'], 'BC': ['B', 'C']}
+        >>> t.remove_member('AC', 'BC')
+        >>> t.members
+        {'AB': ['A', 'B']}
+        """
+        for label in args:
+            if label not in self._members:
+                raise ValueError("No such member exists in the Truss")
+
+            else:
+                self._nodes_occupied.pop((self._members[label][0], self._members[label][1]))
+                self._nodes_occupied.pop((self._members[label][1], self._members[label][0]))
+                self._members.pop(label)
+                self._member_lengths.pop(label)
+                self._internal_forces.pop(label)
+
+    def change_node_label(self, *args):
+        """
+        This method changes the label(s) of the specified node(s).
+
+        Parameters
+        ==========
+        The input(s) of this method are tuple(s) of the form (label, new_label).
+
+        label: String or Symbol
+            The label of the node for which the label has
+            to be changed.
+
+        new_label: String or Symbol
+            The new label of the node.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.continuum_mechanics.truss import Truss
+        >>> t = Truss()
+        >>> t.add_node(('A', 0, 0), ('B', 3, 0))
+        >>> t.nodes
+        [('A', 0, 0), ('B', 3, 0)]
+        >>> t.change_node_label(('A', 'C'), ('B', 'D'))
+        >>> t.nodes
+        [('C', 0, 0), ('D', 3, 0)]
+        """
+        for i in args:
+            label = i[0]
+            new_label = i[1]
+            if label not in self._node_coordinates:
+                raise ValueError("No such node exists for the Truss")
+            elif new_label in self._node_coordinates:
+                raise ValueError("A node with the given label already exists")
+            else:
+                for node in self._nodes:
+                    if node[0] == label:
+                        self._nodes[self._nodes.index((label, node[1], node[2]))] = (new_label, node[1], node[2])
+                        self._node_labels[self._node_labels.index(node[0])] = new_label
+                        self._node_coordinates[new_label] = self._node_coordinates[label]
+                        self._node_coordinates.pop(label)
+                        if node[0] in self._supports:
+                            self._supports[new_label] = self._supports[node[0]]
+                            self._supports.pop(node[0])
+                        if new_label in self._supports:
+                            if self._supports[new_label] == 'pinned':
+                                if 'R_'+str(label)+'_x' in self._reaction_loads and 'R_'+str(label)+'_y' in self._reaction_loads:
+                                    self._reaction_loads['R_'+str(new_label)+'_x'] = self._reaction_loads['R_'+str(label)+'_x']
+                                    self._reaction_loads['R_'+str(new_label)+'_y'] = self._reaction_loads['R_'+str(label)+'_y']
+                                    self._reaction_loads.pop('R_'+str(label)+'_x')
+                                    self._reaction_loads.pop('R_'+str(label)+'_y')
+                                self._loads[new_label] = self._loads[label]
+                                for load in self._loads[new_label]:
+                                    if load[1] == 90:
+                                        load[0] -= Symbol('R_'+str(label)+'_y')
+                                        if load[0] == 0:
+                                            self._loads[label].remove(load)
+                                        break
+                                for load in self._loads[new_label]:
+                                    if load[1] == 0:
+                                        load[0] -= Symbol('R_'+str(label)+'_x')
+                                        if load[0] == 0:
+                                            self._loads[label].remove(load)
+                                        break
+                                self.apply_load(new_label, Symbol('R_'+str(new_label)+'_x'), 0)
+                                self.apply_load(new_label, Symbol('R_'+str(new_label)+'_y'), 90)
+                                self._loads.pop(label)
+                            elif self._supports[new_label] == 'roller':
+                                self._loads[new_label] = self._loads[label]
+                                for load in self._loads[label]:
+                                    if load[1] == 90:
+                                        load[0] -= Symbol('R_'+str(label)+'_y')
+                                        if load[0] == 0:
+                                            self._loads[label].remove(load)
+                                        break
+                                self.apply_load(new_label, Symbol('R_'+str(new_label)+'_y'), 90)
+                                self._loads.pop(label)
+                        else:
+                            if label in self._loads:
+                                self._loads[new_label] = self._loads[label]
+                                self._loads.pop(label)
+                        for member in self._members:
+                            if self._members[member][0] == node[0]:
+                                self._members[member][0] = new_label
+                                self._nodes_occupied[(new_label, self._members[member][1])] = True
+                                self._nodes_occupied[(self._members[member][1], new_label)] = True
+                                self._nodes_occupied.pop((label, self._members[member][1]))
+                                self._nodes_occupied.pop((self._members[member][1], label))
+                            elif self._members[member][1] == node[0]:
+                                self._members[member][1] = new_label
+                                self._nodes_occupied[(self._members[member][0], new_label)] = True
+                                self._nodes_occupied[(new_label, self._members[member][0])] = True
+                                self._nodes_occupied.pop((self._members[member][0], label))
+                                self._nodes_occupied.pop((label, self._members[member][0]))
+
+    def change_member_label(self, *args):
+        """
+        This method changes the label(s) of the specified member(s).
+
+        Parameters
+        ==========
+        The input(s) of this method are tuple(s) of the form (label, new_label)
+
+        label: String or Symbol
+            The label of the member for which the label has
+            to be changed.
+
+        new_label: String or Symbol
+            The new label of the member.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.continuum_mechanics.truss import Truss
+        >>> t = Truss()
+        >>> t.add_node(('A', 0, 0), ('B', 3, 0), ('D', 5, 0))
+        >>> t.nodes
+        [('A', 0, 0), ('B', 3, 0), ('D', 5, 0)]
+        >>> t.change_node_label(('A', 'C'))
+        >>> t.nodes
+        [('C', 0, 0), ('B', 3, 0), ('D', 5, 0)]
+        >>> t.add_member(('BC', 'B', 'C'), ('BD', 'B', 'D'))
+        >>> t.members
+        {'BC': ['B', 'C'], 'BD': ['B', 'D']}
+        >>> t.change_member_label(('BC', 'BC_new'), ('BD', 'BD_new'))
+        >>> t.members
+        {'BC_new': ['B', 'C'], 'BD_new': ['B', 'D']}
+        """
+        for i in args:
+            label = i[0]
+            new_label = i[1]
+            if label not in self._members:
+                raise ValueError("No such member exists for the Truss")
+            else:
+                members_duplicate = list(self._members).copy()
+                for member in members_duplicate:
+                    if member == label:
+                        self._members[new_label] = [self._members[member][0], self._members[member][1]]
+                        self._members.pop(label)
+                        self._member_lengths[new_label] = self._member_lengths[label]
+                        self._member_lengths.pop(label)
+                        self._internal_forces[new_label] = self._internal_forces[label]
+                        self._internal_forces.pop(label)
+
+    def apply_load(self, *args):
+        """
+        This method applies external load(s) at the specified node(s).
+
+        Parameters
+        ==========
+        The input(s) of the method are tuple(s) of the form (location, magnitude, direction).
+
+        location: String or Symbol
+            Label of the Node at which load is applied.
+
+        magnitude: Sympifyable
+            Magnitude of the load applied. It must always be positive and any changes in
+            the direction of the load are not reflected here.
+
+        direction: Sympifyable
+            The angle, in degrees, that the load vector makes with the horizontal
+            in the counter-clockwise direction. It takes the values 0 to 360,
+            inclusive.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.continuum_mechanics.truss import Truss
+        >>> from sympy import symbols
+        >>> t = Truss()
+        >>> t.add_node(('A', 0, 0), ('B', 3, 0))
+        >>> P = symbols('P')
+        >>> t.apply_load(('A', P, 90), ('A', P/2, 45), ('A', P/4, 90))
+        >>> t.loads
+        {'A': [[P, 90], [P/2, 45], [P/4, 90]]}
+        """
+        for i in args:
+            location = i[0]
+            magnitude = i[1]
+            direction = i[2]
+            magnitude = sympify(magnitude)
+            direction = sympify(direction)
+
+            if location not in self._node_coordinates:
+                raise ValueError("Load must be applied at a known node")
+
+            else:
+                if location in self._loads:
+                    self._loads[location].append([magnitude, direction])
+                else:
+                    self._loads[location] = [[magnitude, direction]]
+
+    def remove_load(self, *args):
+        """
+        This method removes already
+        present external load(s) at specified node(s).
+
+        Parameters
+        ==========
+        The input(s) of this method are tuple(s) of the form (location, magnitude, direction).
+
+        location: String or Symbol
+            Label of the Node at which load is applied and is to be removed.
+
+        magnitude: Sympifyable
+            Magnitude of the load applied.
+
+        direction: Sympifyable
+            The angle, in degrees, that the load vector makes with the horizontal
+            in the counter-clockwise direction. It takes the values 0 to 360,
+            inclusive.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.continuum_mechanics.truss import Truss
+        >>> from sympy import symbols
+        >>> t = Truss()
+        >>> t.add_node(('A', 0, 0), ('B', 3, 0))
+        >>> P = symbols('P')
+        >>> t.apply_load(('A', P, 90), ('A', P/2, 45), ('A', P/4, 90))
+        >>> t.loads
+        {'A': [[P, 90], [P/2, 45], [P/4, 90]]}
+        >>> t.remove_load(('A', P/4, 90), ('A', P/2, 45))
+        >>> t.loads
+        {'A': [[P, 90]]}
+        """
+        for i in args:
+            location = i[0]
+            magnitude = i[1]
+            direction = i[2]
+            magnitude = sympify(magnitude)
+            direction = sympify(direction)
+
+            if location not in self._node_coordinates:
+                raise ValueError("Load must be removed from a known node")
+
+            else:
+                if [magnitude, direction] not in self._loads[location]:
+                    raise ValueError("No load of this magnitude and direction has been applied at this node")
+                else:
+                    self._loads[location].remove([magnitude, direction])
+            if self._loads[location] == []:
+                self._loads.pop(location)
+
+    def apply_support(self, *args):
+        """
+        This method adds a pinned or roller support at specified node(s).
+
+        Parameters
+        ==========
+        The input(s) of this method are of the form (location, type).
+
+        location: String or Symbol
+            Label of the Node at which support is added.
+
+        type: String
+            Type of the support being provided at the node.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.continuum_mechanics.truss import Truss
+        >>> t = Truss()
+        >>> t.add_node(('A', 0, 0), ('B', 3, 0))
+        >>> t.apply_support(('A', 'pinned'), ('B', 'roller'))
+        >>> t.supports
+        {'A': 'pinned', 'B': 'roller'}
+        """
+        for i in args:
+            location = i[0]
+            type = i[1]
+            if location not in self._node_coordinates:
+                raise ValueError("Support must be added on a known node")
+
+            else:
+                if location not in self._supports:
+                    if type == 'pinned':
+                        self.apply_load((location, Symbol('R_'+str(location)+'_x'), 0))
+                        self.apply_load((location, Symbol('R_'+str(location)+'_y'), 90))
+                    elif type == 'roller':
+                        self.apply_load((location, Symbol('R_'+str(location)+'_y'), 90))
+                elif self._supports[location] == 'pinned':
+                    if type == 'roller':
+                        self.remove_load((location, Symbol('R_'+str(location)+'_x'), 0))
+                elif self._supports[location] == 'roller':
+                    if type == 'pinned':
+                        self.apply_load((location, Symbol('R_'+str(location)+'_x'), 0))
+                self._supports[location] = type
+
+    def remove_support(self, *args):
+        """
+        This method removes support from specified node(s.)
+
+        Parameters
+        ==========
+
+        locations: String or Symbol
+            Label of the Node(s) at which support is to be removed.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.continuum_mechanics.truss import Truss
+        >>> t = Truss()
+        >>> t.add_node(('A', 0, 0), ('B', 3, 0))
+        >>> t.apply_support(('A', 'pinned'), ('B', 'roller'))
+        >>> t.supports
+        {'A': 'pinned', 'B': 'roller'}
+        >>> t.remove_support('A','B')
+        >>> t.supports
+        {}
+        """
+        for location in args:
+
+            if location not in self._node_coordinates:
+                raise ValueError("No such node exists in the Truss")
+
+            elif location not in self._supports:
+                raise ValueError("No support has been added to the given node")
+
+            else:
+                if self._supports[location] == 'pinned':
+                    self.remove_load((location, Symbol('R_'+str(location)+'_x'), 0))
+                    self.remove_load((location, Symbol('R_'+str(location)+'_y'), 90))
+                elif self._supports[location] == 'roller':
+                    self.remove_load((location, Symbol('R_'+str(location)+'_y'), 90))
+                self._supports.pop(location)
+
+    def solve(self):
+        """
+        This method solves for all reaction forces of all supports and all internal forces
+        of all the members in the truss, provided the Truss is solvable.
+
+        A Truss is solvable if the following condition is met,
+
+        2n >= r + m
+
+        Where n is the number of nodes, r is the number of reaction forces, where each pinned
+        support has 2 reaction forces and each roller has 1, and m is the number of members.
+
+        The given condition is derived from the fact that a system of equations is solvable
+        only when the number of variables is lesser than or equal to the number of equations.
+        Equilibrium Equations in x and y directions give two equations per node giving 2n number
+        equations. However, the truss needs to be stable as well and may be unstable if 2n > r + m.
+        The number of variables is simply the sum of the number of reaction forces and member
+        forces.
+
+        .. note::
+           The sign convention for the internal forces present in a member revolves around whether each
+           force is compressive or tensile. While forming equations for each node, internal force due
+           to a member on the node is assumed to be away from the node i.e. each force is assumed to
+           be compressive by default. Hence, a positive value for an internal force implies the
+           presence of compressive force in the member and a negative value implies a tensile force.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.continuum_mechanics.truss import Truss
+        >>> t = Truss()
+        >>> t.add_node(("node_1", 0, 0), ("node_2", 6, 0), ("node_3", 2, 2), ("node_4", 2, 0))
+        >>> t.add_member(("member_1", "node_1", "node_4"), ("member_2", "node_2", "node_4"), ("member_3", "node_1", "node_3"))
+        >>> t.add_member(("member_4", "node_2", "node_3"), ("member_5", "node_3", "node_4"))
+        >>> t.apply_load(("node_4", 10, 270))
+        >>> t.apply_support(("node_1", "pinned"), ("node_2", "roller"))
+        >>> t.solve()
+        >>> t.reaction_loads
+        {'R_node_1_x': 0, 'R_node_1_y': 20/3, 'R_node_2_y': 10/3}
+        >>> t.internal_forces
+        {'member_1': 20/3, 'member_2': 20/3, 'member_3': -20*sqrt(2)/3, 'member_4': -10*sqrt(5)/3, 'member_5': 10}
+        """
+        count_reaction_loads = 0
+        for node in self._nodes:
+            if node[0] in self._supports:
+                if self._supports[node[0]]=='pinned':
+                    count_reaction_loads += 2
+                elif self._supports[node[0]]=='roller':
+                    count_reaction_loads += 1
+        if 2*len(self._nodes) != len(self._members) + count_reaction_loads:
+            raise ValueError("The given truss cannot be solved")
+        coefficients_matrix = [[0 for i in range(2*len(self._nodes))] for j in range(2*len(self._nodes))]
+        load_matrix = zeros(2*len(self.nodes), 1)
+        load_matrix_row = 0
+        for node in self._nodes:
+            if node[0] in self._loads:
+                for load in self._loads[node[0]]:
+                    if load[0]!=Symbol('R_'+str(node[0])+'_x') and load[0]!=Symbol('R_'+str(node[0])+'_y'):
+                        load_matrix[load_matrix_row] -= load[0]*cos(pi*load[1]/180)
+                        load_matrix[load_matrix_row + 1] -= load[0]*sin(pi*load[1]/180)
+            load_matrix_row += 2
+        cols = 0
+        row = 0
+        for node in self._nodes:
+            if node[0] in self._supports:
+                if self._supports[node[0]]=='pinned':
+                    coefficients_matrix[row][cols] += 1
+                    coefficients_matrix[row+1][cols+1] += 1
+                    cols += 2
+                elif self._supports[node[0]]=='roller':
+                    coefficients_matrix[row+1][cols] += 1
+                    cols += 1
+            row += 2
+        for member in self._members:
+            start = self._members[member][0]
+            end = self._members[member][1]
+            length = sqrt((self._node_coordinates[start][0]-self._node_coordinates[end][0])**2 + (self._node_coordinates[start][1]-self._node_coordinates[end][1])**2)
+            start_index = self._node_labels.index(start)
+            end_index = self._node_labels.index(end)
+            horizontal_component_start = (self._node_coordinates[end][0]-self._node_coordinates[start][0])/length
+            vertical_component_start = (self._node_coordinates[end][1]-self._node_coordinates[start][1])/length
+            horizontal_component_end = (self._node_coordinates[start][0]-self._node_coordinates[end][0])/length
+            vertical_component_end = (self._node_coordinates[start][1]-self._node_coordinates[end][1])/length
+            coefficients_matrix[start_index*2][cols] += horizontal_component_start
+            coefficients_matrix[start_index*2+1][cols] += vertical_component_start
+            coefficients_matrix[end_index*2][cols] += horizontal_component_end
+            coefficients_matrix[end_index*2+1][cols] += vertical_component_end
+            cols += 1
+        forces_matrix = (Matrix(coefficients_matrix)**-1)*load_matrix
+        self._reaction_loads = {}
+        i = 0
+        min_load = inf
+        for node in self._nodes:
+            if node[0] in self._loads:
+                for load in self._loads[node[0]]:
+                    if type(load[0]) not in [Symbol, Mul, Add]:
+                        min_load = min(min_load, load[0])
+        for j in range(len(forces_matrix)):
+            if type(forces_matrix[j]) not in [Symbol, Mul, Add]:
+                if abs(forces_matrix[j]/min_load) <1E-10:
+                    forces_matrix[j] = 0
+        for node in self._nodes:
+            if node[0] in self._supports:
+                if self._supports[node[0]]=='pinned':
+                    self._reaction_loads['R_'+str(node[0])+'_x'] = forces_matrix[i]
+                    self._reaction_loads['R_'+str(node[0])+'_y'] = forces_matrix[i+1]
+                    i += 2
+                elif self._supports[node[0]]=='roller':
+                    self._reaction_loads['R_'+str(node[0])+'_y'] = forces_matrix[i]
+                    i += 1
+        for member in self._members:
+            self._internal_forces[member] = forces_matrix[i]
+            i += 1
+        return
+
+    @doctest_depends_on(modules=('numpy',))
+    def draw(self, subs_dict=None):
+        """
+        Returns a plot object of the Truss with all its nodes, members,
+        supports and loads.
+
+        .. note::
+            The user must be careful while entering load values in their
+            directions. The draw function assumes a sign convention that
+            is used for plotting loads.
+
+            Given a right-handed coordinate system with XYZ coordinates,
+            the supports are assumed to be such that the reaction forces of a
+            pinned support is in the +X and +Y direction while those of a
+            roller support is in the +Y direction. For the load, the range
+            of angles, one can input goes all the way to 360 degrees which, in the
+            the plot is the angle that the load vector makes with the positive x-axis in the anticlockwise direction.
+
+            For example, for a 90-degree angle, the load will be a vertically
+            directed along +Y while a 270-degree angle denotes a vertical
+            load as well but along -Y.
+
+        Examples
+        ========
+
+        .. plot::
+            :context: close-figs
+            :format: doctest
+            :include-source: True
+
+            >>> from sympy.physics.continuum_mechanics.truss import Truss
+            >>> import math
+            >>> t = Truss()
+            >>> t.add_node(("A", -4, 0), ("B", 0, 0), ("C", 4, 0), ("D", 8, 0))
+            >>> t.add_node(("E", 6, 2/math.sqrt(3)))
+            >>> t.add_node(("F", 2, 2*math.sqrt(3)))
+            >>> t.add_node(("G", -2, 2/math.sqrt(3)))
+            >>> t.add_member(("AB","A","B"), ("BC","B","C"), ("CD","C","D"))
+            >>> t.add_member(("AG","A","G"), ("GB","G","B"), ("GF","G","F"))
+            >>> t.add_member(("BF","B","F"), ("FC","F","C"), ("CE","C","E"))
+            >>> t.add_member(("FE","F","E"), ("DE","D","E"))
+            >>> t.apply_support(("A","pinned"), ("D","roller"))
+            >>> t.apply_load(("G", 3, 90), ("E", 3, 90), ("F", 2, 90))
+            >>> p = t.draw()
+            >>> p  # doctest: +ELLIPSIS
+            Plot object containing:
+            [0]: cartesian line: 1 for x over (1.0, 1.0)
+            ...
+            >>> p.show()
+        """
+        if not numpy:
+            raise ImportError("To use this function numpy module is required")
+
+        x = Symbol('x')
+
+        markers = []
+        annotations = []
+        rectangles = []
+
+        node_markers = self._draw_nodes(subs_dict)
+        markers += node_markers
+
+        member_rectangles = self._draw_members()
+        rectangles += member_rectangles
+
+        support_markers = self._draw_supports()
+        markers += support_markers
+
+        load_annotations = self._draw_loads()
+        annotations += load_annotations
+
+        xmax = -INF
+        xmin = INF
+        ymax = -INF
+        ymin = INF
+
+        for node in self._node_coordinates:
+            xmax = max(xmax, self._node_coordinates[node][0])
+            xmin = min(xmin, self._node_coordinates[node][0])
+            ymax = max(ymax, self._node_coordinates[node][1])
+            ymin = min(ymin, self._node_coordinates[node][1])
+
+        lim = max(xmax*1.1-xmin*0.8+1, ymax*1.1-ymin*0.8+1)
+
+        if lim==xmax*1.1-xmin*0.8+1:
+            sing_plot = plot(1, (x, 1, 1), markers=markers, show=False, annotations=annotations, xlim=(xmin-0.05*lim, xmax*1.1), ylim=(xmin-0.05*lim, xmax*1.1), axis=False, rectangles=rectangles)
+
+        else:
+            sing_plot = plot(1, (x, 1, 1), markers=markers, show=False, annotations=annotations, xlim=(ymin-0.05*lim, ymax*1.1), ylim=(ymin-0.05*lim, ymax*1.1), axis=False, rectangles=rectangles)
+
+        return sing_plot
+
+
+    def _draw_nodes(self, subs_dict):
+        node_markers = []
+
+        for node in self._node_coordinates:
+            if (type(self._node_coordinates[node][0]) in (Symbol, Quantity)):
+                if self._node_coordinates[node][0] in subs_dict:
+                    self._node_coordinates[node][0] = subs_dict[self._node_coordinates[node][0]]
+                else:
+                    raise ValueError("provided substituted dictionary is not adequate")
+            elif (type(self._node_coordinates[node][0]) == Mul):
+                objects = self._node_coordinates[node][0].as_coeff_Mul()
+                for object in objects:
+                    if type(object) in (Symbol, Quantity):
+                        if subs_dict==None or object not in subs_dict:
+                            raise ValueError("provided substituted dictionary is not adequate")
+                        else:
+                            self._node_coordinates[node][0] /= object
+                            self._node_coordinates[node][0] *= subs_dict[object]
+
+            if (type(self._node_coordinates[node][1]) in (Symbol, Quantity)):
+                if self._node_coordinates[node][1] in subs_dict:
+                    self._node_coordinates[node][1] = subs_dict[self._node_coordinates[node][1]]
+                else:
+                    raise ValueError("provided substituted dictionary is not adequate")
+            elif (type(self._node_coordinates[node][1]) == Mul):
+                objects = self._node_coordinates[node][1].as_coeff_Mul()
+                for object in objects:
+                    if type(object) in (Symbol, Quantity):
+                        if subs_dict==None or object not in subs_dict:
+                            raise ValueError("provided substituted dictionary is not adequate")
+                        else:
+                            self._node_coordinates[node][1] /= object
+                            self._node_coordinates[node][1] *= subs_dict[object]
+
+        for node in self._node_coordinates:
+            node_markers.append(
+                {
+                    'args':[[self._node_coordinates[node][0]], [self._node_coordinates[node][1]]],
+                    'marker':'o',
+                    'markersize':5,
+                    'color':'black'
+                }
+            )
+        return node_markers
+
+    def _draw_members(self):
+
+        member_rectangles = []
+
+        xmax = -INF
+        xmin = INF
+        ymax = -INF
+        ymin = INF
+
+        for node in self._node_coordinates:
+            xmax = max(xmax, self._node_coordinates[node][0])
+            xmin = min(xmin, self._node_coordinates[node][0])
+            ymax = max(ymax, self._node_coordinates[node][1])
+            ymin = min(ymin, self._node_coordinates[node][1])
+
+        if abs(1.1*xmax-0.8*xmin)>abs(1.1*ymax-0.8*ymin):
+            max_diff = 1.1*xmax-0.8*xmin
+        else:
+            max_diff = 1.1*ymax-0.8*ymin
+
+        for member in self._members:
+            x1 = self._node_coordinates[self._members[member][0]][0]
+            y1 = self._node_coordinates[self._members[member][0]][1]
+            x2 = self._node_coordinates[self._members[member][1]][0]
+            y2 = self._node_coordinates[self._members[member][1]][1]
+            if x2!=x1 and y2!=y1:
+                if x2>x1:
+                    member_rectangles.append(
+                        {
+                            'xy':(x1-0.005*max_diff*cos(pi/4+atan((y2-y1)/(x2-x1)))/2, y1-0.005*max_diff*sin(pi/4+atan((y2-y1)/(x2-x1)))/2),
+                            'width':sqrt((x1-x2)**2+(y1-y2)**2)+0.005*max_diff/math.sqrt(2),
+                            'height':0.005*max_diff,
+                            'angle':180*atan((y2-y1)/(x2-x1))/pi,
+                            'color':'brown'
+                        }
+                    )
+                else:
+                    member_rectangles.append(
+                        {
+                            'xy':(x2-0.005*max_diff*cos(pi/4+atan((y2-y1)/(x2-x1)))/2, y2-0.005*max_diff*sin(pi/4+atan((y2-y1)/(x2-x1)))/2),
+                            'width':sqrt((x1-x2)**2+(y1-y2)**2)+0.005*max_diff/math.sqrt(2),
+                            'height':0.005*max_diff,
+                            'angle':180*atan((y2-y1)/(x2-x1))/pi,
+                            'color':'brown'
+                        }
+                    )
+            elif y2==y1:
+                if x2>x1:
+                    member_rectangles.append(
+                        {
+                            'xy':(x1-0.005*max_diff/2, y1-0.005*max_diff/2),
+                            'width':sqrt((x1-x2)**2+(y1-y2)**2),
+                            'height':0.005*max_diff,
+                            'angle':90*(1-math.copysign(1, x2-x1)),
+                            'color':'brown'
+                        }
+                    )
+                else:
+                    member_rectangles.append(
+                        {
+                            'xy':(x1-0.005*max_diff/2, y1-0.005*max_diff/2),
+                            'width':sqrt((x1-x2)**2+(y1-y2)**2),
+                            'height':-0.005*max_diff,
+                            'angle':90*(1-math.copysign(1, x2-x1)),
+                            'color':'brown'
+                        }
+                    )
+            else:
+                if y1<y2:
+                    member_rectangles.append(
+                        {
+                            'xy':(x1-0.005*max_diff/2, y1-0.005*max_diff/2),
+                            'width':sqrt((x1-x2)**2+(y1-y2)**2)+0.005*max_diff/2,
+                            'height':0.005*max_diff,
+                            'angle':90*math.copysign(1, y2-y1),
+                            'color':'brown'
+                        }
+                    )
+                else:
+                    member_rectangles.append(
+                        {
+                            'xy':(x2-0.005*max_diff/2, y2-0.005*max_diff/2),
+                            'width':-(sqrt((x1-x2)**2+(y1-y2)**2)+0.005*max_diff/2),
+                            'height':0.005*max_diff,
+                            'angle':90*math.copysign(1, y2-y1),
+                            'color':'brown'
+                        }
+                    )
+
+        return member_rectangles
+
+    def _draw_supports(self):
+        support_markers = []
+
+        xmax = -INF
+        xmin = INF
+        ymax = -INF
+        ymin = INF
+
+        for node in self._node_coordinates:
+            xmax = max(xmax, self._node_coordinates[node][0])
+            xmin = min(xmin, self._node_coordinates[node][0])
+            ymax = max(ymax, self._node_coordinates[node][1])
+            ymin = min(ymin, self._node_coordinates[node][1])
+        if abs(1.1*xmax-0.8*xmin)>abs(1.1*ymax-0.8*ymin):
+            max_diff = 1.1*xmax-0.8*xmin
+        else:
+            max_diff = 1.1*ymax-0.8*ymin
+
+        for node in self._supports:
+            if self._supports[node]=='pinned':
+                support_markers.append(
+                    {
+                        'args':[
+                            [self._node_coordinates[node][0]],
+                            [self._node_coordinates[node][1]]
+                        ],
+                        'marker':6,
+                        'markersize':15,
+                        'color':'black',
+                        'markerfacecolor':'none'
+                    }
+                )
+                support_markers.append(
+                    {
+                        'args':[
+                            [self._node_coordinates[node][0]],
+                            [self._node_coordinates[node][1]-0.035*max_diff]
+                        ],
+                        'marker':'_',
+                        'markersize':14,
+                        'color':'black'
+                    }
+                )
+
+            elif self._supports[node]=='roller':
+                support_markers.append(
+                    {
+                        'args':[
+                            [self._node_coordinates[node][0]],
+                            [self._node_coordinates[node][1]-0.02*max_diff]
+                        ],
+                        'marker':'o',
+                        'markersize':11,
+                        'color':'black',
+                        'markerfacecolor':'none'
+                    }
+                )
+                support_markers.append(
+                    {
+                        'args':[
+                            [self._node_coordinates[node][0]],
+                            [self._node_coordinates[node][1]-0.0375*max_diff]
+                        ],
+                        'marker':'_',
+                        'markersize':14,
+                        'color':'black'
+                    }
+                )
+        return support_markers
+
+    def _draw_loads(self):
+        load_annotations = []
+
+        xmax = -INF
+        xmin = INF
+        ymax = -INF
+        ymin = INF
+
+        for node in self._node_coordinates:
+            xmax = max(xmax, self._node_coordinates[node][0])
+            xmin = min(xmin, self._node_coordinates[node][0])
+            ymax = max(ymax, self._node_coordinates[node][1])
+            ymin = min(ymin, self._node_coordinates[node][1])
+
+        if abs(1.1*xmax-0.8*xmin)>abs(1.1*ymax-0.8*ymin):
+            max_diff = 1.1*xmax-0.8*xmin+5
+        else:
+            max_diff = 1.1*ymax-0.8*ymin+5
+
+        for node in self._loads:
+            for load in self._loads[node]:
+                if load[0] in [Symbol('R_'+str(node)+'_x'), Symbol('R_'+str(node)+'_y')]:
+                    continue
+                x = self._node_coordinates[node][0]
+                y = self._node_coordinates[node][1]
+                load_annotations.append(
+                    {
+                        'text':'',
+                        'xy':(
+                            x-math.cos(pi*load[1]/180)*(max_diff/100),
+                            y-math.sin(pi*load[1]/180)*(max_diff/100)
+                        ),
+                        'xytext':(
+                            x-(max_diff/100+abs(xmax-xmin)+abs(ymax-ymin))*math.cos(pi*load[1]/180)/20,
+                            y-(max_diff/100+abs(xmax-xmin)+abs(ymax-ymin))*math.sin(pi*load[1]/180)/20
+                        ),
+                        'arrowprops':{'width':1.5, 'headlength':5, 'headwidth':5, 'facecolor':'black'}
+                    }
+                )
+        return load_annotations
diff --git a/parrot/lib/python3.10/site-packages/sympy/physics/control/__init__.py b/parrot/lib/python3.10/site-packages/sympy/physics/control/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..fb8c13ff147b3603466c8c4b2d9c8c0b25e3b360
--- /dev/null
+++ b/parrot/lib/python3.10/site-packages/sympy/physics/control/__init__.py
@@ -0,0 +1,16 @@
+from .lti import (TransferFunction, Series, MIMOSeries, Parallel, MIMOParallel,
+    Feedback, MIMOFeedback, TransferFunctionMatrix, StateSpace, gbt, bilinear, forward_diff,
+    backward_diff, phase_margin, gain_margin)
+from .control_plots import (pole_zero_numerical_data, pole_zero_plot, step_response_numerical_data,
+    step_response_plot, impulse_response_numerical_data, impulse_response_plot, ramp_response_numerical_data,
+    ramp_response_plot, bode_magnitude_numerical_data, bode_phase_numerical_data, bode_magnitude_plot,
+    bode_phase_plot, bode_plot)
+
+__all__ = ['TransferFunction', 'Series', 'MIMOSeries', 'Parallel',
+    'MIMOParallel', 'Feedback', 'MIMOFeedback', 'TransferFunctionMatrix', 'StateSpace',
+    'gbt', 'bilinear', 'forward_diff', 'backward_diff', 'phase_margin', 'gain_margin',
+    'pole_zero_numerical_data', 'pole_zero_plot', 'step_response_numerical_data',
+    'step_response_plot', 'impulse_response_numerical_data', 'impulse_response_plot',
+    'ramp_response_numerical_data', 'ramp_response_plot',
+    'bode_magnitude_numerical_data', 'bode_phase_numerical_data',
+    'bode_magnitude_plot', 'bode_phase_plot', 'bode_plot']
diff --git a/parrot/lib/python3.10/site-packages/sympy/physics/control/__pycache__/__init__.cpython-310.pyc b/parrot/lib/python3.10/site-packages/sympy/physics/control/__pycache__/__init__.cpython-310.pyc
new file mode 100644
index 0000000000000000000000000000000000000000..db43080a0a6404fb4531e9e0c20dc11bc1c1268f
Binary files /dev/null and b/parrot/lib/python3.10/site-packages/sympy/physics/control/__pycache__/__init__.cpython-310.pyc differ
diff --git a/parrot/lib/python3.10/site-packages/sympy/physics/control/__pycache__/control_plots.cpython-310.pyc b/parrot/lib/python3.10/site-packages/sympy/physics/control/__pycache__/control_plots.cpython-310.pyc
new file mode 100644
index 0000000000000000000000000000000000000000..c2dabe927ddff430aff9255e8a144d889c8eea06
Binary files /dev/null and b/parrot/lib/python3.10/site-packages/sympy/physics/control/__pycache__/control_plots.cpython-310.pyc differ
diff --git a/parrot/lib/python3.10/site-packages/sympy/physics/control/control_plots.py b/parrot/lib/python3.10/site-packages/sympy/physics/control/control_plots.py
new file mode 100644
index 0000000000000000000000000000000000000000..3742de329e61a84ff604accaced369261bc4befe
--- /dev/null
+++ b/parrot/lib/python3.10/site-packages/sympy/physics/control/control_plots.py
@@ -0,0 +1,978 @@
+from sympy.core.numbers import I, pi
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.polys.partfrac import apart
+from sympy.core.symbol import Dummy
+from sympy.external import import_module
+from sympy.functions import arg, Abs
+from sympy.integrals.laplace import _fast_inverse_laplace
+from sympy.physics.control.lti import SISOLinearTimeInvariant
+from sympy.plotting.series import LineOver1DRangeSeries
+from sympy.polys.polytools import Poly
+from sympy.printing.latex import latex
+
+__all__ = ['pole_zero_numerical_data', 'pole_zero_plot',
+    'step_response_numerical_data', 'step_response_plot',
+    'impulse_response_numerical_data', 'impulse_response_plot',
+    'ramp_response_numerical_data', 'ramp_response_plot',
+    'bode_magnitude_numerical_data', 'bode_phase_numerical_data',
+    'bode_magnitude_plot', 'bode_phase_plot', 'bode_plot']
+
+matplotlib = import_module(
+        'matplotlib', import_kwargs={'fromlist': ['pyplot']},
+        catch=(RuntimeError,))
+
+numpy = import_module('numpy')
+
+if matplotlib:
+    plt = matplotlib.pyplot
+
+if numpy:
+    np = numpy  # Matplotlib already has numpy as a compulsory dependency. No need to install it separately.
+
+
+def _check_system(system):
+    """Function to check whether the dynamical system passed for plots is
+    compatible or not."""
+    if not isinstance(system, SISOLinearTimeInvariant):
+        raise NotImplementedError("Only SISO LTI systems are currently supported.")
+    sys = system.to_expr()
+    len_free_symbols = len(sys.free_symbols)
+    if len_free_symbols > 1:
+        raise ValueError("Extra degree of freedom found. Make sure"
+            " that there are no free symbols in the dynamical system other"
+            " than the variable of Laplace transform.")
+    if sys.has(exp):
+        # Should test that exp is not part of a constant, in which case
+        # no exception is required, compare exp(s) with s*exp(1)
+        raise NotImplementedError("Time delay terms are not supported.")
+
+
+def pole_zero_numerical_data(system):
+    """
+    Returns the numerical data of poles and zeros of the system.
+    It is internally used by ``pole_zero_plot`` to get the data
+    for plotting poles and zeros. Users can use this data to further
+    analyse the dynamics of the system or plot using a different
+    backend/plotting-module.
+
+    Parameters
+    ==========
+
+    system : SISOLinearTimeInvariant
+        The system for which the pole-zero data is to be computed.
+
+    Returns
+    =======
+
+    tuple : (zeros, poles)
+        zeros = Zeros of the system. NumPy array of complex numbers.
+        poles = Poles of the system. NumPy array of complex numbers.
+
+    Raises
+    ======
+
+    NotImplementedError
+        When a SISO LTI system is not passed.
+
+        When time delay terms are present in the system.
+
+    ValueError
+        When more than one free symbol is present in the system.
+        The only variable in the transfer function should be
+        the variable of the Laplace transform.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import s
+    >>> from sympy.physics.control.lti import TransferFunction
+    >>> from sympy.physics.control.control_plots import pole_zero_numerical_data
+    >>> tf1 = TransferFunction(s**2 + 1, s**4 + 4*s**3 + 6*s**2 + 5*s + 2, s)
+    >>> pole_zero_numerical_data(tf1)   # doctest: +SKIP
+    ([-0.+1.j  0.-1.j], [-2. +0.j        -0.5+0.8660254j -0.5-0.8660254j -1. +0.j       ])
+
+    See Also
+    ========
+
+    pole_zero_plot
+
+    """
+    _check_system(system)
+    system = system.doit()  # Get the equivalent TransferFunction object.
+
+    num_poly = Poly(system.num, system.var).all_coeffs()
+    den_poly = Poly(system.den, system.var).all_coeffs()
+
+    num_poly = np.array(num_poly, dtype=np.complex128)
+    den_poly = np.array(den_poly, dtype=np.complex128)
+
+    zeros = np.roots(num_poly)
+    poles = np.roots(den_poly)
+
+    return zeros, poles
+
+
+def pole_zero_plot(system, pole_color='blue', pole_markersize=10,
+    zero_color='orange', zero_markersize=7, grid=True, show_axes=True,
+    show=True, **kwargs):
+    r"""
+    Returns the Pole-Zero plot (also known as PZ Plot or PZ Map) of a system.
+
+    A Pole-Zero plot is a graphical representation of a system's poles and
+    zeros. It is plotted on a complex plane, with circular markers representing
+    the system's zeros and 'x' shaped markers representing the system's poles.
+
+    Parameters
+    ==========
+
+    system : SISOLinearTimeInvariant type systems
+        The system for which the pole-zero plot is to be computed.
+    pole_color : str, tuple, optional
+        The color of the pole points on the plot. Default color
+        is blue. The color can be provided as a matplotlib color string,
+        or a 3-tuple of floats each in the 0-1 range.
+    pole_markersize : Number, optional
+        The size of the markers used to mark the poles in the plot.
+        Default pole markersize is 10.
+    zero_color : str, tuple, optional
+        The color of the zero points on the plot. Default color
+        is orange. The color can be provided as a matplotlib color string,
+        or a 3-tuple of floats each in the 0-1 range.
+    zero_markersize : Number, optional
+        The size of the markers used to mark the zeros in the plot.
+        Default zero markersize is 7.
+    grid : boolean, optional
+        If ``True``, the plot will have a grid. Defaults to True.
+    show_axes : boolean, optional
+        If ``True``, the coordinate axes will be shown. Defaults to False.
+    show : boolean, optional
+        If ``True``, the plot will be displayed otherwise
+        the equivalent matplotlib ``plot`` object will be returned.
+        Defaults to True.
+
+    Examples
+    ========
+
+    .. plot::
+        :context: close-figs
+        :format: doctest
+        :include-source: True
+
+        >>> from sympy.abc import s
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> from sympy.physics.control.control_plots import pole_zero_plot
+        >>> tf1 = TransferFunction(s**2 + 1, s**4 + 4*s**3 + 6*s**2 + 5*s + 2, s)
+        >>> pole_zero_plot(tf1)   # doctest: +SKIP
+
+    See Also
+    ========
+
+    pole_zero_numerical_data
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Pole%E2%80%93zero_plot
+
+    """
+    zeros, poles = pole_zero_numerical_data(system)
+
+    zero_real = np.real(zeros)
+    zero_imag = np.imag(zeros)
+
+    pole_real = np.real(poles)
+    pole_imag = np.imag(poles)
+
+    plt.plot(pole_real, pole_imag, 'x', mfc='none',
+        markersize=pole_markersize, color=pole_color)
+    plt.plot(zero_real, zero_imag, 'o', markersize=zero_markersize,
+        color=zero_color)
+    plt.xlabel('Real Axis')
+    plt.ylabel('Imaginary Axis')
+    plt.title(f'Poles and Zeros of ${latex(system)}$', pad=20)
+
+    if grid:
+        plt.grid()
+    if show_axes:
+        plt.axhline(0, color='black')
+        plt.axvline(0, color='black')
+    if show:
+        plt.show()
+        return
+
+    return plt
+
+
+def step_response_numerical_data(system, prec=8, lower_limit=0,
+    upper_limit=10, **kwargs):
+    """
+    Returns the numerical values of the points in the step response plot
+    of a SISO continuous-time system. By default, adaptive sampling
+    is used. If the user wants to instead get an uniformly
+    sampled response, then ``adaptive`` kwarg should be passed ``False``
+    and ``n`` must be passed as additional kwargs.
+    Refer to the parameters of class :class:`sympy.plotting.series.LineOver1DRangeSeries`
+    for more details.
+
+    Parameters
+    ==========
+
+    system : SISOLinearTimeInvariant
+        The system for which the unit step response data is to be computed.
+    prec : int, optional
+        The decimal point precision for the point coordinate values.
+        Defaults to 8.
+    lower_limit : Number, optional
+        The lower limit of the plot range. Defaults to 0.
+    upper_limit : Number, optional
+        The upper limit of the plot range. Defaults to 10.
+    kwargs :
+        Additional keyword arguments are passed to the underlying
+        :class:`sympy.plotting.series.LineOver1DRangeSeries` class.
+
+    Returns
+    =======
+
+    tuple : (x, y)
+        x = Time-axis values of the points in the step response. NumPy array.
+        y = Amplitude-axis values of the points in the step response. NumPy array.
+
+    Raises
+    ======
+
+    NotImplementedError
+        When a SISO LTI system is not passed.
+
+        When time delay terms are present in the system.
+
+    ValueError
+        When more than one free symbol is present in the system.
+        The only variable in the transfer function should be
+        the variable of the Laplace transform.
+
+        When ``lower_limit`` parameter is less than 0.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import s
+    >>> from sympy.physics.control.lti import TransferFunction
+    >>> from sympy.physics.control.control_plots import step_response_numerical_data
+    >>> tf1 = TransferFunction(s, s**2 + 5*s + 8, s)
+    >>> step_response_numerical_data(tf1)   # doctest: +SKIP
+    ([0.0, 0.025413462339411542, 0.0484508722725343, ... , 9.670250533855183, 9.844291913708725, 10.0],
+    [0.0, 0.023844582399907256, 0.042894276802320226, ..., 6.828770759094287e-12, 6.456457160755703e-12])
+
+    See Also
+    ========
+
+    step_response_plot
+
+    """
+    if lower_limit < 0:
+        raise ValueError("Lower limit of time must be greater "
+            "than or equal to zero.")
+    _check_system(system)
+    _x = Dummy("x")
+    expr = system.to_expr()/(system.var)
+    expr = apart(expr, system.var, full=True)
+    _y = _fast_inverse_laplace(expr, system.var, _x).evalf(prec)
+    return LineOver1DRangeSeries(_y, (_x, lower_limit, upper_limit),
+        **kwargs).get_points()
+
+
+def step_response_plot(system, color='b', prec=8, lower_limit=0,
+    upper_limit=10, show_axes=False, grid=True, show=True, **kwargs):
+    r"""
+    Returns the unit step response of a continuous-time system. It is
+    the response of the system when the input signal is a step function.
+
+    Parameters
+    ==========
+
+    system : SISOLinearTimeInvariant type
+        The LTI SISO system for which the Step Response is to be computed.
+    color : str, tuple, optional
+        The color of the line. Default is Blue.
+    show : boolean, optional
+        If ``True``, the plot will be displayed otherwise
+        the equivalent matplotlib ``plot`` object will be returned.
+        Defaults to True.
+    lower_limit : Number, optional
+        The lower limit of the plot range. Defaults to 0.
+    upper_limit : Number, optional
+        The upper limit of the plot range. Defaults to 10.
+    prec : int, optional
+        The decimal point precision for the point coordinate values.
+        Defaults to 8.
+    show_axes : boolean, optional
+        If ``True``, the coordinate axes will be shown. Defaults to False.
+    grid : boolean, optional
+        If ``True``, the plot will have a grid. Defaults to True.
+
+    Examples
+    ========
+
+    .. plot::
+        :context: close-figs
+        :format: doctest
+        :include-source: True
+
+        >>> from sympy.abc import s
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> from sympy.physics.control.control_plots import step_response_plot
+        >>> tf1 = TransferFunction(8*s**2 + 18*s + 32, s**3 + 6*s**2 + 14*s + 24, s)
+        >>> step_response_plot(tf1)   # doctest: +SKIP
+
+    See Also
+    ========
+
+    impulse_response_plot, ramp_response_plot
+
+    References
+    ==========
+
+    .. [1] https://www.mathworks.com/help/control/ref/lti.step.html
+
+    """
+    x, y = step_response_numerical_data(system, prec=prec,
+        lower_limit=lower_limit, upper_limit=upper_limit, **kwargs)
+    plt.plot(x, y, color=color)
+    plt.xlabel('Time (s)')
+    plt.ylabel('Amplitude')
+    plt.title(f'Unit Step Response of ${latex(system)}$', pad=20)
+
+    if grid:
+        plt.grid()
+    if show_axes:
+        plt.axhline(0, color='black')
+        plt.axvline(0, color='black')
+    if show:
+        plt.show()
+        return
+
+    return plt
+
+
+def impulse_response_numerical_data(system, prec=8, lower_limit=0,
+    upper_limit=10, **kwargs):
+    """
+    Returns the numerical values of the points in the impulse response plot
+    of a SISO continuous-time system. By default, adaptive sampling
+    is used. If the user wants to instead get an uniformly
+    sampled response, then ``adaptive`` kwarg should be passed ``False``
+    and ``n`` must be passed as additional kwargs.
+    Refer to the parameters of class :class:`sympy.plotting.series.LineOver1DRangeSeries`
+    for more details.
+
+    Parameters
+    ==========
+
+    system : SISOLinearTimeInvariant
+        The system for which the impulse response data is to be computed.
+    prec : int, optional
+        The decimal point precision for the point coordinate values.
+        Defaults to 8.
+    lower_limit : Number, optional
+        The lower limit of the plot range. Defaults to 0.
+    upper_limit : Number, optional
+        The upper limit of the plot range. Defaults to 10.
+    kwargs :
+        Additional keyword arguments are passed to the underlying
+        :class:`sympy.plotting.series.LineOver1DRangeSeries` class.
+
+    Returns
+    =======
+
+    tuple : (x, y)
+        x = Time-axis values of the points in the impulse response. NumPy array.
+        y = Amplitude-axis values of the points in the impulse response. NumPy array.
+
+    Raises
+    ======
+
+    NotImplementedError
+        When a SISO LTI system is not passed.
+
+        When time delay terms are present in the system.
+
+    ValueError
+        When more than one free symbol is present in the system.
+        The only variable in the transfer function should be
+        the variable of the Laplace transform.
+
+        When ``lower_limit`` parameter is less than 0.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import s
+    >>> from sympy.physics.control.lti import TransferFunction
+    >>> from sympy.physics.control.control_plots import impulse_response_numerical_data
+    >>> tf1 = TransferFunction(s, s**2 + 5*s + 8, s)
+    >>> impulse_response_numerical_data(tf1)   # doctest: +SKIP
+    ([0.0, 0.06616480200395854,... , 9.854500743565858, 10.0],
+    [0.9999999799999999, 0.7042848373025861,...,7.170748906965121e-13, -5.1901263495547205e-12])
+
+    See Also
+    ========
+
+    impulse_response_plot
+
+    """
+    if lower_limit < 0:
+        raise ValueError("Lower limit of time must be greater "
+            "than or equal to zero.")
+    _check_system(system)
+    _x = Dummy("x")
+    expr = system.to_expr()
+    expr = apart(expr, system.var, full=True)
+    _y = _fast_inverse_laplace(expr, system.var, _x).evalf(prec)
+    return LineOver1DRangeSeries(_y, (_x, lower_limit, upper_limit),
+        **kwargs).get_points()
+
+
+def impulse_response_plot(system, color='b', prec=8, lower_limit=0,
+    upper_limit=10, show_axes=False, grid=True, show=True, **kwargs):
+    r"""
+    Returns the unit impulse response (Input is the Dirac-Delta Function) of a
+    continuous-time system.
+
+    Parameters
+    ==========
+
+    system : SISOLinearTimeInvariant type
+        The LTI SISO system for which the Impulse Response is to be computed.
+    color : str, tuple, optional
+        The color of the line. Default is Blue.
+    show : boolean, optional
+        If ``True``, the plot will be displayed otherwise
+        the equivalent matplotlib ``plot`` object will be returned.
+        Defaults to True.
+    lower_limit : Number, optional
+        The lower limit of the plot range. Defaults to 0.
+    upper_limit : Number, optional
+        The upper limit of the plot range. Defaults to 10.
+    prec : int, optional
+        The decimal point precision for the point coordinate values.
+        Defaults to 8.
+    show_axes : boolean, optional
+        If ``True``, the coordinate axes will be shown. Defaults to False.
+    grid : boolean, optional
+        If ``True``, the plot will have a grid. Defaults to True.
+
+    Examples
+    ========
+
+    .. plot::
+        :context: close-figs
+        :format: doctest
+        :include-source: True
+
+        >>> from sympy.abc import s
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> from sympy.physics.control.control_plots import impulse_response_plot
+        >>> tf1 = TransferFunction(8*s**2 + 18*s + 32, s**3 + 6*s**2 + 14*s + 24, s)
+        >>> impulse_response_plot(tf1)   # doctest: +SKIP
+
+    See Also
+    ========
+
+    step_response_plot, ramp_response_plot
+
+    References
+    ==========
+
+    .. [1] https://www.mathworks.com/help/control/ref/dynamicsystem.impulse.html
+
+    """
+    x, y = impulse_response_numerical_data(system, prec=prec,
+        lower_limit=lower_limit, upper_limit=upper_limit, **kwargs)
+    plt.plot(x, y, color=color)
+    plt.xlabel('Time (s)')
+    plt.ylabel('Amplitude')
+    plt.title(f'Impulse Response of ${latex(system)}$', pad=20)
+
+    if grid:
+        plt.grid()
+    if show_axes:
+        plt.axhline(0, color='black')
+        plt.axvline(0, color='black')
+    if show:
+        plt.show()
+        return
+
+    return plt
+
+
+def ramp_response_numerical_data(system, slope=1, prec=8,
+    lower_limit=0, upper_limit=10, **kwargs):
+    """
+    Returns the numerical values of the points in the ramp response plot
+    of a SISO continuous-time system. By default, adaptive sampling
+    is used. If the user wants to instead get an uniformly
+    sampled response, then ``adaptive`` kwarg should be passed ``False``
+    and ``n`` must be passed as additional kwargs.
+    Refer to the parameters of class :class:`sympy.plotting.series.LineOver1DRangeSeries`
+    for more details.
+
+    Parameters
+    ==========
+
+    system : SISOLinearTimeInvariant
+        The system for which the ramp response data is to be computed.
+    slope : Number, optional
+        The slope of the input ramp function. Defaults to 1.
+    prec : int, optional
+        The decimal point precision for the point coordinate values.
+        Defaults to 8.
+    lower_limit : Number, optional
+        The lower limit of the plot range. Defaults to 0.
+    upper_limit : Number, optional
+        The upper limit of the plot range. Defaults to 10.
+    kwargs :
+        Additional keyword arguments are passed to the underlying
+        :class:`sympy.plotting.series.LineOver1DRangeSeries` class.
+
+    Returns
+    =======
+
+    tuple : (x, y)
+        x = Time-axis values of the points in the ramp response plot. NumPy array.
+        y = Amplitude-axis values of the points in the ramp response plot. NumPy array.
+
+    Raises
+    ======
+
+    NotImplementedError
+        When a SISO LTI system is not passed.
+
+        When time delay terms are present in the system.
+
+    ValueError
+        When more than one free symbol is present in the system.
+        The only variable in the transfer function should be
+        the variable of the Laplace transform.
+
+        When ``lower_limit`` parameter is less than 0.
+
+        When ``slope`` is negative.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import s
+    >>> from sympy.physics.control.lti import TransferFunction
+    >>> from sympy.physics.control.control_plots import ramp_response_numerical_data
+    >>> tf1 = TransferFunction(s, s**2 + 5*s + 8, s)
+    >>> ramp_response_numerical_data(tf1)   # doctest: +SKIP
+    (([0.0, 0.12166980856813935,..., 9.861246379582118, 10.0],
+    [1.4504508011325967e-09, 0.006046440489058766,..., 0.12499999999568202, 0.12499999999661349]))
+
+    See Also
+    ========
+
+    ramp_response_plot
+
+    """
+    if slope < 0:
+        raise ValueError("Slope must be greater than or equal"
+            " to zero.")
+    if lower_limit < 0:
+        raise ValueError("Lower limit of time must be greater "
+            "than or equal to zero.")
+    _check_system(system)
+    _x = Dummy("x")
+    expr = (slope*system.to_expr())/((system.var)**2)
+    expr = apart(expr, system.var, full=True)
+    _y = _fast_inverse_laplace(expr, system.var, _x).evalf(prec)
+    return LineOver1DRangeSeries(_y, (_x, lower_limit, upper_limit),
+        **kwargs).get_points()
+
+
+def ramp_response_plot(system, slope=1, color='b', prec=8, lower_limit=0,
+    upper_limit=10, show_axes=False, grid=True, show=True, **kwargs):
+    r"""
+    Returns the ramp response of a continuous-time system.
+
+    Ramp function is defined as the straight line
+    passing through origin ($f(x) = mx$). The slope of
+    the ramp function can be varied by the user and
+    the default value is 1.
+
+    Parameters
+    ==========
+
+    system : SISOLinearTimeInvariant type
+        The LTI SISO system for which the Ramp Response is to be computed.
+    slope : Number, optional
+        The slope of the input ramp function. Defaults to 1.
+    color : str, tuple, optional
+        The color of the line. Default is Blue.
+    show : boolean, optional
+        If ``True``, the plot will be displayed otherwise
+        the equivalent matplotlib ``plot`` object will be returned.
+        Defaults to True.
+    lower_limit : Number, optional
+        The lower limit of the plot range. Defaults to 0.
+    upper_limit : Number, optional
+        The upper limit of the plot range. Defaults to 10.
+    prec : int, optional
+        The decimal point precision for the point coordinate values.
+        Defaults to 8.
+    show_axes : boolean, optional
+        If ``True``, the coordinate axes will be shown. Defaults to False.
+    grid : boolean, optional
+        If ``True``, the plot will have a grid. Defaults to True.
+
+    Examples
+    ========
+
+    .. plot::
+        :context: close-figs
+        :format: doctest
+        :include-source: True
+
+        >>> from sympy.abc import s
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> from sympy.physics.control.control_plots import ramp_response_plot
+        >>> tf1 = TransferFunction(s, (s+4)*(s+8), s)
+        >>> ramp_response_plot(tf1, upper_limit=2)   # doctest: +SKIP
+
+    See Also
+    ========
+
+    step_response_plot, impulse_response_plot
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Ramp_function
+
+    """
+    x, y = ramp_response_numerical_data(system, slope=slope, prec=prec,
+        lower_limit=lower_limit, upper_limit=upper_limit, **kwargs)
+    plt.plot(x, y, color=color)
+    plt.xlabel('Time (s)')
+    plt.ylabel('Amplitude')
+    plt.title(f'Ramp Response of ${latex(system)}$ [Slope = {slope}]', pad=20)
+
+    if grid:
+        plt.grid()
+    if show_axes:
+        plt.axhline(0, color='black')
+        plt.axvline(0, color='black')
+    if show:
+        plt.show()
+        return
+
+    return plt
+
+
+def bode_magnitude_numerical_data(system, initial_exp=-5, final_exp=5, freq_unit='rad/sec', **kwargs):
+    """
+    Returns the numerical data of the Bode magnitude plot of the system.
+    It is internally used by ``bode_magnitude_plot`` to get the data
+    for plotting Bode magnitude plot. Users can use this data to further
+    analyse the dynamics of the system or plot using a different
+    backend/plotting-module.
+
+    Parameters
+    ==========
+
+    system : SISOLinearTimeInvariant
+        The system for which the data is to be computed.
+    initial_exp : Number, optional
+        The initial exponent of 10 of the semilog plot. Defaults to -5.
+    final_exp : Number, optional
+        The final exponent of 10 of the semilog plot. Defaults to 5.
+    freq_unit : string, optional
+        User can choose between ``'rad/sec'`` (radians/second) and ``'Hz'`` (Hertz) as frequency units.
+
+    Returns
+    =======
+
+    tuple : (x, y)
+        x = x-axis values of the Bode magnitude plot.
+        y = y-axis values of the Bode magnitude plot.
+
+    Raises
+    ======
+
+    NotImplementedError
+        When a SISO LTI system is not passed.
+
+        When time delay terms are present in the system.
+
+    ValueError
+        When more than one free symbol is present in the system.
+        The only variable in the transfer function should be
+        the variable of the Laplace transform.
+
+        When incorrect frequency units are given as input.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import s
+    >>> from sympy.physics.control.lti import TransferFunction
+    >>> from sympy.physics.control.control_plots import bode_magnitude_numerical_data
+    >>> tf1 = TransferFunction(s**2 + 1, s**4 + 4*s**3 + 6*s**2 + 5*s + 2, s)
+    >>> bode_magnitude_numerical_data(tf1)   # doctest: +SKIP
+    ([1e-05, 1.5148378120533502e-05,..., 68437.36188804005, 100000.0],
+    [-6.020599914256786, -6.0205999155219505,..., -193.4117304087953, -200.00000000260573])
+
+    See Also
+    ========
+
+    bode_magnitude_plot, bode_phase_numerical_data
+
+    """
+    _check_system(system)
+    expr = system.to_expr()
+    freq_units = ('rad/sec', 'Hz')
+    if freq_unit not in freq_units:
+        raise ValueError('Only "rad/sec" and "Hz" are accepted frequency units.')
+
+    _w = Dummy("w", real=True)
+    if freq_unit == 'Hz':
+        repl = I*_w*2*pi
+    else:
+        repl = I*_w
+    w_expr = expr.subs({system.var: repl})
+
+    mag = 20*log(Abs(w_expr), 10)
+
+    x, y = LineOver1DRangeSeries(mag,
+        (_w, 10**initial_exp, 10**final_exp), xscale='log', **kwargs).get_points()
+
+    return x, y
+
+
+def bode_magnitude_plot(system, initial_exp=-5, final_exp=5,
+    color='b', show_axes=False, grid=True, show=True, freq_unit='rad/sec', **kwargs):
+    r"""
+    Returns the Bode magnitude plot of a continuous-time system.
+
+    See ``bode_plot`` for all the parameters.
+    """
+    x, y = bode_magnitude_numerical_data(system, initial_exp=initial_exp,
+        final_exp=final_exp, freq_unit=freq_unit)
+    plt.plot(x, y, color=color, **kwargs)
+    plt.xscale('log')
+
+
+    plt.xlabel('Frequency (%s) [Log Scale]' % freq_unit)
+    plt.ylabel('Magnitude (dB)')
+    plt.title(f'Bode Plot (Magnitude) of ${latex(system)}$', pad=20)
+
+    if grid:
+        plt.grid(True)
+    if show_axes:
+        plt.axhline(0, color='black')
+        plt.axvline(0, color='black')
+    if show:
+        plt.show()
+        return
+
+    return plt
+
+
+def bode_phase_numerical_data(system, initial_exp=-5, final_exp=5, freq_unit='rad/sec', phase_unit='rad', phase_unwrap = True, **kwargs):
+    """
+    Returns the numerical data of the Bode phase plot of the system.
+    It is internally used by ``bode_phase_plot`` to get the data
+    for plotting Bode phase plot. Users can use this data to further
+    analyse the dynamics of the system or plot using a different
+    backend/plotting-module.
+
+    Parameters
+    ==========
+
+    system : SISOLinearTimeInvariant
+        The system for which the Bode phase plot data is to be computed.
+    initial_exp : Number, optional
+        The initial exponent of 10 of the semilog plot. Defaults to -5.
+    final_exp : Number, optional
+        The final exponent of 10 of the semilog plot. Defaults to 5.
+    freq_unit : string, optional
+        User can choose between ``'rad/sec'`` (radians/second) and '``'Hz'`` (Hertz) as frequency units.
+    phase_unit : string, optional
+        User can choose between ``'rad'`` (radians) and ``'deg'`` (degree) as phase units.
+    phase_unwrap : bool, optional
+        Set to ``True`` by default.
+
+    Returns
+    =======
+
+    tuple : (x, y)
+        x = x-axis values of the Bode phase plot.
+        y = y-axis values of the Bode phase plot.
+
+    Raises
+    ======
+
+    NotImplementedError
+        When a SISO LTI system is not passed.
+
+        When time delay terms are present in the system.
+
+    ValueError
+        When more than one free symbol is present in the system.
+        The only variable in the transfer function should be
+        the variable of the Laplace transform.
+
+        When incorrect frequency or phase units are given as input.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import s
+    >>> from sympy.physics.control.lti import TransferFunction
+    >>> from sympy.physics.control.control_plots import bode_phase_numerical_data
+    >>> tf1 = TransferFunction(s**2 + 1, s**4 + 4*s**3 + 6*s**2 + 5*s + 2, s)
+    >>> bode_phase_numerical_data(tf1)   # doctest: +SKIP
+    ([1e-05, 1.4472354033813751e-05, 2.035581932165858e-05,..., 47577.3248186011, 67884.09326036123, 100000.0],
+    [-2.5000000000291665e-05, -3.6180885085e-05, -5.08895483066e-05,...,-3.1415085799262523, -3.14155265358979])
+
+    See Also
+    ========
+
+    bode_magnitude_plot, bode_phase_numerical_data
+
+    """
+    _check_system(system)
+    expr = system.to_expr()
+    freq_units = ('rad/sec', 'Hz')
+    phase_units = ('rad', 'deg')
+    if freq_unit not in freq_units:
+        raise ValueError('Only "rad/sec" and "Hz" are accepted frequency units.')
+    if phase_unit not in phase_units:
+        raise ValueError('Only "rad" and "deg" are accepted phase units.')
+
+    _w = Dummy("w", real=True)
+    if freq_unit == 'Hz':
+        repl = I*_w*2*pi
+    else:
+        repl = I*_w
+    w_expr = expr.subs({system.var: repl})
+
+    if phase_unit == 'deg':
+        phase = arg(w_expr)*180/pi
+    else:
+        phase = arg(w_expr)
+
+    x, y = LineOver1DRangeSeries(phase,
+        (_w, 10**initial_exp, 10**final_exp), xscale='log', **kwargs).get_points()
+
+    half = None
+    if phase_unwrap:
+        if(phase_unit == 'rad'):
+            half = pi
+        elif(phase_unit == 'deg'):
+            half = 180
+    if half:
+        unit = 2*half
+        for i in range(1, len(y)):
+            diff = y[i] - y[i - 1]
+            if diff > half:      # Jump from -half to half
+                y[i] = (y[i] - unit)
+            elif diff < -half:   # Jump from half to -half
+                y[i] = (y[i] + unit)
+
+    return x, y
+
+
+def bode_phase_plot(system, initial_exp=-5, final_exp=5,
+    color='b', show_axes=False, grid=True, show=True, freq_unit='rad/sec', phase_unit='rad', phase_unwrap=True, **kwargs):
+    r"""
+    Returns the Bode phase plot of a continuous-time system.
+
+    See ``bode_plot`` for all the parameters.
+    """
+    x, y = bode_phase_numerical_data(system, initial_exp=initial_exp,
+        final_exp=final_exp, freq_unit=freq_unit, phase_unit=phase_unit, phase_unwrap=phase_unwrap)
+    plt.plot(x, y, color=color, **kwargs)
+    plt.xscale('log')
+
+    plt.xlabel('Frequency (%s) [Log Scale]' % freq_unit)
+    plt.ylabel('Phase (%s)' % phase_unit)
+    plt.title(f'Bode Plot (Phase) of ${latex(system)}$', pad=20)
+
+    if grid:
+        plt.grid(True)
+    if show_axes:
+        plt.axhline(0, color='black')
+        plt.axvline(0, color='black')
+    if show:
+        plt.show()
+        return
+
+    return plt
+
+
+def bode_plot(system, initial_exp=-5, final_exp=5,
+    grid=True, show_axes=False, show=True, freq_unit='rad/sec', phase_unit='rad', phase_unwrap=True, **kwargs):
+    r"""
+    Returns the Bode phase and magnitude plots of a continuous-time system.
+
+    Parameters
+    ==========
+
+    system : SISOLinearTimeInvariant type
+        The LTI SISO system for which the Bode Plot is to be computed.
+    initial_exp : Number, optional
+        The initial exponent of 10 of the semilog plot. Defaults to -5.
+    final_exp : Number, optional
+        The final exponent of 10 of the semilog plot. Defaults to 5.
+    show : boolean, optional
+        If ``True``, the plot will be displayed otherwise
+        the equivalent matplotlib ``plot`` object will be returned.
+        Defaults to True.
+    prec : int, optional
+        The decimal point precision for the point coordinate values.
+        Defaults to 8.
+    grid : boolean, optional
+        If ``True``, the plot will have a grid. Defaults to True.
+    show_axes : boolean, optional
+        If ``True``, the coordinate axes will be shown. Defaults to False.
+    freq_unit : string, optional
+        User can choose between ``'rad/sec'`` (radians/second) and ``'Hz'`` (Hertz) as frequency units.
+    phase_unit : string, optional
+        User can choose between ``'rad'`` (radians) and ``'deg'`` (degree) as phase units.
+
+    Examples
+    ========
+
+    .. plot::
+        :context: close-figs
+        :format: doctest
+        :include-source: True
+
+        >>> from sympy.abc import s
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> from sympy.physics.control.control_plots import bode_plot
+        >>> tf1 = TransferFunction(1*s**2 + 0.1*s + 7.5, 1*s**4 + 0.12*s**3 + 9*s**2, s)
+        >>> bode_plot(tf1, initial_exp=0.2, final_exp=0.7)   # doctest: +SKIP
+
+    See Also
+    ========
+
+    bode_magnitude_plot, bode_phase_plot
+
+    """
+    plt.subplot(211)
+    mag = bode_magnitude_plot(system, initial_exp=initial_exp, final_exp=final_exp,
+        show=False, grid=grid, show_axes=show_axes,
+        freq_unit=freq_unit, **kwargs)
+    mag.title(f'Bode Plot of ${latex(system)}$', pad=20)
+    mag.xlabel(None)
+    plt.subplot(212)
+    bode_phase_plot(system, initial_exp=initial_exp, final_exp=final_exp,
+        show=False, grid=grid, show_axes=show_axes, freq_unit=freq_unit, phase_unit=phase_unit, phase_unwrap=phase_unwrap, **kwargs).title(None)
+
+    if show:
+        plt.show()
+        return
+
+    return plt
diff --git a/parrot/lib/python3.10/site-packages/sympy/physics/control/lti.py b/parrot/lib/python3.10/site-packages/sympy/physics/control/lti.py
new file mode 100644
index 0000000000000000000000000000000000000000..54349e50e087077435ed2fcdf01c2aed23f0edea
--- /dev/null
+++ b/parrot/lib/python3.10/site-packages/sympy/physics/control/lti.py
@@ -0,0 +1,4304 @@
+from typing import Type
+from sympy import Interval, numer, Rational, solveset
+from sympy.core.add import Add
+from sympy.core.basic import Basic
+from sympy.core.containers import Tuple
+from sympy.core.evalf import EvalfMixin
+from sympy.core.expr import Expr
+from sympy.core.function import expand
+from sympy.core.logic import fuzzy_and
+from sympy.core.mul import Mul
+from sympy.core.numbers import I, pi, oo
+from sympy.core.power import Pow
+from sympy.core.singleton import S
+from sympy.core.symbol import Dummy, Symbol
+from sympy.functions import Abs
+from sympy.core.sympify import sympify, _sympify
+from sympy.matrices import Matrix, ImmutableMatrix, ImmutableDenseMatrix, eye, ShapeError, zeros
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.matrices.expressions import MatMul, MatAdd
+from sympy.polys import Poly, rootof
+from sympy.polys.polyroots import roots
+from sympy.polys.polytools import (cancel, degree)
+from sympy.series import limit
+from sympy.utilities.misc import filldedent
+
+from mpmath.libmp.libmpf import prec_to_dps
+
+__all__ = ['TransferFunction', 'Series', 'MIMOSeries', 'Parallel', 'MIMOParallel',
+    'Feedback', 'MIMOFeedback', 'TransferFunctionMatrix', 'StateSpace', 'gbt', 'bilinear', 'forward_diff', 'backward_diff',
+    'phase_margin', 'gain_margin']
+
+def _roots(poly, var):
+    """ like roots, but works on higher-order polynomials. """
+    r = roots(poly, var, multiple=True)
+    n = degree(poly)
+    if len(r) != n:
+        r = [rootof(poly, var, k) for k in range(n)]
+    return r
+
+def gbt(tf, sample_per, alpha):
+    r"""
+    Returns falling coefficients of H(z) from numerator and denominator.
+
+    Explanation
+    ===========
+
+    Where H(z) is the corresponding discretized transfer function,
+    discretized with the generalised bilinear transformation method.
+    H(z) is obtained from the continuous transfer function H(s)
+    by substituting $s(z) = \frac{z-1}{T(\alpha z + (1-\alpha))}$ into H(s), where T is the
+    sample period.
+    Coefficients are falling, i.e. $H(z) = \frac{az+b}{cz+d}$ is returned
+    as [a, b], [c, d].
+
+    Examples
+    ========
+
+    >>> from sympy.physics.control.lti import TransferFunction, gbt
+    >>> from sympy.abc import s, L, R, T
+
+    >>> tf = TransferFunction(1, s*L + R, s)
+    >>> numZ, denZ = gbt(tf, T, 0.5)
+    >>> numZ
+    [T/(2*(L + R*T/2)), T/(2*(L + R*T/2))]
+    >>> denZ
+    [1, (-L + R*T/2)/(L + R*T/2)]
+
+    >>> numZ, denZ = gbt(tf, T, 0)
+    >>> numZ
+    [T/L]
+    >>> denZ
+    [1, (-L + R*T)/L]
+
+    >>> numZ, denZ = gbt(tf, T, 1)
+    >>> numZ
+    [T/(L + R*T), 0]
+    >>> denZ
+    [1, -L/(L + R*T)]
+
+    >>> numZ, denZ = gbt(tf, T, 0.3)
+    >>> numZ
+    [3*T/(10*(L + 3*R*T/10)), 7*T/(10*(L + 3*R*T/10))]
+    >>> denZ
+    [1, (-L + 7*R*T/10)/(L + 3*R*T/10)]
+
+    References
+    ==========
+
+    .. [1] https://www.polyu.edu.hk/ama/profile/gfzhang/Research/ZCC09_IJC.pdf
+    """
+    if not tf.is_SISO:
+        raise NotImplementedError("Not implemented for MIMO systems.")
+
+    T = sample_per  # and sample period T
+    s = tf.var
+    z =  s         # dummy discrete variable z
+
+    np = tf.num.as_poly(s).all_coeffs()
+    dp = tf.den.as_poly(s).all_coeffs()
+    alpha = Rational(alpha).limit_denominator(1000)
+
+    # The next line results from multiplying H(z) with z^N/z^N
+    N = max(len(np), len(dp)) - 1
+    num = Add(*[ T**(N-i) * c * (z-1)**i * (alpha * z + 1 - alpha)**(N-i) for c, i in zip(np[::-1], range(len(np))) ])
+    den = Add(*[ T**(N-i) * c * (z-1)**i * (alpha * z + 1 - alpha)**(N-i) for c, i in zip(dp[::-1], range(len(dp))) ])
+
+    num_coefs = num.as_poly(z).all_coeffs()
+    den_coefs = den.as_poly(z).all_coeffs()
+
+    para = den_coefs[0]
+    num_coefs = [coef/para for coef in num_coefs]
+    den_coefs = [coef/para for coef in den_coefs]
+
+    return num_coefs, den_coefs
+
+def bilinear(tf, sample_per):
+    r"""
+    Returns falling coefficients of H(z) from numerator and denominator.
+
+    Explanation
+    ===========
+
+    Where H(z) is the corresponding discretized transfer function,
+    discretized with the bilinear transform method.
+    H(z) is obtained from the continuous transfer function H(s)
+    by substituting $s(z) = \frac{2}{T}\frac{z-1}{z+1}$ into H(s), where T is the
+    sample period.
+    Coefficients are falling, i.e. $H(z) = \frac{az+b}{cz+d}$ is returned
+    as [a, b], [c, d].
+
+    Examples
+    ========
+
+    >>> from sympy.physics.control.lti import TransferFunction, bilinear
+    >>> from sympy.abc import s, L, R, T
+
+    >>> tf = TransferFunction(1, s*L + R, s)
+    >>> numZ, denZ = bilinear(tf, T)
+    >>> numZ
+    [T/(2*(L + R*T/2)), T/(2*(L + R*T/2))]
+    >>> denZ
+    [1, (-L + R*T/2)/(L + R*T/2)]
+    """
+    return gbt(tf, sample_per, S.Half)
+
+def forward_diff(tf, sample_per):
+    r"""
+    Returns falling coefficients of H(z) from numerator and denominator.
+
+    Explanation
+    ===========
+
+    Where H(z) is the corresponding discretized transfer function,
+    discretized with the forward difference transform method.
+    H(z) is obtained from the continuous transfer function H(s)
+    by substituting $s(z) = \frac{z-1}{T}$ into H(s), where T is the
+    sample period.
+    Coefficients are falling, i.e. $H(z) = \frac{az+b}{cz+d}$ is returned
+    as [a, b], [c, d].
+
+    Examples
+    ========
+
+    >>> from sympy.physics.control.lti import TransferFunction, forward_diff
+    >>> from sympy.abc import s, L, R, T
+
+    >>> tf = TransferFunction(1, s*L + R, s)
+    >>> numZ, denZ = forward_diff(tf, T)
+    >>> numZ
+    [T/L]
+    >>> denZ
+    [1, (-L + R*T)/L]
+    """
+    return gbt(tf, sample_per, S.Zero)
+
+def backward_diff(tf, sample_per):
+    r"""
+    Returns falling coefficients of H(z) from numerator and denominator.
+
+    Explanation
+    ===========
+
+    Where H(z) is the corresponding discretized transfer function,
+    discretized with the backward difference transform method.
+    H(z) is obtained from the continuous transfer function H(s)
+    by substituting $s(z) =  \frac{z-1}{Tz}$ into H(s), where T is the
+    sample period.
+    Coefficients are falling, i.e. $H(z) = \frac{az+b}{cz+d}$ is returned
+    as [a, b], [c, d].
+
+    Examples
+    ========
+
+    >>> from sympy.physics.control.lti import TransferFunction, backward_diff
+    >>> from sympy.abc import s, L, R, T
+
+    >>> tf = TransferFunction(1, s*L + R, s)
+    >>> numZ, denZ = backward_diff(tf, T)
+    >>> numZ
+    [T/(L + R*T), 0]
+    >>> denZ
+    [1, -L/(L + R*T)]
+    """
+    return gbt(tf, sample_per, S.One)
+
+def phase_margin(system):
+    r"""
+    Returns the phase margin of a continuous time system.
+    Only applicable to Transfer Functions which can generate valid bode plots.
+
+    Raises
+    ======
+
+    NotImplementedError
+        When time delay terms are present in the system.
+
+    ValueError
+        When a SISO LTI system is not passed.
+
+        When more than one free symbol is present in the system.
+        The only variable in the transfer function should be
+        the variable of the Laplace transform.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.control import TransferFunction, phase_margin
+    >>> from sympy.abc import s
+
+    >>> tf = TransferFunction(1, s**3 + 2*s**2 + s, s)
+    >>> phase_margin(tf)
+    180*(-pi + atan((-1 + (-2*18**(1/3)/(9 + sqrt(93))**(1/3) + 12**(1/3)*(9 + sqrt(93))**(1/3))**2/36)/(-12**(1/3)*(9 + sqrt(93))**(1/3)/3 + 2*18**(1/3)/(3*(9 + sqrt(93))**(1/3)))))/pi + 180
+    >>> phase_margin(tf).n()
+    21.3863897518751
+
+    >>> tf1 = TransferFunction(s**3, s**2 + 5*s, s)
+    >>> phase_margin(tf1)
+    -180 + 180*(atan(sqrt(2)*(-51/10 - sqrt(101)/10)*sqrt(1 + sqrt(101))/(2*(sqrt(101)/2 + 51/2))) + pi)/pi
+    >>> phase_margin(tf1).n()
+    -25.1783920627277
+
+    >>> tf2 = TransferFunction(1, s + 1, s)
+    >>> phase_margin(tf2)
+    -180
+
+    See Also
+    ========
+
+    gain_margin
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Phase_margin
+
+    """
+    from sympy.functions import arg
+
+    if not isinstance(system, SISOLinearTimeInvariant):
+        raise ValueError("Margins are only applicable for SISO LTI systems.")
+
+    _w = Dummy("w", real=True)
+    repl = I*_w
+    expr = system.to_expr()
+    len_free_symbols = len(expr.free_symbols)
+    if expr.has(exp):
+        raise NotImplementedError("Margins for systems with Time delay terms are not supported.")
+    elif len_free_symbols > 1:
+        raise ValueError("Extra degree of freedom found. Make sure"
+            " that there are no free symbols in the dynamical system other"
+            " than the variable of Laplace transform.")
+
+    w_expr = expr.subs({system.var: repl})
+
+    mag = 20*log(Abs(w_expr), 10)
+    mag_sol = list(solveset(mag, _w, Interval(0, oo, left_open=True)))
+
+    if (len(mag_sol) == 0):
+      pm = S(-180)
+    else:
+      wcp = mag_sol[0]
+      pm = ((arg(w_expr)*S(180)/pi).subs({_w:wcp}) + S(180)) % 360
+
+    if(pm >= 180):
+        pm = pm - 360
+
+    return pm
+
+def gain_margin(system):
+    r"""
+    Returns the gain margin of a continuous time system.
+    Only applicable to Transfer Functions which can generate valid bode plots.
+
+    Raises
+    ======
+
+    NotImplementedError
+        When time delay terms are present in the system.
+
+    ValueError
+        When a SISO LTI system is not passed.
+
+        When more than one free symbol is present in the system.
+        The only variable in the transfer function should be
+        the variable of the Laplace transform.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.control import TransferFunction, gain_margin
+    >>> from sympy.abc import s
+
+    >>> tf = TransferFunction(1, s**3 + 2*s**2 + s, s)
+    >>> gain_margin(tf)
+    20*log(2)/log(10)
+    >>> gain_margin(tf).n()
+    6.02059991327962
+
+    >>> tf1 = TransferFunction(s**3, s**2 + 5*s, s)
+    >>> gain_margin(tf1)
+    oo
+
+    See Also
+    ========
+
+    phase_margin
+
+    References
+    ==========
+
+    https://en.wikipedia.org/wiki/Bode_plot
+
+    """
+    if not isinstance(system, SISOLinearTimeInvariant):
+        raise ValueError("Margins are only applicable for SISO LTI systems.")
+
+    _w = Dummy("w", real=True)
+    repl = I*_w
+    expr = system.to_expr()
+    len_free_symbols = len(expr.free_symbols)
+    if expr.has(exp):
+        raise NotImplementedError("Margins for systems with Time delay terms are not supported.")
+    elif len_free_symbols > 1:
+        raise ValueError("Extra degree of freedom found. Make sure"
+            " that there are no free symbols in the dynamical system other"
+            " than the variable of Laplace transform.")
+
+    w_expr = expr.subs({system.var: repl})
+
+    mag = 20*log(Abs(w_expr), 10)
+    phase = w_expr
+    phase_sol = list(solveset(numer(phase.as_real_imag()[1].cancel()),_w, Interval(0, oo, left_open = True)))
+
+    if (len(phase_sol) == 0):
+        gm = oo
+    else:
+        wcg = phase_sol[0]
+        gm = -mag.subs({_w:wcg})
+
+    return gm
+
+class LinearTimeInvariant(Basic, EvalfMixin):
+    """A common class for all the Linear Time-Invariant Dynamical Systems."""
+
+    _clstype: Type
+
+    # Users should not directly interact with this class.
+    def __new__(cls, *system, **kwargs):
+        if cls is LinearTimeInvariant:
+            raise NotImplementedError('The LTICommon class is not meant to be used directly.')
+        return super(LinearTimeInvariant, cls).__new__(cls, *system, **kwargs)
+
+    @classmethod
+    def _check_args(cls, args):
+        if not args:
+            raise ValueError("At least 1 argument must be passed.")
+        if not all(isinstance(arg, cls._clstype) for arg in args):
+            raise TypeError(f"All arguments must be of type {cls._clstype}.")
+        var_set = {arg.var for arg in args}
+        if len(var_set) != 1:
+            raise ValueError(filldedent(f"""
+                All transfer functions should use the same complex variable
+                of the Laplace transform. {len(var_set)} different
+                values found."""))
+
+    @property
+    def is_SISO(self):
+        """Returns `True` if the passed LTI system is SISO else returns False."""
+        return self._is_SISO
+
+
+class SISOLinearTimeInvariant(LinearTimeInvariant):
+    """A common class for all the SISO Linear Time-Invariant Dynamical Systems."""
+    # Users should not directly interact with this class.
+    _is_SISO = True
+
+
+class MIMOLinearTimeInvariant(LinearTimeInvariant):
+    """A common class for all the MIMO Linear Time-Invariant Dynamical Systems."""
+    # Users should not directly interact with this class.
+    _is_SISO = False
+
+
+SISOLinearTimeInvariant._clstype = SISOLinearTimeInvariant
+MIMOLinearTimeInvariant._clstype = MIMOLinearTimeInvariant
+
+
+def _check_other_SISO(func):
+    def wrapper(*args, **kwargs):
+        if not isinstance(args[-1], SISOLinearTimeInvariant):
+            return NotImplemented
+        else:
+            return func(*args, **kwargs)
+    return wrapper
+
+
+def _check_other_MIMO(func):
+    def wrapper(*args, **kwargs):
+        if not isinstance(args[-1], MIMOLinearTimeInvariant):
+            return NotImplemented
+        else:
+            return func(*args, **kwargs)
+    return wrapper
+
+
+class TransferFunction(SISOLinearTimeInvariant):
+    r"""
+    A class for representing LTI (Linear, time-invariant) systems that can be strictly described
+    by ratio of polynomials in the Laplace transform complex variable. The arguments
+    are ``num``, ``den``, and ``var``, where ``num`` and ``den`` are numerator and
+    denominator polynomials of the ``TransferFunction`` respectively, and the third argument is
+    a complex variable of the Laplace transform used by these polynomials of the transfer function.
+    ``num`` and ``den`` can be either polynomials or numbers, whereas ``var``
+    has to be a :py:class:`~.Symbol`.
+
+    Explanation
+    ===========
+
+    Generally, a dynamical system representing a physical model can be described in terms of Linear
+    Ordinary Differential Equations like -
+
+            $\small{b_{m}y^{\left(m\right)}+b_{m-1}y^{\left(m-1\right)}+\dots+b_{1}y^{\left(1\right)}+b_{0}y=
+            a_{n}x^{\left(n\right)}+a_{n-1}x^{\left(n-1\right)}+\dots+a_{1}x^{\left(1\right)}+a_{0}x}$
+
+    Here, $x$ is the input signal and $y$ is the output signal and superscript on both is the order of derivative
+    (not exponent). Derivative is taken with respect to the independent variable, $t$. Also, generally $m$ is greater
+    than $n$.
+
+    It is not feasible to analyse the properties of such systems in their native form therefore, we use
+    mathematical tools like Laplace transform to get a better perspective. Taking the Laplace transform
+    of both the sides in the equation (at zero initial conditions), we get -
+
+            $\small{\mathcal{L}[b_{m}y^{\left(m\right)}+b_{m-1}y^{\left(m-1\right)}+\dots+b_{1}y^{\left(1\right)}+b_{0}y]=
+            \mathcal{L}[a_{n}x^{\left(n\right)}+a_{n-1}x^{\left(n-1\right)}+\dots+a_{1}x^{\left(1\right)}+a_{0}x]}$
+
+    Using the linearity property of Laplace transform and also considering zero initial conditions
+    (i.e. $\small{y(0^{-}) = 0}$, $\small{y'(0^{-}) = 0}$ and so on), the equation
+    above gets translated to -
+
+            $\small{b_{m}\mathcal{L}[y^{\left(m\right)}]+\dots+b_{1}\mathcal{L}[y^{\left(1\right)}]+b_{0}\mathcal{L}[y]=
+            a_{n}\mathcal{L}[x^{\left(n\right)}]+\dots+a_{1}\mathcal{L}[x^{\left(1\right)}]+a_{0}\mathcal{L}[x]}$
+
+    Now, applying Derivative property of Laplace transform,
+
+            $\small{b_{m}s^{m}\mathcal{L}[y]+\dots+b_{1}s\mathcal{L}[y]+b_{0}\mathcal{L}[y]=
+            a_{n}s^{n}\mathcal{L}[x]+\dots+a_{1}s\mathcal{L}[x]+a_{0}\mathcal{L}[x]}$
+
+    Here, the superscript on $s$ is **exponent**. Note that the zero initial conditions assumption, mentioned above, is very important
+    and cannot be ignored otherwise the dynamical system cannot be considered time-independent and the simplified equation above
+    cannot be reached.
+
+    Collecting $\mathcal{L}[y]$ and $\mathcal{L}[x]$ terms from both the sides and taking the ratio
+    $\frac{ \mathcal{L}\left\{y\right\} }{ \mathcal{L}\left\{x\right\} }$, we get the typical rational form of transfer
+    function.
+
+    The numerator of the transfer function is, therefore, the Laplace transform of the output signal
+    (The signals are represented as functions of time) and similarly, the denominator
+    of the transfer function is the Laplace transform of the input signal. It is also a convention
+    to denote the input and output signal's Laplace transform with capital alphabets like shown below.
+
+            $H(s) = \frac{Y(s)}{X(s)} = \frac{ \mathcal{L}\left\{y(t)\right\} }{ \mathcal{L}\left\{x(t)\right\} }$
+
+    $s$, also known as complex frequency, is a complex variable in the Laplace domain. It corresponds to the
+    equivalent variable $t$, in the time domain. Transfer functions are sometimes also referred to as the Laplace
+    transform of the system's impulse response. Transfer function, $H$, is represented as a rational
+    function in $s$ like,
+
+            $H(s) =\ \frac{a_{n}s^{n}+a_{n-1}s^{n-1}+\dots+a_{1}s+a_{0}}{b_{m}s^{m}+b_{m-1}s^{m-1}+\dots+b_{1}s+b_{0}}$
+
+    Parameters
+    ==========
+
+    num : Expr, Number
+        The numerator polynomial of the transfer function.
+    den : Expr, Number
+        The denominator polynomial of the transfer function.
+    var : Symbol
+        Complex variable of the Laplace transform used by the
+        polynomials of the transfer function.
+
+    Raises
+    ======
+
+    TypeError
+        When ``var`` is not a Symbol or when ``num`` or ``den`` is not a
+        number or a polynomial.
+    ValueError
+        When ``den`` is zero.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import s, p, a
+    >>> from sympy.physics.control.lti import TransferFunction
+    >>> tf1 = TransferFunction(s + a, s**2 + s + 1, s)
+    >>> tf1
+    TransferFunction(a + s, s**2 + s + 1, s)
+    >>> tf1.num
+    a + s
+    >>> tf1.den
+    s**2 + s + 1
+    >>> tf1.var
+    s
+    >>> tf1.args
+    (a + s, s**2 + s + 1, s)
+
+    Any complex variable can be used for ``var``.
+
+    >>> tf2 = TransferFunction(a*p**3 - a*p**2 + s*p, p + a**2, p)
+    >>> tf2
+    TransferFunction(a*p**3 - a*p**2 + p*s, a**2 + p, p)
+    >>> tf3 = TransferFunction((p + 3)*(p - 1), (p - 1)*(p + 5), p)
+    >>> tf3
+    TransferFunction((p - 1)*(p + 3), (p - 1)*(p + 5), p)
+
+    To negate a transfer function the ``-`` operator can be prepended:
+
+    >>> tf4 = TransferFunction(-a + s, p**2 + s, p)
+    >>> -tf4
+    TransferFunction(a - s, p**2 + s, p)
+    >>> tf5 = TransferFunction(s**4 - 2*s**3 + 5*s + 4, s + 4, s)
+    >>> -tf5
+    TransferFunction(-s**4 + 2*s**3 - 5*s - 4, s + 4, s)
+
+    You can use a float or an integer (or other constants) as numerator and denominator:
+
+    >>> tf6 = TransferFunction(1/2, 4, s)
+    >>> tf6.num
+    0.500000000000000
+    >>> tf6.den
+    4
+    >>> tf6.var
+    s
+    >>> tf6.args
+    (0.5, 4, s)
+
+    You can take the integer power of a transfer function using the ``**`` operator:
+
+    >>> tf7 = TransferFunction(s + a, s - a, s)
+    >>> tf7**3
+    TransferFunction((a + s)**3, (-a + s)**3, s)
+    >>> tf7**0
+    TransferFunction(1, 1, s)
+    >>> tf8 = TransferFunction(p + 4, p - 3, p)
+    >>> tf8**-1
+    TransferFunction(p - 3, p + 4, p)
+
+    Addition, subtraction, and multiplication of transfer functions can form
+    unevaluated ``Series`` or ``Parallel`` objects.
+
+    >>> tf9 = TransferFunction(s + 1, s**2 + s + 1, s)
+    >>> tf10 = TransferFunction(s - p, s + 3, s)
+    >>> tf11 = TransferFunction(4*s**2 + 2*s - 4, s - 1, s)
+    >>> tf12 = TransferFunction(1 - s, s**2 + 4, s)
+    >>> tf9 + tf10
+    Parallel(TransferFunction(s + 1, s**2 + s + 1, s), TransferFunction(-p + s, s + 3, s))
+    >>> tf10 - tf11
+    Parallel(TransferFunction(-p + s, s + 3, s), TransferFunction(-4*s**2 - 2*s + 4, s - 1, s))
+    >>> tf9 * tf10
+    Series(TransferFunction(s + 1, s**2 + s + 1, s), TransferFunction(-p + s, s + 3, s))
+    >>> tf10 - (tf9 + tf12)
+    Parallel(TransferFunction(-p + s, s + 3, s), TransferFunction(-s - 1, s**2 + s + 1, s), TransferFunction(s - 1, s**2 + 4, s))
+    >>> tf10 - (tf9 * tf12)
+    Parallel(TransferFunction(-p + s, s + 3, s), Series(TransferFunction(-1, 1, s), TransferFunction(s + 1, s**2 + s + 1, s), TransferFunction(1 - s, s**2 + 4, s)))
+    >>> tf11 * tf10 * tf9
+    Series(TransferFunction(4*s**2 + 2*s - 4, s - 1, s), TransferFunction(-p + s, s + 3, s), TransferFunction(s + 1, s**2 + s + 1, s))
+    >>> tf9 * tf11 + tf10 * tf12
+    Parallel(Series(TransferFunction(s + 1, s**2 + s + 1, s), TransferFunction(4*s**2 + 2*s - 4, s - 1, s)), Series(TransferFunction(-p + s, s + 3, s), TransferFunction(1 - s, s**2 + 4, s)))
+    >>> (tf9 + tf12) * (tf10 + tf11)
+    Series(Parallel(TransferFunction(s + 1, s**2 + s + 1, s), TransferFunction(1 - s, s**2 + 4, s)), Parallel(TransferFunction(-p + s, s + 3, s), TransferFunction(4*s**2 + 2*s - 4, s - 1, s)))
+
+    These unevaluated ``Series`` or ``Parallel`` objects can convert into the
+    resultant transfer function using ``.doit()`` method or by ``.rewrite(TransferFunction)``.
+
+    >>> ((tf9 + tf10) * tf12).doit()
+    TransferFunction((1 - s)*((-p + s)*(s**2 + s + 1) + (s + 1)*(s + 3)), (s + 3)*(s**2 + 4)*(s**2 + s + 1), s)
+    >>> (tf9 * tf10 - tf11 * tf12).rewrite(TransferFunction)
+    TransferFunction(-(1 - s)*(s + 3)*(s**2 + s + 1)*(4*s**2 + 2*s - 4) + (-p + s)*(s - 1)*(s + 1)*(s**2 + 4), (s - 1)*(s + 3)*(s**2 + 4)*(s**2 + s + 1), s)
+
+    See Also
+    ========
+
+    Feedback, Series, Parallel
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Transfer_function
+    .. [2] https://en.wikipedia.org/wiki/Laplace_transform
+
+    """
+    def __new__(cls, num, den, var):
+        num, den = _sympify(num), _sympify(den)
+
+        if not isinstance(var, Symbol):
+            raise TypeError("Variable input must be a Symbol.")
+
+        if den == 0:
+            raise ValueError("TransferFunction cannot have a zero denominator.")
+
+        if (((isinstance(num, (Expr, TransferFunction, Series, Parallel)) and num.has(Symbol)) or num.is_number) and
+            ((isinstance(den, (Expr, TransferFunction, Series, Parallel)) and den.has(Symbol)) or den.is_number)):
+            return super(TransferFunction, cls).__new__(cls, num, den, var)
+
+        else:
+            raise TypeError("Unsupported type for numerator or denominator of TransferFunction.")
+
+    @classmethod
+    def from_rational_expression(cls, expr, var=None):
+        r"""
+        Creates a new ``TransferFunction`` efficiently from a rational expression.
+
+        Parameters
+        ==========
+
+        expr : Expr, Number
+            The rational expression representing the ``TransferFunction``.
+        var : Symbol, optional
+            Complex variable of the Laplace transform used by the
+            polynomials of the transfer function.
+
+        Raises
+        ======
+
+        ValueError
+            When ``expr`` is of type ``Number`` and optional parameter ``var``
+            is not passed.
+
+            When ``expr`` has more than one variables and an optional parameter
+            ``var`` is not passed.
+        ZeroDivisionError
+            When denominator of ``expr`` is zero or it has ``ComplexInfinity``
+            in its numerator.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> expr1 = (s + 5)/(3*s**2 + 2*s + 1)
+        >>> tf1 = TransferFunction.from_rational_expression(expr1)
+        >>> tf1
+        TransferFunction(s + 5, 3*s**2 + 2*s + 1, s)
+        >>> expr2 = (a*p**3 - a*p**2 + s*p)/(p + a**2)  # Expr with more than one variables
+        >>> tf2 = TransferFunction.from_rational_expression(expr2, p)
+        >>> tf2
+        TransferFunction(a*p**3 - a*p**2 + p*s, a**2 + p, p)
+
+        In case of conflict between two or more variables in a expression, SymPy will
+        raise a ``ValueError``, if ``var`` is not passed by the user.
+
+        >>> tf = TransferFunction.from_rational_expression((a + a*s)/(s**2 + s + 1))
+        Traceback (most recent call last):
+        ...
+        ValueError: Conflicting values found for positional argument `var` ({a, s}). Specify it manually.
+
+        This can be corrected by specifying the ``var`` parameter manually.
+
+        >>> tf = TransferFunction.from_rational_expression((a + a*s)/(s**2 + s + 1), s)
+        >>> tf
+        TransferFunction(a*s + a, s**2 + s + 1, s)
+
+        ``var`` also need to be specified when ``expr`` is a ``Number``
+
+        >>> tf3 = TransferFunction.from_rational_expression(10, s)
+        >>> tf3
+        TransferFunction(10, 1, s)
+
+        """
+        expr = _sympify(expr)
+        if var is None:
+            _free_symbols = expr.free_symbols
+            _len_free_symbols = len(_free_symbols)
+            if _len_free_symbols == 1:
+                var = list(_free_symbols)[0]
+            elif _len_free_symbols == 0:
+                raise ValueError(filldedent("""
+                    Positional argument `var` not found in the
+                    TransferFunction defined. Specify it manually."""))
+            else:
+                raise ValueError(filldedent("""
+                    Conflicting values found for positional argument `var` ({}).
+                    Specify it manually.""".format(_free_symbols)))
+
+        _num, _den = expr.as_numer_denom()
+        if _den == 0 or _num.has(S.ComplexInfinity):
+            raise ZeroDivisionError("TransferFunction cannot have a zero denominator.")
+        return cls(_num, _den, var)
+
+    @classmethod
+    def from_coeff_lists(cls, num_list, den_list, var):
+        r"""
+        Creates a new ``TransferFunction`` efficiently from a list of coefficients.
+
+        Parameters
+        ==========
+
+        num_list : Sequence
+            Sequence comprising of numerator coefficients.
+        den_list : Sequence
+            Sequence comprising of denominator coefficients.
+        var : Symbol
+            Complex variable of the Laplace transform used by the
+            polynomials of the transfer function.
+
+        Raises
+        ======
+
+        ZeroDivisionError
+            When the constructed denominator is zero.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> num = [1, 0, 2]
+        >>> den = [3, 2, 2, 1]
+        >>> tf = TransferFunction.from_coeff_lists(num, den, s)
+        >>> tf
+        TransferFunction(s**2 + 2, 3*s**3 + 2*s**2 + 2*s + 1, s)
+
+        # Create a Transfer Function with more than one variable
+        >>> tf1 = TransferFunction.from_coeff_lists([p, 1], [2*p, 0, 4], s)
+        >>> tf1
+        TransferFunction(p*s + 1, 2*p*s**2 + 4, s)
+
+        """
+        num_list = num_list[::-1]
+        den_list = den_list[::-1]
+        num_var_powers = [var**i for i in range(len(num_list))]
+        den_var_powers = [var**i for i in range(len(den_list))]
+
+        _num = sum(coeff * var_power for coeff, var_power in zip(num_list, num_var_powers))
+        _den = sum(coeff * var_power for coeff, var_power in zip(den_list, den_var_powers))
+
+        if _den == 0:
+            raise ZeroDivisionError("TransferFunction cannot have a zero denominator.")
+
+        return cls(_num, _den, var)
+
+    @classmethod
+    def from_zpk(cls, zeros, poles, gain, var):
+        r"""
+        Creates a new ``TransferFunction`` from given zeros, poles and gain.
+
+        Parameters
+        ==========
+
+        zeros : Sequence
+            Sequence comprising of zeros of transfer function.
+        poles : Sequence
+            Sequence comprising of poles of transfer function.
+        gain : Number, Symbol, Expression
+            A scalar value specifying gain of the model.
+        var : Symbol
+            Complex variable of the Laplace transform used by the
+            polynomials of the transfer function.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, k
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> zeros = [1, 2, 3]
+        >>> poles = [6, 5, 4]
+        >>> gain = 7
+        >>> tf = TransferFunction.from_zpk(zeros, poles, gain, s)
+        >>> tf
+        TransferFunction(7*(s - 3)*(s - 2)*(s - 1), (s - 6)*(s - 5)*(s - 4), s)
+
+        # Create a Transfer Function with variable poles and zeros
+        >>> tf1 = TransferFunction.from_zpk([p, k], [p + k, p - k], 2, s)
+        >>> tf1
+        TransferFunction(2*(-k + s)*(-p + s), (-k - p + s)*(k - p + s), s)
+
+        # Complex poles or zeros are acceptable
+        >>> tf2 = TransferFunction.from_zpk([0], [1-1j, 1+1j, 2], -2, s)
+        >>> tf2
+        TransferFunction(-2*s, (s - 2)*(s - 1.0 - 1.0*I)*(s - 1.0 + 1.0*I), s)
+
+        """
+        num_poly = 1
+        den_poly = 1
+        for zero in zeros:
+            num_poly *= var - zero
+        for pole in poles:
+            den_poly *= var - pole
+
+        return cls(gain*num_poly, den_poly, var)
+
+    @property
+    def num(self):
+        """
+        Returns the numerator polynomial of the transfer function.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> G1 = TransferFunction(s**2 + p*s + 3, s - 4, s)
+        >>> G1.num
+        p*s + s**2 + 3
+        >>> G2 = TransferFunction((p + 5)*(p - 3), (p - 3)*(p + 1), p)
+        >>> G2.num
+        (p - 3)*(p + 5)
+
+        """
+        return self.args[0]
+
+    @property
+    def den(self):
+        """
+        Returns the denominator polynomial of the transfer function.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> G1 = TransferFunction(s + 4, p**3 - 2*p + 4, s)
+        >>> G1.den
+        p**3 - 2*p + 4
+        >>> G2 = TransferFunction(3, 4, s)
+        >>> G2.den
+        4
+
+        """
+        return self.args[1]
+
+    @property
+    def var(self):
+        """
+        Returns the complex variable of the Laplace transform used by the polynomials of
+        the transfer function.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> G1 = TransferFunction(p**2 + 2*p + 4, p - 6, p)
+        >>> G1.var
+        p
+        >>> G2 = TransferFunction(0, s - 5, s)
+        >>> G2.var
+        s
+
+        """
+        return self.args[2]
+
+    def _eval_subs(self, old, new):
+        arg_num = self.num.subs(old, new)
+        arg_den = self.den.subs(old, new)
+        argnew = TransferFunction(arg_num, arg_den, self.var)
+        return self if old == self.var else argnew
+
+    def _eval_evalf(self, prec):
+        return TransferFunction(
+            self.num._eval_evalf(prec),
+            self.den._eval_evalf(prec),
+            self.var)
+
+    def _eval_simplify(self, **kwargs):
+        tf = cancel(Mul(self.num, 1/self.den, evaluate=False), expand=False).as_numer_denom()
+        num_, den_ = tf[0], tf[1]
+        return TransferFunction(num_, den_, self.var)
+
+    def _eval_rewrite_as_StateSpace(self, *args):
+        """
+        Returns the equivalent space space model of the transfer function model.
+        The state space model will be returned in the controllable cannonical form.
+
+        Unlike the space state to transfer function model conversion, the transfer function
+        to state space model conversion is not unique. There can be multiple state space
+        representations of a given transfer function model.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s
+        >>> from sympy.physics.control import TransferFunction, StateSpace
+        >>> tf = TransferFunction(s**2 + 1, s**3 + 2*s + 10, s)
+        >>> tf.rewrite(StateSpace)
+        StateSpace(Matrix([
+        [  0,  1, 0],
+        [  0,  0, 1],
+        [-10, -2, 0]]), Matrix([
+        [0],
+        [0],
+        [1]]), Matrix([[1, 0, 1]]), Matrix([[0]]))
+
+        """
+        if not self.is_proper:
+            raise ValueError("Transfer Function must be proper.")
+
+        num_poly = Poly(self.num, self.var)
+        den_poly = Poly(self.den, self.var)
+        n = den_poly.degree()
+
+        num_coeffs = num_poly.all_coeffs()
+        den_coeffs = den_poly.all_coeffs()
+        diff = n - num_poly.degree()
+        num_coeffs = [0]*diff + num_coeffs
+
+        a = den_coeffs[1:]
+        a_mat = Matrix([[(-1)*coefficient/den_coeffs[0] for coefficient in reversed(a)]])
+        vert = zeros(n-1, 1)
+        mat = eye(n-1)
+        A = vert.row_join(mat)
+        A = A.col_join(a_mat)
+
+        B = zeros(n, 1)
+        B[n-1] = 1
+
+        i = n
+        C = []
+        while(i > 0):
+            C.append(num_coeffs[i] - den_coeffs[i]*num_coeffs[0])
+            i -= 1
+        C = Matrix([C])
+
+        D = Matrix([num_coeffs[0]])
+
+        return StateSpace(A, B, C, D)
+
+    def expand(self):
+        """
+        Returns the transfer function with numerator and denominator
+        in expanded form.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a, b
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> G1 = TransferFunction((a - s)**2, (s**2 + a)**2, s)
+        >>> G1.expand()
+        TransferFunction(a**2 - 2*a*s + s**2, a**2 + 2*a*s**2 + s**4, s)
+        >>> G2 = TransferFunction((p + 3*b)*(p - b), (p - b)*(p + 2*b), p)
+        >>> G2.expand()
+        TransferFunction(-3*b**2 + 2*b*p + p**2, -2*b**2 + b*p + p**2, p)
+
+        """
+        return TransferFunction(expand(self.num), expand(self.den), self.var)
+
+    def dc_gain(self):
+        """
+        Computes the gain of the response as the frequency approaches zero.
+
+        The DC gain is infinite for systems with pure integrators.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a, b
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> tf1 = TransferFunction(s + 3, s**2 - 9, s)
+        >>> tf1.dc_gain()
+        -1/3
+        >>> tf2 = TransferFunction(p**2, p - 3 + p**3, p)
+        >>> tf2.dc_gain()
+        0
+        >>> tf3 = TransferFunction(a*p**2 - b, s + b, s)
+        >>> tf3.dc_gain()
+        (a*p**2 - b)/b
+        >>> tf4 = TransferFunction(1, s, s)
+        >>> tf4.dc_gain()
+        oo
+
+        """
+        m = Mul(self.num, Pow(self.den, -1, evaluate=False), evaluate=False)
+        return limit(m, self.var, 0)
+
+    def poles(self):
+        """
+        Returns the poles of a transfer function.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> tf1 = TransferFunction((p + 3)*(p - 1), (p - 1)*(p + 5), p)
+        >>> tf1.poles()
+        [-5, 1]
+        >>> tf2 = TransferFunction((1 - s)**2, (s**2 + 1)**2, s)
+        >>> tf2.poles()
+        [I, I, -I, -I]
+        >>> tf3 = TransferFunction(s**2, a*s + p, s)
+        >>> tf3.poles()
+        [-p/a]
+
+        """
+        return _roots(Poly(self.den, self.var), self.var)
+
+    def zeros(self):
+        """
+        Returns the zeros of a transfer function.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> tf1 = TransferFunction((p + 3)*(p - 1), (p - 1)*(p + 5), p)
+        >>> tf1.zeros()
+        [-3, 1]
+        >>> tf2 = TransferFunction((1 - s)**2, (s**2 + 1)**2, s)
+        >>> tf2.zeros()
+        [1, 1]
+        >>> tf3 = TransferFunction(s**2, a*s + p, s)
+        >>> tf3.zeros()
+        [0, 0]
+
+        """
+        return _roots(Poly(self.num, self.var), self.var)
+
+    def eval_frequency(self, other):
+        """
+        Returns the system response at any point in the real or complex plane.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> from sympy import I
+        >>> tf1 = TransferFunction(1, s**2 + 2*s + 1, s)
+        >>> omega = 0.1
+        >>> tf1.eval_frequency(I*omega)
+        1/(0.99 + 0.2*I)
+        >>> tf2 = TransferFunction(s**2, a*s + p, s)
+        >>> tf2.eval_frequency(2)
+        4/(2*a + p)
+        >>> tf2.eval_frequency(I*2)
+        -4/(2*I*a + p)
+        """
+        arg_num = self.num.subs(self.var, other)
+        arg_den = self.den.subs(self.var, other)
+        argnew = TransferFunction(arg_num, arg_den, self.var).to_expr()
+        return argnew.expand()
+
+    def is_stable(self):
+        """
+        Returns True if the transfer function is asymptotically stable; else False.
+
+        This would not check the marginal or conditional stability of the system.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a
+        >>> from sympy import symbols
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> q, r = symbols('q, r', negative=True)
+        >>> tf1 = TransferFunction((1 - s)**2, (s + 1)**2, s)
+        >>> tf1.is_stable()
+        True
+        >>> tf2 = TransferFunction((1 - p)**2, (s**2 + 1)**2, s)
+        >>> tf2.is_stable()
+        False
+        >>> tf3 = TransferFunction(4, q*s - r, s)
+        >>> tf3.is_stable()
+        False
+        >>> tf4 = TransferFunction(p + 1, a*p - s**2, p)
+        >>> tf4.is_stable() is None   # Not enough info about the symbols to determine stability
+        True
+
+        """
+        return fuzzy_and(pole.as_real_imag()[0].is_negative for pole in self.poles())
+
+    def __add__(self, other):
+        if isinstance(other, (TransferFunction, Series)):
+            if not self.var == other.var:
+                raise ValueError(filldedent("""
+                    All the transfer functions should use the same complex variable
+                    of the Laplace transform."""))
+            return Parallel(self, other)
+        elif isinstance(other, Parallel):
+            if not self.var == other.var:
+                raise ValueError(filldedent("""
+                    All the transfer functions should use the same complex variable
+                    of the Laplace transform."""))
+            arg_list = list(other.args)
+            return Parallel(self, *arg_list)
+        else:
+            raise ValueError("TransferFunction cannot be added with {}.".
+                format(type(other)))
+
+    def __radd__(self, other):
+        return self + other
+
+    def __sub__(self, other):
+        if isinstance(other, (TransferFunction, Series)):
+            if not self.var == other.var:
+                raise ValueError(filldedent("""
+                    All the transfer functions should use the same complex variable
+                    of the Laplace transform."""))
+            return Parallel(self, -other)
+        elif isinstance(other, Parallel):
+            if not self.var == other.var:
+                raise ValueError(filldedent("""
+                    All the transfer functions should use the same complex variable
+                    of the Laplace transform."""))
+            arg_list = [-i for i in list(other.args)]
+            return Parallel(self, *arg_list)
+        else:
+            raise ValueError("{} cannot be subtracted from a TransferFunction."
+                .format(type(other)))
+
+    def __rsub__(self, other):
+        return -self + other
+
+    def __mul__(self, other):
+        if isinstance(other, (TransferFunction, Parallel)):
+            if not self.var == other.var:
+                raise ValueError(filldedent("""
+                    All the transfer functions should use the same complex variable
+                    of the Laplace transform."""))
+            return Series(self, other)
+        elif isinstance(other, Series):
+            if not self.var == other.var:
+                raise ValueError(filldedent("""
+                    All the transfer functions should use the same complex variable
+                    of the Laplace transform."""))
+            arg_list = list(other.args)
+            return Series(self, *arg_list)
+        else:
+            raise ValueError("TransferFunction cannot be multiplied with {}."
+                .format(type(other)))
+
+    __rmul__ = __mul__
+
+    def __truediv__(self, other):
+        if isinstance(other, TransferFunction):
+            if not self.var == other.var:
+                raise ValueError(filldedent("""
+                    All the transfer functions should use the same complex variable
+                    of the Laplace transform."""))
+            return Series(self, TransferFunction(other.den, other.num, self.var))
+        elif (isinstance(other, Parallel) and len(other.args
+                ) == 2 and isinstance(other.args[0], TransferFunction)
+            and isinstance(other.args[1], (Series, TransferFunction))):
+
+            if not self.var == other.var:
+                raise ValueError(filldedent("""
+                    Both TransferFunction and Parallel should use the
+                    same complex variable of the Laplace transform."""))
+            if other.args[1] == self:
+                # plant and controller with unit feedback.
+                return Feedback(self, other.args[0])
+            other_arg_list = list(other.args[1].args) if isinstance(
+                other.args[1], Series) else other.args[1]
+            if other_arg_list == other.args[1]:
+                return Feedback(self, other_arg_list)
+            elif self in other_arg_list:
+                other_arg_list.remove(self)
+            else:
+                return Feedback(self, Series(*other_arg_list))
+
+            if len(other_arg_list) == 1:
+                return Feedback(self, *other_arg_list)
+            else:
+                return Feedback(self, Series(*other_arg_list))
+        else:
+            raise ValueError("TransferFunction cannot be divided by {}.".
+                format(type(other)))
+
+    __rtruediv__ = __truediv__
+
+    def __pow__(self, p):
+        p = sympify(p)
+        if not p.is_Integer:
+            raise ValueError("Exponent must be an integer.")
+        if p is S.Zero:
+            return TransferFunction(1, 1, self.var)
+        elif p > 0:
+            num_, den_ = self.num**p, self.den**p
+        else:
+            p = abs(p)
+            num_, den_ = self.den**p, self.num**p
+
+        return TransferFunction(num_, den_, self.var)
+
+    def __neg__(self):
+        return TransferFunction(-self.num, self.den, self.var)
+
+    @property
+    def is_proper(self):
+        """
+        Returns True if degree of the numerator polynomial is less than
+        or equal to degree of the denominator polynomial, else False.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a, b
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> tf1 = TransferFunction(b*s**2 + p**2 - a*p + s, b - p**2, s)
+        >>> tf1.is_proper
+        False
+        >>> tf2 = TransferFunction(p**2 - 4*p, p**3 + 3*p + 2, p)
+        >>> tf2.is_proper
+        True
+
+        """
+        return degree(self.num, self.var) <= degree(self.den, self.var)
+
+    @property
+    def is_strictly_proper(self):
+        """
+        Returns True if degree of the numerator polynomial is strictly less
+        than degree of the denominator polynomial, else False.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a, b
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> tf1 = TransferFunction(a*p**2 + b*s, s - p, s)
+        >>> tf1.is_strictly_proper
+        False
+        >>> tf2 = TransferFunction(s**3 - 2, s**4 + 5*s + 6, s)
+        >>> tf2.is_strictly_proper
+        True
+
+        """
+        return degree(self.num, self.var) < degree(self.den, self.var)
+
+    @property
+    def is_biproper(self):
+        """
+        Returns True if degree of the numerator polynomial is equal to
+        degree of the denominator polynomial, else False.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a, b
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> tf1 = TransferFunction(a*p**2 + b*s, s - p, s)
+        >>> tf1.is_biproper
+        True
+        >>> tf2 = TransferFunction(p**2, p + a, p)
+        >>> tf2.is_biproper
+        False
+
+        """
+        return degree(self.num, self.var) == degree(self.den, self.var)
+
+    def to_expr(self):
+        """
+        Converts a ``TransferFunction`` object to SymPy Expr.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a, b
+        >>> from sympy.physics.control.lti import TransferFunction
+        >>> from sympy import Expr
+        >>> tf1 = TransferFunction(s, a*s**2 + 1, s)
+        >>> tf1.to_expr()
+        s/(a*s**2 + 1)
+        >>> isinstance(_, Expr)
+        True
+        >>> tf2 = TransferFunction(1, (p + 3*b)*(b - p), p)
+        >>> tf2.to_expr()
+        1/((b - p)*(3*b + p))
+        >>> tf3 = TransferFunction((s - 2)*(s - 3), (s - 1)*(s - 2)*(s - 3), s)
+        >>> tf3.to_expr()
+        ((s - 3)*(s - 2))/(((s - 3)*(s - 2)*(s - 1)))
+
+        """
+
+        if self.num != 1:
+            return Mul(self.num, Pow(self.den, -1, evaluate=False), evaluate=False)
+        else:
+            return Pow(self.den, -1, evaluate=False)
+
+
+def _flatten_args(args, _cls):
+    temp_args = []
+    for arg in args:
+        if isinstance(arg, _cls):
+            temp_args.extend(arg.args)
+        else:
+            temp_args.append(arg)
+    return tuple(temp_args)
+
+
+def _dummify_args(_arg, var):
+    dummy_dict = {}
+    dummy_arg_list = []
+
+    for arg in _arg:
+        _s = Dummy()
+        dummy_dict[_s] = var
+        dummy_arg = arg.subs({var: _s})
+        dummy_arg_list.append(dummy_arg)
+
+    return dummy_arg_list, dummy_dict
+
+
+class Series(SISOLinearTimeInvariant):
+    r"""
+    A class for representing a series configuration of SISO systems.
+
+    Parameters
+    ==========
+
+    args : SISOLinearTimeInvariant
+        SISO systems in a series configuration.
+    evaluate : Boolean, Keyword
+        When passed ``True``, returns the equivalent
+        ``Series(*args).doit()``. Set to ``False`` by default.
+
+    Raises
+    ======
+
+    ValueError
+        When no argument is passed.
+
+        ``var`` attribute is not same for every system.
+    TypeError
+        Any of the passed ``*args`` has unsupported type
+
+        A combination of SISO and MIMO systems is
+        passed. There should be homogeneity in the
+        type of systems passed, SISO in this case.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import s, p, a, b
+    >>> from sympy.physics.control.lti import TransferFunction, Series, Parallel
+    >>> tf1 = TransferFunction(a*p**2 + b*s, s - p, s)
+    >>> tf2 = TransferFunction(s**3 - 2, s**4 + 5*s + 6, s)
+    >>> tf3 = TransferFunction(p**2, p + s, s)
+    >>> S1 = Series(tf1, tf2)
+    >>> S1
+    Series(TransferFunction(a*p**2 + b*s, -p + s, s), TransferFunction(s**3 - 2, s**4 + 5*s + 6, s))
+    >>> S1.var
+    s
+    >>> S2 = Series(tf2, Parallel(tf3, -tf1))
+    >>> S2
+    Series(TransferFunction(s**3 - 2, s**4 + 5*s + 6, s), Parallel(TransferFunction(p**2, p + s, s), TransferFunction(-a*p**2 - b*s, -p + s, s)))
+    >>> S2.var
+    s
+    >>> S3 = Series(Parallel(tf1, tf2), Parallel(tf2, tf3))
+    >>> S3
+    Series(Parallel(TransferFunction(a*p**2 + b*s, -p + s, s), TransferFunction(s**3 - 2, s**4 + 5*s + 6, s)), Parallel(TransferFunction(s**3 - 2, s**4 + 5*s + 6, s), TransferFunction(p**2, p + s, s)))
+    >>> S3.var
+    s
+
+    You can get the resultant transfer function by using ``.doit()`` method:
+
+    >>> S3 = Series(tf1, tf2, -tf3)
+    >>> S3.doit()
+    TransferFunction(-p**2*(s**3 - 2)*(a*p**2 + b*s), (-p + s)*(p + s)*(s**4 + 5*s + 6), s)
+    >>> S4 = Series(tf2, Parallel(tf1, -tf3))
+    >>> S4.doit()
+    TransferFunction((s**3 - 2)*(-p**2*(-p + s) + (p + s)*(a*p**2 + b*s)), (-p + s)*(p + s)*(s**4 + 5*s + 6), s)
+
+    Notes
+    =====
+
+    All the transfer functions should use the same complex variable
+    ``var`` of the Laplace transform.
+
+    See Also
+    ========
+
+    MIMOSeries, Parallel, TransferFunction, Feedback
+
+    """
+    def __new__(cls, *args, evaluate=False):
+
+        args = _flatten_args(args, Series)
+        cls._check_args(args)
+        obj = super().__new__(cls, *args)
+
+        return obj.doit() if evaluate else obj
+
+    @property
+    def var(self):
+        """
+        Returns the complex variable used by all the transfer functions.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import p
+        >>> from sympy.physics.control.lti import TransferFunction, Series, Parallel
+        >>> G1 = TransferFunction(p**2 + 2*p + 4, p - 6, p)
+        >>> G2 = TransferFunction(p, 4 - p, p)
+        >>> G3 = TransferFunction(0, p**4 - 1, p)
+        >>> Series(G1, G2).var
+        p
+        >>> Series(-G3, Parallel(G1, G2)).var
+        p
+
+        """
+        return self.args[0].var
+
+    def doit(self, **hints):
+        """
+        Returns the resultant transfer function obtained after evaluating
+        the transfer functions in series configuration.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a, b
+        >>> from sympy.physics.control.lti import TransferFunction, Series
+        >>> tf1 = TransferFunction(a*p**2 + b*s, s - p, s)
+        >>> tf2 = TransferFunction(s**3 - 2, s**4 + 5*s + 6, s)
+        >>> Series(tf2, tf1).doit()
+        TransferFunction((s**3 - 2)*(a*p**2 + b*s), (-p + s)*(s**4 + 5*s + 6), s)
+        >>> Series(-tf1, -tf2).doit()
+        TransferFunction((2 - s**3)*(-a*p**2 - b*s), (-p + s)*(s**4 + 5*s + 6), s)
+
+        """
+
+        _num_arg = (arg.doit().num for arg in self.args)
+        _den_arg = (arg.doit().den for arg in self.args)
+        res_num = Mul(*_num_arg, evaluate=True)
+        res_den = Mul(*_den_arg, evaluate=True)
+        return TransferFunction(res_num, res_den, self.var)
+
+    def _eval_rewrite_as_TransferFunction(self, *args, **kwargs):
+        return self.doit()
+
+    @_check_other_SISO
+    def __add__(self, other):
+
+        if isinstance(other, Parallel):
+            arg_list = list(other.args)
+            return Parallel(self, *arg_list)
+
+        return Parallel(self, other)
+
+    __radd__ = __add__
+
+    @_check_other_SISO
+    def __sub__(self, other):
+        return self + (-other)
+
+    def __rsub__(self, other):
+        return -self + other
+
+    @_check_other_SISO
+    def __mul__(self, other):
+
+        arg_list = list(self.args)
+        return Series(*arg_list, other)
+
+    def __truediv__(self, other):
+        if isinstance(other, TransferFunction):
+            return Series(*self.args, TransferFunction(other.den, other.num, other.var))
+        elif isinstance(other, Series):
+            tf_self = self.rewrite(TransferFunction)
+            tf_other = other.rewrite(TransferFunction)
+            return tf_self / tf_other
+        elif (isinstance(other, Parallel) and len(other.args) == 2
+            and isinstance(other.args[0], TransferFunction) and isinstance(other.args[1], Series)):
+
+            if not self.var == other.var:
+                raise ValueError(filldedent("""
+                    All the transfer functions should use the same complex variable
+                    of the Laplace transform."""))
+            self_arg_list = set(self.args)
+            other_arg_list = set(other.args[1].args)
+            res = list(self_arg_list ^ other_arg_list)
+            if len(res) == 0:
+                return Feedback(self, other.args[0])
+            elif len(res) == 1:
+                return Feedback(self, *res)
+            else:
+                return Feedback(self, Series(*res))
+        else:
+            raise ValueError("This transfer function expression is invalid.")
+
+    def __neg__(self):
+        return Series(TransferFunction(-1, 1, self.var), self)
+
+    def to_expr(self):
+        """Returns the equivalent ``Expr`` object."""
+        return Mul(*(arg.to_expr() for arg in self.args), evaluate=False)
+
+    @property
+    def is_proper(self):
+        """
+        Returns True if degree of the numerator polynomial of the resultant transfer
+        function is less than or equal to degree of the denominator polynomial of
+        the same, else False.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a, b
+        >>> from sympy.physics.control.lti import TransferFunction, Series
+        >>> tf1 = TransferFunction(b*s**2 + p**2 - a*p + s, b - p**2, s)
+        >>> tf2 = TransferFunction(p**2 - 4*p, p**3 + 3*s + 2, s)
+        >>> tf3 = TransferFunction(s, s**2 + s + 1, s)
+        >>> S1 = Series(-tf2, tf1)
+        >>> S1.is_proper
+        False
+        >>> S2 = Series(tf1, tf2, tf3)
+        >>> S2.is_proper
+        True
+
+        """
+        return self.doit().is_proper
+
+    @property
+    def is_strictly_proper(self):
+        """
+        Returns True if degree of the numerator polynomial of the resultant transfer
+        function is strictly less than degree of the denominator polynomial of
+        the same, else False.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a, b
+        >>> from sympy.physics.control.lti import TransferFunction, Series
+        >>> tf1 = TransferFunction(a*p**2 + b*s, s - p, s)
+        >>> tf2 = TransferFunction(s**3 - 2, s**2 + 5*s + 6, s)
+        >>> tf3 = TransferFunction(1, s**2 + s + 1, s)
+        >>> S1 = Series(tf1, tf2)
+        >>> S1.is_strictly_proper
+        False
+        >>> S2 = Series(tf1, tf2, tf3)
+        >>> S2.is_strictly_proper
+        True
+
+        """
+        return self.doit().is_strictly_proper
+
+    @property
+    def is_biproper(self):
+        r"""
+        Returns True if degree of the numerator polynomial of the resultant transfer
+        function is equal to degree of the denominator polynomial of
+        the same, else False.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a, b
+        >>> from sympy.physics.control.lti import TransferFunction, Series
+        >>> tf1 = TransferFunction(a*p**2 + b*s, s - p, s)
+        >>> tf2 = TransferFunction(p, s**2, s)
+        >>> tf3 = TransferFunction(s**2, 1, s)
+        >>> S1 = Series(tf1, -tf2)
+        >>> S1.is_biproper
+        False
+        >>> S2 = Series(tf2, tf3)
+        >>> S2.is_biproper
+        True
+
+        """
+        return self.doit().is_biproper
+
+
+def _mat_mul_compatible(*args):
+    """To check whether shapes are compatible for matrix mul."""
+    return all(args[i].num_outputs == args[i+1].num_inputs for i in range(len(args)-1))
+
+
+class MIMOSeries(MIMOLinearTimeInvariant):
+    r"""
+    A class for representing a series configuration of MIMO systems.
+
+    Parameters
+    ==========
+
+    args : MIMOLinearTimeInvariant
+        MIMO systems in a series configuration.
+    evaluate : Boolean, Keyword
+        When passed ``True``, returns the equivalent
+        ``MIMOSeries(*args).doit()``. Set to ``False`` by default.
+
+    Raises
+    ======
+
+    ValueError
+        When no argument is passed.
+
+        ``var`` attribute is not same for every system.
+
+        ``num_outputs`` of the MIMO system is not equal to the
+        ``num_inputs`` of its adjacent MIMO system. (Matrix
+        multiplication constraint, basically)
+    TypeError
+        Any of the passed ``*args`` has unsupported type
+
+        A combination of SISO and MIMO systems is
+        passed. There should be homogeneity in the
+        type of systems passed, MIMO in this case.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import s
+    >>> from sympy.physics.control.lti import MIMOSeries, TransferFunctionMatrix
+    >>> from sympy import Matrix, pprint
+    >>> mat_a = Matrix([[5*s], [5]])  # 2 Outputs 1 Input
+    >>> mat_b = Matrix([[5, 1/(6*s**2)]])  # 1 Output 2 Inputs
+    >>> mat_c = Matrix([[1, s], [5/s, 1]])  # 2 Outputs 2 Inputs
+    >>> tfm_a = TransferFunctionMatrix.from_Matrix(mat_a, s)
+    >>> tfm_b = TransferFunctionMatrix.from_Matrix(mat_b, s)
+    >>> tfm_c = TransferFunctionMatrix.from_Matrix(mat_c, s)
+    >>> MIMOSeries(tfm_c, tfm_b, tfm_a)
+    MIMOSeries(TransferFunctionMatrix(((TransferFunction(1, 1, s), TransferFunction(s, 1, s)), (TransferFunction(5, s, s), TransferFunction(1, 1, s)))), TransferFunctionMatrix(((TransferFunction(5, 1, s), TransferFunction(1, 6*s**2, s)),)), TransferFunctionMatrix(((TransferFunction(5*s, 1, s),), (TransferFunction(5, 1, s),))))
+    >>> pprint(_, use_unicode=False)  #  For Better Visualization
+    [5*s]                 [1  s]
+    [---]    [5   1  ]    [-  -]
+    [ 1 ]    [-  ----]    [1  1]
+    [   ]   *[1     2]   *[    ]
+    [ 5 ]    [   6*s ]{t} [5  1]
+    [ - ]                 [-  -]
+    [ 1 ]{t}              [s  1]{t}
+    >>> MIMOSeries(tfm_c, tfm_b, tfm_a).doit()
+    TransferFunctionMatrix(((TransferFunction(150*s**4 + 25*s, 6*s**3, s), TransferFunction(150*s**4 + 5*s, 6*s**2, s)), (TransferFunction(150*s**3 + 25, 6*s**3, s), TransferFunction(150*s**3 + 5, 6*s**2, s))))
+    >>> pprint(_, use_unicode=False)  # (2 Inputs -A-> 2 Outputs) -> (2 Inputs -B-> 1 Output) -> (1 Input -C-> 2 Outputs) is equivalent to (2 Inputs -Series Equivalent-> 2 Outputs).
+    [     4              4      ]
+    [150*s  + 25*s  150*s  + 5*s]
+    [-------------  ------------]
+    [        3             2    ]
+    [     6*s           6*s     ]
+    [                           ]
+    [      3              3     ]
+    [ 150*s  + 25    150*s  + 5 ]
+    [ -----------    ---------- ]
+    [        3             2    ]
+    [     6*s           6*s     ]{t}
+
+    Notes
+    =====
+
+    All the transfer function matrices should use the same complex variable ``var`` of the Laplace transform.
+
+    ``MIMOSeries(A, B)`` is not equivalent to ``A*B``. It is always in the reverse order, that is ``B*A``.
+
+    See Also
+    ========
+
+    Series, MIMOParallel
+
+    """
+    def __new__(cls, *args, evaluate=False):
+
+        cls._check_args(args)
+
+        if _mat_mul_compatible(*args):
+            obj = super().__new__(cls, *args)
+
+        else:
+            raise ValueError(filldedent("""
+                Number of input signals do not match the number
+                of output signals of adjacent systems for some args."""))
+
+        return obj.doit() if evaluate else obj
+
+    @property
+    def var(self):
+        """
+        Returns the complex variable used by all the transfer functions.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import p
+        >>> from sympy.physics.control.lti import TransferFunction, MIMOSeries, TransferFunctionMatrix
+        >>> G1 = TransferFunction(p**2 + 2*p + 4, p - 6, p)
+        >>> G2 = TransferFunction(p, 4 - p, p)
+        >>> G3 = TransferFunction(0, p**4 - 1, p)
+        >>> tfm_1 = TransferFunctionMatrix([[G1, G2, G3]])
+        >>> tfm_2 = TransferFunctionMatrix([[G1], [G2], [G3]])
+        >>> MIMOSeries(tfm_2, tfm_1).var
+        p
+
+        """
+        return self.args[0].var
+
+    @property
+    def num_inputs(self):
+        """Returns the number of input signals of the series system."""
+        return self.args[0].num_inputs
+
+    @property
+    def num_outputs(self):
+        """Returns the number of output signals of the series system."""
+        return self.args[-1].num_outputs
+
+    @property
+    def shape(self):
+        """Returns the shape of the equivalent MIMO system."""
+        return self.num_outputs, self.num_inputs
+
+    def doit(self, cancel=False, **kwargs):
+        """
+        Returns the resultant transfer function matrix obtained after evaluating
+        the MIMO systems arranged in a series configuration.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a, b
+        >>> from sympy.physics.control.lti import TransferFunction, MIMOSeries, TransferFunctionMatrix
+        >>> tf1 = TransferFunction(a*p**2 + b*s, s - p, s)
+        >>> tf2 = TransferFunction(s**3 - 2, s**4 + 5*s + 6, s)
+        >>> tfm1 = TransferFunctionMatrix([[tf1, tf2], [tf2, tf2]])
+        >>> tfm2 = TransferFunctionMatrix([[tf2, tf1], [tf1, tf1]])
+        >>> MIMOSeries(tfm2, tfm1).doit()
+        TransferFunctionMatrix(((TransferFunction(2*(-p + s)*(s**3 - 2)*(a*p**2 + b*s)*(s**4 + 5*s + 6), (-p + s)**2*(s**4 + 5*s + 6)**2, s), TransferFunction((-p + s)**2*(s**3 - 2)*(a*p**2 + b*s) + (-p + s)*(a*p**2 + b*s)**2*(s**4 + 5*s + 6), (-p + s)**3*(s**4 + 5*s + 6), s)), (TransferFunction((-p + s)*(s**3 - 2)**2*(s**4 + 5*s + 6) + (s**3 - 2)*(a*p**2 + b*s)*(s**4 + 5*s + 6)**2, (-p + s)*(s**4 + 5*s + 6)**3, s), TransferFunction(2*(s**3 - 2)*(a*p**2 + b*s), (-p + s)*(s**4 + 5*s + 6), s))))
+
+        """
+        _arg = (arg.doit()._expr_mat for arg in reversed(self.args))
+
+        if cancel:
+            res = MatMul(*_arg, evaluate=True)
+            return TransferFunctionMatrix.from_Matrix(res, self.var)
+
+        _dummy_args, _dummy_dict = _dummify_args(_arg, self.var)
+        res = MatMul(*_dummy_args, evaluate=True)
+        temp_tfm = TransferFunctionMatrix.from_Matrix(res, self.var)
+        return temp_tfm.subs(_dummy_dict)
+
+    def _eval_rewrite_as_TransferFunctionMatrix(self, *args, **kwargs):
+        return self.doit()
+
+    @_check_other_MIMO
+    def __add__(self, other):
+
+        if isinstance(other, MIMOParallel):
+            arg_list = list(other.args)
+            return MIMOParallel(self, *arg_list)
+
+        return MIMOParallel(self, other)
+
+    __radd__ = __add__
+
+    @_check_other_MIMO
+    def __sub__(self, other):
+        return self + (-other)
+
+    def __rsub__(self, other):
+        return -self + other
+
+    @_check_other_MIMO
+    def __mul__(self, other):
+
+        if isinstance(other, MIMOSeries):
+            self_arg_list = list(self.args)
+            other_arg_list = list(other.args)
+            return MIMOSeries(*other_arg_list, *self_arg_list)  # A*B = MIMOSeries(B, A)
+
+        arg_list = list(self.args)
+        return MIMOSeries(other, *arg_list)
+
+    def __neg__(self):
+        arg_list = list(self.args)
+        arg_list[0] = -arg_list[0]
+        return MIMOSeries(*arg_list)
+
+
+class Parallel(SISOLinearTimeInvariant):
+    r"""
+    A class for representing a parallel configuration of SISO systems.
+
+    Parameters
+    ==========
+
+    args : SISOLinearTimeInvariant
+        SISO systems in a parallel arrangement.
+    evaluate : Boolean, Keyword
+        When passed ``True``, returns the equivalent
+        ``Parallel(*args).doit()``. Set to ``False`` by default.
+
+    Raises
+    ======
+
+    ValueError
+        When no argument is passed.
+
+        ``var`` attribute is not same for every system.
+    TypeError
+        Any of the passed ``*args`` has unsupported type
+
+        A combination of SISO and MIMO systems is
+        passed. There should be homogeneity in the
+        type of systems passed.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import s, p, a, b
+    >>> from sympy.physics.control.lti import TransferFunction, Parallel, Series
+    >>> tf1 = TransferFunction(a*p**2 + b*s, s - p, s)
+    >>> tf2 = TransferFunction(s**3 - 2, s**4 + 5*s + 6, s)
+    >>> tf3 = TransferFunction(p**2, p + s, s)
+    >>> P1 = Parallel(tf1, tf2)
+    >>> P1
+    Parallel(TransferFunction(a*p**2 + b*s, -p + s, s), TransferFunction(s**3 - 2, s**4 + 5*s + 6, s))
+    >>> P1.var
+    s
+    >>> P2 = Parallel(tf2, Series(tf3, -tf1))
+    >>> P2
+    Parallel(TransferFunction(s**3 - 2, s**4 + 5*s + 6, s), Series(TransferFunction(p**2, p + s, s), TransferFunction(-a*p**2 - b*s, -p + s, s)))
+    >>> P2.var
+    s
+    >>> P3 = Parallel(Series(tf1, tf2), Series(tf2, tf3))
+    >>> P3
+    Parallel(Series(TransferFunction(a*p**2 + b*s, -p + s, s), TransferFunction(s**3 - 2, s**4 + 5*s + 6, s)), Series(TransferFunction(s**3 - 2, s**4 + 5*s + 6, s), TransferFunction(p**2, p + s, s)))
+    >>> P3.var
+    s
+
+    You can get the resultant transfer function by using ``.doit()`` method:
+
+    >>> Parallel(tf1, tf2, -tf3).doit()
+    TransferFunction(-p**2*(-p + s)*(s**4 + 5*s + 6) + (-p + s)*(p + s)*(s**3 - 2) + (p + s)*(a*p**2 + b*s)*(s**4 + 5*s + 6), (-p + s)*(p + s)*(s**4 + 5*s + 6), s)
+    >>> Parallel(tf2, Series(tf1, -tf3)).doit()
+    TransferFunction(-p**2*(a*p**2 + b*s)*(s**4 + 5*s + 6) + (-p + s)*(p + s)*(s**3 - 2), (-p + s)*(p + s)*(s**4 + 5*s + 6), s)
+
+    Notes
+    =====
+
+    All the transfer functions should use the same complex variable
+    ``var`` of the Laplace transform.
+
+    See Also
+    ========
+
+    Series, TransferFunction, Feedback
+
+    """
+    def __new__(cls, *args, evaluate=False):
+
+        args = _flatten_args(args, Parallel)
+        cls._check_args(args)
+        obj = super().__new__(cls, *args)
+
+        return obj.doit() if evaluate else obj
+
+    @property
+    def var(self):
+        """
+        Returns the complex variable used by all the transfer functions.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import p
+        >>> from sympy.physics.control.lti import TransferFunction, Parallel, Series
+        >>> G1 = TransferFunction(p**2 + 2*p + 4, p - 6, p)
+        >>> G2 = TransferFunction(p, 4 - p, p)
+        >>> G3 = TransferFunction(0, p**4 - 1, p)
+        >>> Parallel(G1, G2).var
+        p
+        >>> Parallel(-G3, Series(G1, G2)).var
+        p
+
+        """
+        return self.args[0].var
+
+    def doit(self, **hints):
+        """
+        Returns the resultant transfer function obtained after evaluating
+        the transfer functions in parallel configuration.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a, b
+        >>> from sympy.physics.control.lti import TransferFunction, Parallel
+        >>> tf1 = TransferFunction(a*p**2 + b*s, s - p, s)
+        >>> tf2 = TransferFunction(s**3 - 2, s**4 + 5*s + 6, s)
+        >>> Parallel(tf2, tf1).doit()
+        TransferFunction((-p + s)*(s**3 - 2) + (a*p**2 + b*s)*(s**4 + 5*s + 6), (-p + s)*(s**4 + 5*s + 6), s)
+        >>> Parallel(-tf1, -tf2).doit()
+        TransferFunction((2 - s**3)*(-p + s) + (-a*p**2 - b*s)*(s**4 + 5*s + 6), (-p + s)*(s**4 + 5*s + 6), s)
+
+        """
+
+        _arg = (arg.doit().to_expr() for arg in self.args)
+        res = Add(*_arg).as_numer_denom()
+        return TransferFunction(*res, self.var)
+
+    def _eval_rewrite_as_TransferFunction(self, *args, **kwargs):
+        return self.doit()
+
+    @_check_other_SISO
+    def __add__(self, other):
+
+        self_arg_list = list(self.args)
+        return Parallel(*self_arg_list, other)
+
+    __radd__ = __add__
+
+    @_check_other_SISO
+    def __sub__(self, other):
+        return self + (-other)
+
+    def __rsub__(self, other):
+        return -self + other
+
+    @_check_other_SISO
+    def __mul__(self, other):
+
+        if isinstance(other, Series):
+            arg_list = list(other.args)
+            return Series(self, *arg_list)
+
+        return Series(self, other)
+
+    def __neg__(self):
+        return Series(TransferFunction(-1, 1, self.var), self)
+
+    def to_expr(self):
+        """Returns the equivalent ``Expr`` object."""
+        return Add(*(arg.to_expr() for arg in self.args), evaluate=False)
+
+    @property
+    def is_proper(self):
+        """
+        Returns True if degree of the numerator polynomial of the resultant transfer
+        function is less than or equal to degree of the denominator polynomial of
+        the same, else False.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a, b
+        >>> from sympy.physics.control.lti import TransferFunction, Parallel
+        >>> tf1 = TransferFunction(b*s**2 + p**2 - a*p + s, b - p**2, s)
+        >>> tf2 = TransferFunction(p**2 - 4*p, p**3 + 3*s + 2, s)
+        >>> tf3 = TransferFunction(s, s**2 + s + 1, s)
+        >>> P1 = Parallel(-tf2, tf1)
+        >>> P1.is_proper
+        False
+        >>> P2 = Parallel(tf2, tf3)
+        >>> P2.is_proper
+        True
+
+        """
+        return self.doit().is_proper
+
+    @property
+    def is_strictly_proper(self):
+        """
+        Returns True if degree of the numerator polynomial of the resultant transfer
+        function is strictly less than degree of the denominator polynomial of
+        the same, else False.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a, b
+        >>> from sympy.physics.control.lti import TransferFunction, Parallel
+        >>> tf1 = TransferFunction(a*p**2 + b*s, s - p, s)
+        >>> tf2 = TransferFunction(s**3 - 2, s**4 + 5*s + 6, s)
+        >>> tf3 = TransferFunction(s, s**2 + s + 1, s)
+        >>> P1 = Parallel(tf1, tf2)
+        >>> P1.is_strictly_proper
+        False
+        >>> P2 = Parallel(tf2, tf3)
+        >>> P2.is_strictly_proper
+        True
+
+        """
+        return self.doit().is_strictly_proper
+
+    @property
+    def is_biproper(self):
+        """
+        Returns True if degree of the numerator polynomial of the resultant transfer
+        function is equal to degree of the denominator polynomial of
+        the same, else False.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a, b
+        >>> from sympy.physics.control.lti import TransferFunction, Parallel
+        >>> tf1 = TransferFunction(a*p**2 + b*s, s - p, s)
+        >>> tf2 = TransferFunction(p**2, p + s, s)
+        >>> tf3 = TransferFunction(s, s**2 + s + 1, s)
+        >>> P1 = Parallel(tf1, -tf2)
+        >>> P1.is_biproper
+        True
+        >>> P2 = Parallel(tf2, tf3)
+        >>> P2.is_biproper
+        False
+
+        """
+        return self.doit().is_biproper
+
+
+class MIMOParallel(MIMOLinearTimeInvariant):
+    r"""
+    A class for representing a parallel configuration of MIMO systems.
+
+    Parameters
+    ==========
+
+    args : MIMOLinearTimeInvariant
+        MIMO Systems in a parallel arrangement.
+    evaluate : Boolean, Keyword
+        When passed ``True``, returns the equivalent
+        ``MIMOParallel(*args).doit()``. Set to ``False`` by default.
+
+    Raises
+    ======
+
+    ValueError
+        When no argument is passed.
+
+        ``var`` attribute is not same for every system.
+
+        All MIMO systems passed do not have same shape.
+    TypeError
+        Any of the passed ``*args`` has unsupported type
+
+        A combination of SISO and MIMO systems is
+        passed. There should be homogeneity in the
+        type of systems passed, MIMO in this case.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import s
+    >>> from sympy.physics.control.lti import TransferFunctionMatrix, MIMOParallel
+    >>> from sympy import Matrix, pprint
+    >>> expr_1 = 1/s
+    >>> expr_2 = s/(s**2-1)
+    >>> expr_3 = (2 + s)/(s**2 - 1)
+    >>> expr_4 = 5
+    >>> tfm_a = TransferFunctionMatrix.from_Matrix(Matrix([[expr_1, expr_2], [expr_3, expr_4]]), s)
+    >>> tfm_b = TransferFunctionMatrix.from_Matrix(Matrix([[expr_2, expr_1], [expr_4, expr_3]]), s)
+    >>> tfm_c = TransferFunctionMatrix.from_Matrix(Matrix([[expr_3, expr_4], [expr_1, expr_2]]), s)
+    >>> MIMOParallel(tfm_a, tfm_b, tfm_c)
+    MIMOParallel(TransferFunctionMatrix(((TransferFunction(1, s, s), TransferFunction(s, s**2 - 1, s)), (TransferFunction(s + 2, s**2 - 1, s), TransferFunction(5, 1, s)))), TransferFunctionMatrix(((TransferFunction(s, s**2 - 1, s), TransferFunction(1, s, s)), (TransferFunction(5, 1, s), TransferFunction(s + 2, s**2 - 1, s)))), TransferFunctionMatrix(((TransferFunction(s + 2, s**2 - 1, s), TransferFunction(5, 1, s)), (TransferFunction(1, s, s), TransferFunction(s, s**2 - 1, s)))))
+    >>> pprint(_, use_unicode=False)  #  For Better Visualization
+    [  1       s   ]      [  s       1   ]      [s + 2     5   ]
+    [  -     ------]      [------    -   ]      [------    -   ]
+    [  s      2    ]      [ 2        s   ]      [ 2        1   ]
+    [        s  - 1]      [s  - 1        ]      [s  - 1        ]
+    [              ]    + [              ]    + [              ]
+    [s + 2     5   ]      [  5     s + 2 ]      [  1       s   ]
+    [------    -   ]      [  -     ------]      [  -     ------]
+    [ 2        1   ]      [  1      2    ]      [  s      2    ]
+    [s  - 1        ]{t}   [        s  - 1]{t}   [        s  - 1]{t}
+    >>> MIMOParallel(tfm_a, tfm_b, tfm_c).doit()
+    TransferFunctionMatrix(((TransferFunction(s**2 + s*(2*s + 2) - 1, s*(s**2 - 1), s), TransferFunction(2*s**2 + 5*s*(s**2 - 1) - 1, s*(s**2 - 1), s)), (TransferFunction(s**2 + s*(s + 2) + 5*s*(s**2 - 1) - 1, s*(s**2 - 1), s), TransferFunction(5*s**2 + 2*s - 3, s**2 - 1, s))))
+    >>> pprint(_, use_unicode=False)
+    [       2                              2       / 2    \    ]
+    [      s  + s*(2*s + 2) - 1         2*s  + 5*s*\s  - 1/ - 1]
+    [      --------------------         -----------------------]
+    [             / 2    \                       / 2    \      ]
+    [           s*\s  - 1/                     s*\s  - 1/      ]
+    [                                                          ]
+    [ 2                   / 2    \             2               ]
+    [s  + s*(s + 2) + 5*s*\s  - 1/ - 1      5*s  + 2*s - 3     ]
+    [---------------------------------      --------------     ]
+    [              / 2    \                      2             ]
+    [            s*\s  - 1/                     s  - 1         ]{t}
+
+    Notes
+    =====
+
+    All the transfer function matrices should use the same complex variable
+    ``var`` of the Laplace transform.
+
+    See Also
+    ========
+
+    Parallel, MIMOSeries
+
+    """
+    def __new__(cls, *args, evaluate=False):
+
+        args = _flatten_args(args, MIMOParallel)
+
+        cls._check_args(args)
+
+        if any(arg.shape != args[0].shape for arg in args):
+             raise TypeError("Shape of all the args is not equal.")
+
+        obj = super().__new__(cls, *args)
+
+        return obj.doit() if evaluate else obj
+
+    @property
+    def var(self):
+        """
+        Returns the complex variable used by all the systems.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import p
+        >>> from sympy.physics.control.lti import TransferFunction, TransferFunctionMatrix, MIMOParallel
+        >>> G1 = TransferFunction(p**2 + 2*p + 4, p - 6, p)
+        >>> G2 = TransferFunction(p, 4 - p, p)
+        >>> G3 = TransferFunction(0, p**4 - 1, p)
+        >>> G4 = TransferFunction(p**2, p**2 - 1, p)
+        >>> tfm_a = TransferFunctionMatrix([[G1, G2], [G3, G4]])
+        >>> tfm_b = TransferFunctionMatrix([[G2, G1], [G4, G3]])
+        >>> MIMOParallel(tfm_a, tfm_b).var
+        p
+
+        """
+        return self.args[0].var
+
+    @property
+    def num_inputs(self):
+        """Returns the number of input signals of the parallel system."""
+        return self.args[0].num_inputs
+
+    @property
+    def num_outputs(self):
+        """Returns the number of output signals of the parallel system."""
+        return self.args[0].num_outputs
+
+    @property
+    def shape(self):
+        """Returns the shape of the equivalent MIMO system."""
+        return self.num_outputs, self.num_inputs
+
+    def doit(self, **hints):
+        """
+        Returns the resultant transfer function matrix obtained after evaluating
+        the MIMO systems arranged in a parallel configuration.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p, a, b
+        >>> from sympy.physics.control.lti import TransferFunction, MIMOParallel, TransferFunctionMatrix
+        >>> tf1 = TransferFunction(a*p**2 + b*s, s - p, s)
+        >>> tf2 = TransferFunction(s**3 - 2, s**4 + 5*s + 6, s)
+        >>> tfm_1 = TransferFunctionMatrix([[tf1, tf2], [tf2, tf1]])
+        >>> tfm_2 = TransferFunctionMatrix([[tf2, tf1], [tf1, tf2]])
+        >>> MIMOParallel(tfm_1, tfm_2).doit()
+        TransferFunctionMatrix(((TransferFunction((-p + s)*(s**3 - 2) + (a*p**2 + b*s)*(s**4 + 5*s + 6), (-p + s)*(s**4 + 5*s + 6), s), TransferFunction((-p + s)*(s**3 - 2) + (a*p**2 + b*s)*(s**4 + 5*s + 6), (-p + s)*(s**4 + 5*s + 6), s)), (TransferFunction((-p + s)*(s**3 - 2) + (a*p**2 + b*s)*(s**4 + 5*s + 6), (-p + s)*(s**4 + 5*s + 6), s), TransferFunction((-p + s)*(s**3 - 2) + (a*p**2 + b*s)*(s**4 + 5*s + 6), (-p + s)*(s**4 + 5*s + 6), s))))
+
+        """
+        _arg = (arg.doit()._expr_mat for arg in self.args)
+        res = MatAdd(*_arg, evaluate=True)
+        return TransferFunctionMatrix.from_Matrix(res, self.var)
+
+    def _eval_rewrite_as_TransferFunctionMatrix(self, *args, **kwargs):
+        return self.doit()
+
+    @_check_other_MIMO
+    def __add__(self, other):
+
+        self_arg_list = list(self.args)
+        return MIMOParallel(*self_arg_list, other)
+
+    __radd__ = __add__
+
+    @_check_other_MIMO
+    def __sub__(self, other):
+        return self + (-other)
+
+    def __rsub__(self, other):
+        return -self + other
+
+    @_check_other_MIMO
+    def __mul__(self, other):
+
+        if isinstance(other, MIMOSeries):
+            arg_list = list(other.args)
+            return MIMOSeries(*arg_list, self)
+
+        return MIMOSeries(other, self)
+
+    def __neg__(self):
+        arg_list = [-arg for arg in list(self.args)]
+        return MIMOParallel(*arg_list)
+
+
+class Feedback(TransferFunction):
+    r"""
+    A class for representing closed-loop feedback interconnection between two
+    SISO input/output systems.
+
+    The first argument, ``sys1``, is the feedforward part of the closed-loop
+    system or in simple words, the dynamical model representing the process
+    to be controlled. The second argument, ``sys2``, is the feedback system
+    and controls the fed back signal to ``sys1``. Both ``sys1`` and ``sys2``
+    can either be ``Series`` or ``TransferFunction`` objects.
+
+    Parameters
+    ==========
+
+    sys1 : Series, TransferFunction
+        The feedforward path system.
+    sys2 : Series, TransferFunction, optional
+        The feedback path system (often a feedback controller).
+        It is the model sitting on the feedback path.
+
+        If not specified explicitly, the sys2 is
+        assumed to be unit (1.0) transfer function.
+    sign : int, optional
+        The sign of feedback. Can either be ``1``
+        (for positive feedback) or ``-1`` (for negative feedback).
+        Default value is `-1`.
+
+    Raises
+    ======
+
+    ValueError
+        When ``sys1`` and ``sys2`` are not using the
+        same complex variable of the Laplace transform.
+
+        When a combination of ``sys1`` and ``sys2`` yields
+        zero denominator.
+
+    TypeError
+        When either ``sys1`` or ``sys2`` is not a ``Series`` or a
+        ``TransferFunction`` object.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import s
+    >>> from sympy.physics.control.lti import TransferFunction, Feedback
+    >>> plant = TransferFunction(3*s**2 + 7*s - 3, s**2 - 4*s + 2, s)
+    >>> controller = TransferFunction(5*s - 10, s + 7, s)
+    >>> F1 = Feedback(plant, controller)
+    >>> F1
+    Feedback(TransferFunction(3*s**2 + 7*s - 3, s**2 - 4*s + 2, s), TransferFunction(5*s - 10, s + 7, s), -1)
+    >>> F1.var
+    s
+    >>> F1.args
+    (TransferFunction(3*s**2 + 7*s - 3, s**2 - 4*s + 2, s), TransferFunction(5*s - 10, s + 7, s), -1)
+
+    You can get the feedforward and feedback path systems by using ``.sys1`` and ``.sys2`` respectively.
+
+    >>> F1.sys1
+    TransferFunction(3*s**2 + 7*s - 3, s**2 - 4*s + 2, s)
+    >>> F1.sys2
+    TransferFunction(5*s - 10, s + 7, s)
+
+    You can get the resultant closed loop transfer function obtained by negative feedback
+    interconnection using ``.doit()`` method.
+
+    >>> F1.doit()
+    TransferFunction((s + 7)*(s**2 - 4*s + 2)*(3*s**2 + 7*s - 3), ((s + 7)*(s**2 - 4*s + 2) + (5*s - 10)*(3*s**2 + 7*s - 3))*(s**2 - 4*s + 2), s)
+    >>> G = TransferFunction(2*s**2 + 5*s + 1, s**2 + 2*s + 3, s)
+    >>> C = TransferFunction(5*s + 10, s + 10, s)
+    >>> F2 = Feedback(G*C, TransferFunction(1, 1, s))
+    >>> F2.doit()
+    TransferFunction((s + 10)*(5*s + 10)*(s**2 + 2*s + 3)*(2*s**2 + 5*s + 1), (s + 10)*((s + 10)*(s**2 + 2*s + 3) + (5*s + 10)*(2*s**2 + 5*s + 1))*(s**2 + 2*s + 3), s)
+
+    To negate a ``Feedback`` object, the ``-`` operator can be prepended:
+
+    >>> -F1
+    Feedback(TransferFunction(-3*s**2 - 7*s + 3, s**2 - 4*s + 2, s), TransferFunction(10 - 5*s, s + 7, s), -1)
+    >>> -F2
+    Feedback(Series(TransferFunction(-1, 1, s), TransferFunction(2*s**2 + 5*s + 1, s**2 + 2*s + 3, s), TransferFunction(5*s + 10, s + 10, s)), TransferFunction(-1, 1, s), -1)
+
+    See Also
+    ========
+
+    MIMOFeedback, Series, Parallel
+
+    """
+    def __new__(cls, sys1, sys2=None, sign=-1):
+        if not sys2:
+            sys2 = TransferFunction(1, 1, sys1.var)
+
+        if not (isinstance(sys1, (TransferFunction, Series, Feedback))
+            and isinstance(sys2, (TransferFunction, Series, Feedback))):
+            raise TypeError("Unsupported type for `sys1` or `sys2` of Feedback.")
+
+        if sign not in [-1, 1]:
+            raise ValueError(filldedent("""
+                Unsupported type for feedback. `sign` arg should
+                either be 1 (positive feedback loop) or -1
+                (negative feedback loop)."""))
+
+        if Mul(sys1.to_expr(), sys2.to_expr()).simplify() == sign:
+            raise ValueError("The equivalent system will have zero denominator.")
+
+        if sys1.var != sys2.var:
+            raise ValueError(filldedent("""
+                Both `sys1` and `sys2` should be using the
+                same complex variable."""))
+
+        return super(TransferFunction, cls).__new__(cls, sys1, sys2, _sympify(sign))
+
+    @property
+    def sys1(self):
+        """
+        Returns the feedforward system of the feedback interconnection.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p
+        >>> from sympy.physics.control.lti import TransferFunction, Feedback
+        >>> plant = TransferFunction(3*s**2 + 7*s - 3, s**2 - 4*s + 2, s)
+        >>> controller = TransferFunction(5*s - 10, s + 7, s)
+        >>> F1 = Feedback(plant, controller)
+        >>> F1.sys1
+        TransferFunction(3*s**2 + 7*s - 3, s**2 - 4*s + 2, s)
+        >>> G = TransferFunction(2*s**2 + 5*s + 1, p**2 + 2*p + 3, p)
+        >>> C = TransferFunction(5*p + 10, p + 10, p)
+        >>> P = TransferFunction(1 - s, p + 2, p)
+        >>> F2 = Feedback(TransferFunction(1, 1, p), G*C*P)
+        >>> F2.sys1
+        TransferFunction(1, 1, p)
+
+        """
+        return self.args[0]
+
+    @property
+    def sys2(self):
+        """
+        Returns the feedback controller of the feedback interconnection.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p
+        >>> from sympy.physics.control.lti import TransferFunction, Feedback
+        >>> plant = TransferFunction(3*s**2 + 7*s - 3, s**2 - 4*s + 2, s)
+        >>> controller = TransferFunction(5*s - 10, s + 7, s)
+        >>> F1 = Feedback(plant, controller)
+        >>> F1.sys2
+        TransferFunction(5*s - 10, s + 7, s)
+        >>> G = TransferFunction(2*s**2 + 5*s + 1, p**2 + 2*p + 3, p)
+        >>> C = TransferFunction(5*p + 10, p + 10, p)
+        >>> P = TransferFunction(1 - s, p + 2, p)
+        >>> F2 = Feedback(TransferFunction(1, 1, p), G*C*P)
+        >>> F2.sys2
+        Series(TransferFunction(2*s**2 + 5*s + 1, p**2 + 2*p + 3, p), TransferFunction(5*p + 10, p + 10, p), TransferFunction(1 - s, p + 2, p))
+
+        """
+        return self.args[1]
+
+    @property
+    def var(self):
+        """
+        Returns the complex variable of the Laplace transform used by all
+        the transfer functions involved in the feedback interconnection.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p
+        >>> from sympy.physics.control.lti import TransferFunction, Feedback
+        >>> plant = TransferFunction(3*s**2 + 7*s - 3, s**2 - 4*s + 2, s)
+        >>> controller = TransferFunction(5*s - 10, s + 7, s)
+        >>> F1 = Feedback(plant, controller)
+        >>> F1.var
+        s
+        >>> G = TransferFunction(2*s**2 + 5*s + 1, p**2 + 2*p + 3, p)
+        >>> C = TransferFunction(5*p + 10, p + 10, p)
+        >>> P = TransferFunction(1 - s, p + 2, p)
+        >>> F2 = Feedback(TransferFunction(1, 1, p), G*C*P)
+        >>> F2.var
+        p
+
+        """
+        return self.sys1.var
+
+    @property
+    def sign(self):
+        """
+        Returns the type of MIMO Feedback model. ``1``
+        for Positive and ``-1`` for Negative.
+        """
+        return self.args[2]
+
+    @property
+    def num(self):
+        """
+        Returns the numerator of the closed loop feedback system.
+        """
+        return self.sys1
+
+    @property
+    def den(self):
+        """
+        Returns the denominator of the closed loop feedback model.
+        """
+        unit = TransferFunction(1, 1, self.var)
+        arg_list = list(self.sys1.args) if isinstance(self.sys1, Series) else [self.sys1]
+        if self.sign == 1:
+            return Parallel(unit, -Series(self.sys2, *arg_list))
+        return Parallel(unit, Series(self.sys2, *arg_list))
+
+    @property
+    def sensitivity(self):
+        """
+        Returns the sensitivity function of the feedback loop.
+
+        Sensitivity of a Feedback system is the ratio
+        of change in the open loop gain to the change in
+        the closed loop gain.
+
+        .. note::
+            This method would not return the complementary
+            sensitivity function.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import p
+        >>> from sympy.physics.control.lti import TransferFunction, Feedback
+        >>> C = TransferFunction(5*p + 10, p + 10, p)
+        >>> P = TransferFunction(1 - p, p + 2, p)
+        >>> F_1 = Feedback(P, C)
+        >>> F_1.sensitivity
+        1/((1 - p)*(5*p + 10)/((p + 2)*(p + 10)) + 1)
+
+        """
+
+        return 1/(1 - self.sign*self.sys1.to_expr()*self.sys2.to_expr())
+
+    def doit(self, cancel=False, expand=False, **hints):
+        """
+        Returns the resultant transfer function obtained by the
+        feedback interconnection.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s
+        >>> from sympy.physics.control.lti import TransferFunction, Feedback
+        >>> plant = TransferFunction(3*s**2 + 7*s - 3, s**2 - 4*s + 2, s)
+        >>> controller = TransferFunction(5*s - 10, s + 7, s)
+        >>> F1 = Feedback(plant, controller)
+        >>> F1.doit()
+        TransferFunction((s + 7)*(s**2 - 4*s + 2)*(3*s**2 + 7*s - 3), ((s + 7)*(s**2 - 4*s + 2) + (5*s - 10)*(3*s**2 + 7*s - 3))*(s**2 - 4*s + 2), s)
+        >>> G = TransferFunction(2*s**2 + 5*s + 1, s**2 + 2*s + 3, s)
+        >>> F2 = Feedback(G, TransferFunction(1, 1, s))
+        >>> F2.doit()
+        TransferFunction((s**2 + 2*s + 3)*(2*s**2 + 5*s + 1), (s**2 + 2*s + 3)*(3*s**2 + 7*s + 4), s)
+
+        Use kwarg ``expand=True`` to expand the resultant transfer function.
+        Use ``cancel=True`` to cancel out the common terms in numerator and
+        denominator.
+
+        >>> F2.doit(cancel=True, expand=True)
+        TransferFunction(2*s**2 + 5*s + 1, 3*s**2 + 7*s + 4, s)
+        >>> F2.doit(expand=True)
+        TransferFunction(2*s**4 + 9*s**3 + 17*s**2 + 17*s + 3, 3*s**4 + 13*s**3 + 27*s**2 + 29*s + 12, s)
+
+        """
+        arg_list = list(self.sys1.args) if isinstance(self.sys1, Series) else [self.sys1]
+        # F_n and F_d are resultant TFs of num and den of Feedback.
+        F_n, unit = self.sys1.doit(), TransferFunction(1, 1, self.sys1.var)
+        if self.sign == -1:
+            F_d = Parallel(unit, Series(self.sys2, *arg_list)).doit()
+        else:
+            F_d = Parallel(unit, -Series(self.sys2, *arg_list)).doit()
+
+        _resultant_tf = TransferFunction(F_n.num * F_d.den, F_n.den * F_d.num, F_n.var)
+
+        if cancel:
+            _resultant_tf = _resultant_tf.simplify()
+
+        if expand:
+            _resultant_tf = _resultant_tf.expand()
+
+        return _resultant_tf
+
+    def _eval_rewrite_as_TransferFunction(self, num, den, sign, **kwargs):
+        return self.doit()
+
+    def to_expr(self):
+        """
+        Converts a ``Feedback`` object to SymPy Expr.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, a, b
+        >>> from sympy.physics.control.lti import TransferFunction, Feedback
+        >>> from sympy import Expr
+        >>> tf1 = TransferFunction(a+s, 1, s)
+        >>> tf2 = TransferFunction(b+s, 1, s)
+        >>> fd1 = Feedback(tf1, tf2)
+        >>> fd1.to_expr()
+        (a + s)/((a + s)*(b + s) + 1)
+        >>> isinstance(_, Expr)
+        True
+        """
+
+        return self.doit().to_expr()
+
+    def __neg__(self):
+        return Feedback(-self.sys1, -self.sys2, self.sign)
+
+
+def _is_invertible(a, b, sign):
+    """
+    Checks whether a given pair of MIMO
+    systems passed is invertible or not.
+    """
+    _mat = eye(a.num_outputs) - sign*(a.doit()._expr_mat)*(b.doit()._expr_mat)
+    _det = _mat.det()
+
+    return _det != 0
+
+
+class MIMOFeedback(MIMOLinearTimeInvariant):
+    r"""
+    A class for representing closed-loop feedback interconnection between two
+    MIMO input/output systems.
+
+    Parameters
+    ==========
+
+    sys1 : MIMOSeries, TransferFunctionMatrix
+        The MIMO system placed on the feedforward path.
+    sys2 : MIMOSeries, TransferFunctionMatrix
+        The system placed on the feedback path
+        (often a feedback controller).
+    sign : int, optional
+        The sign of feedback. Can either be ``1``
+        (for positive feedback) or ``-1`` (for negative feedback).
+        Default value is `-1`.
+
+    Raises
+    ======
+
+    ValueError
+        When ``sys1`` and ``sys2`` are not using the
+        same complex variable of the Laplace transform.
+
+        Forward path model should have an equal number of inputs/outputs
+        to the feedback path outputs/inputs.
+
+        When product of ``sys1`` and ``sys2`` is not a square matrix.
+
+        When the equivalent MIMO system is not invertible.
+
+    TypeError
+        When either ``sys1`` or ``sys2`` is not a ``MIMOSeries`` or a
+        ``TransferFunctionMatrix`` object.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix, pprint
+    >>> from sympy.abc import s
+    >>> from sympy.physics.control.lti import TransferFunctionMatrix, MIMOFeedback
+    >>> plant_mat = Matrix([[1, 1/s], [0, 1]])
+    >>> controller_mat = Matrix([[10, 0], [0, 10]])  # Constant Gain
+    >>> plant = TransferFunctionMatrix.from_Matrix(plant_mat, s)
+    >>> controller = TransferFunctionMatrix.from_Matrix(controller_mat, s)
+    >>> feedback = MIMOFeedback(plant, controller)  # Negative Feedback (default)
+    >>> pprint(feedback, use_unicode=False)
+    /    [1  1]    [10  0 ]   \-1   [1  1]
+    |    [-  -]    [--  - ]   |     [-  -]
+    |    [1  s]    [1   1 ]   |     [1  s]
+    |I + [    ]   *[      ]   |   * [    ]
+    |    [0  1]    [0   10]   |     [0  1]
+    |    [-  -]    [-   --]   |     [-  -]
+    \    [1  1]{t} [1   1 ]{t}/     [1  1]{t}
+
+    To get the equivalent system matrix, use either ``doit`` or ``rewrite`` method.
+
+    >>> pprint(feedback.doit(), use_unicode=False)
+    [1     1  ]
+    [--  -----]
+    [11  121*s]
+    [         ]
+    [0    1   ]
+    [-    --  ]
+    [1    11  ]{t}
+
+    To negate the ``MIMOFeedback`` object, use ``-`` operator.
+
+    >>> neg_feedback = -feedback
+    >>> pprint(neg_feedback.doit(), use_unicode=False)
+    [-1    -1  ]
+    [---  -----]
+    [11   121*s]
+    [          ]
+    [ 0    -1  ]
+    [ -    --- ]
+    [ 1    11  ]{t}
+
+    See Also
+    ========
+
+    Feedback, MIMOSeries, MIMOParallel
+
+    """
+    def __new__(cls, sys1, sys2, sign=-1):
+        if not (isinstance(sys1, (TransferFunctionMatrix, MIMOSeries))
+            and isinstance(sys2, (TransferFunctionMatrix, MIMOSeries))):
+            raise TypeError("Unsupported type for `sys1` or `sys2` of MIMO Feedback.")
+
+        if sys1.num_inputs != sys2.num_outputs or \
+            sys1.num_outputs != sys2.num_inputs:
+            raise ValueError(filldedent("""
+                Product of `sys1` and `sys2` must
+                yield a square matrix."""))
+
+        if sign not in (-1, 1):
+            raise ValueError(filldedent("""
+                Unsupported type for feedback. `sign` arg should
+                either be 1 (positive feedback loop) or -1
+                (negative feedback loop)."""))
+
+        if not _is_invertible(sys1, sys2, sign):
+            raise ValueError("Non-Invertible system inputted.")
+        if sys1.var != sys2.var:
+            raise ValueError(filldedent("""
+                Both `sys1` and `sys2` should be using the
+                same complex variable."""))
+
+        return super().__new__(cls, sys1, sys2, _sympify(sign))
+
+    @property
+    def sys1(self):
+        r"""
+        Returns the system placed on the feedforward path of the MIMO feedback interconnection.
+
+        Examples
+        ========
+
+        >>> from sympy import pprint
+        >>> from sympy.abc import s
+        >>> from sympy.physics.control.lti import TransferFunction, TransferFunctionMatrix, MIMOFeedback
+        >>> tf1 = TransferFunction(s**2 + s + 1, s**2 - s + 1, s)
+        >>> tf2 = TransferFunction(1, s, s)
+        >>> tf3 = TransferFunction(1, 1, s)
+        >>> sys1 = TransferFunctionMatrix([[tf1, tf2], [tf2, tf1]])
+        >>> sys2 = TransferFunctionMatrix([[tf3, tf3], [tf3, tf2]])
+        >>> F_1 = MIMOFeedback(sys1, sys2, 1)
+        >>> F_1.sys1
+        TransferFunctionMatrix(((TransferFunction(s**2 + s + 1, s**2 - s + 1, s), TransferFunction(1, s, s)), (TransferFunction(1, s, s), TransferFunction(s**2 + s + 1, s**2 - s + 1, s))))
+        >>> pprint(_, use_unicode=False)
+        [ 2                    ]
+        [s  + s + 1      1     ]
+        [----------      -     ]
+        [ 2              s     ]
+        [s  - s + 1            ]
+        [                      ]
+        [             2        ]
+        [    1       s  + s + 1]
+        [    -       ----------]
+        [    s        2        ]
+        [            s  - s + 1]{t}
+
+        """
+        return self.args[0]
+
+    @property
+    def sys2(self):
+        r"""
+        Returns the feedback controller of the MIMO feedback interconnection.
+
+        Examples
+        ========
+
+        >>> from sympy import pprint
+        >>> from sympy.abc import s
+        >>> from sympy.physics.control.lti import TransferFunction, TransferFunctionMatrix, MIMOFeedback
+        >>> tf1 = TransferFunction(s**2, s**3 - s + 1, s)
+        >>> tf2 = TransferFunction(1, s, s)
+        >>> tf3 = TransferFunction(1, 1, s)
+        >>> sys1 = TransferFunctionMatrix([[tf1, tf2], [tf2, tf1]])
+        >>> sys2 = TransferFunctionMatrix([[tf1, tf3], [tf3, tf2]])
+        >>> F_1 = MIMOFeedback(sys1, sys2)
+        >>> F_1.sys2
+        TransferFunctionMatrix(((TransferFunction(s**2, s**3 - s + 1, s), TransferFunction(1, 1, s)), (TransferFunction(1, 1, s), TransferFunction(1, s, s))))
+        >>> pprint(_, use_unicode=False)
+        [     2       ]
+        [    s       1]
+        [----------  -]
+        [ 3          1]
+        [s  - s + 1   ]
+        [             ]
+        [    1       1]
+        [    -       -]
+        [    1       s]{t}
+
+        """
+        return self.args[1]
+
+    @property
+    def var(self):
+        r"""
+        Returns the complex variable of the Laplace transform used by all
+        the transfer functions involved in the MIMO feedback loop.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import p
+        >>> from sympy.physics.control.lti import TransferFunction, TransferFunctionMatrix, MIMOFeedback
+        >>> tf1 = TransferFunction(p, 1 - p, p)
+        >>> tf2 = TransferFunction(1, p, p)
+        >>> tf3 = TransferFunction(1, 1, p)
+        >>> sys1 = TransferFunctionMatrix([[tf1, tf2], [tf2, tf1]])
+        >>> sys2 = TransferFunctionMatrix([[tf1, tf3], [tf3, tf2]])
+        >>> F_1 = MIMOFeedback(sys1, sys2, 1)  # Positive feedback
+        >>> F_1.var
+        p
+
+        """
+        return self.sys1.var
+
+    @property
+    def sign(self):
+        r"""
+        Returns the type of feedback interconnection of two models. ``1``
+        for Positive and ``-1`` for Negative.
+        """
+        return self.args[2]
+
+    @property
+    def sensitivity(self):
+        r"""
+        Returns the sensitivity function matrix of the feedback loop.
+
+        Sensitivity of a closed-loop system is the ratio of change
+        in the open loop gain to the change in the closed loop gain.
+
+        .. note::
+            This method would not return the complementary
+            sensitivity function.
+
+        Examples
+        ========
+
+        >>> from sympy import pprint
+        >>> from sympy.abc import p
+        >>> from sympy.physics.control.lti import TransferFunction, TransferFunctionMatrix, MIMOFeedback
+        >>> tf1 = TransferFunction(p, 1 - p, p)
+        >>> tf2 = TransferFunction(1, p, p)
+        >>> tf3 = TransferFunction(1, 1, p)
+        >>> sys1 = TransferFunctionMatrix([[tf1, tf2], [tf2, tf1]])
+        >>> sys2 = TransferFunctionMatrix([[tf1, tf3], [tf3, tf2]])
+        >>> F_1 = MIMOFeedback(sys1, sys2, 1)  # Positive feedback
+        >>> F_2 = MIMOFeedback(sys1, sys2)  # Negative feedback
+        >>> pprint(F_1.sensitivity, use_unicode=False)
+        [   4      3      2               5      4      2           ]
+        [- p  + 3*p  - 4*p  + 3*p - 1    p  - 2*p  + 3*p  - 3*p + 1 ]
+        [----------------------------  -----------------------------]
+        [  4      3      2              5      4      3      2      ]
+        [ p  + 3*p  - 8*p  + 8*p - 3   p  + 3*p  - 8*p  + 8*p  - 3*p]
+        [                                                           ]
+        [       4    3    2                  3      2               ]
+        [      p  - p  - p  + p           3*p  - 6*p  + 4*p - 1     ]
+        [ --------------------------    --------------------------  ]
+        [  4      3      2               4      3      2            ]
+        [ p  + 3*p  - 8*p  + 8*p - 3    p  + 3*p  - 8*p  + 8*p - 3  ]
+        >>> pprint(F_2.sensitivity, use_unicode=False)
+        [ 4      3      2           5      4      2          ]
+        [p  - 3*p  + 2*p  + p - 1  p  - 2*p  + 3*p  - 3*p + 1]
+        [------------------------  --------------------------]
+        [   4      3                   5      4      2       ]
+        [  p  - 3*p  + 2*p - 1        p  - 3*p  + 2*p  - p   ]
+        [                                                    ]
+        [     4    3    2               4      3             ]
+        [    p  - p  - p  + p        2*p  - 3*p  + 2*p - 1   ]
+        [  -------------------       ---------------------   ]
+        [   4      3                   4      3              ]
+        [  p  - 3*p  + 2*p - 1        p  - 3*p  + 2*p - 1    ]
+
+        """
+        _sys1_mat = self.sys1.doit()._expr_mat
+        _sys2_mat = self.sys2.doit()._expr_mat
+
+        return (eye(self.sys1.num_inputs) - \
+            self.sign*_sys1_mat*_sys2_mat).inv()
+
+    def doit(self, cancel=True, expand=False, **hints):
+        r"""
+        Returns the resultant transfer function matrix obtained by the
+        feedback interconnection.
+
+        Examples
+        ========
+
+        >>> from sympy import pprint
+        >>> from sympy.abc import s
+        >>> from sympy.physics.control.lti import TransferFunction, TransferFunctionMatrix, MIMOFeedback
+        >>> tf1 = TransferFunction(s, 1 - s, s)
+        >>> tf2 = TransferFunction(1, s, s)
+        >>> tf3 = TransferFunction(5, 1, s)
+        >>> tf4 = TransferFunction(s - 1, s, s)
+        >>> tf5 = TransferFunction(0, 1, s)
+        >>> sys1 = TransferFunctionMatrix([[tf1, tf2], [tf3, tf4]])
+        >>> sys2 = TransferFunctionMatrix([[tf3, tf5], [tf5, tf5]])
+        >>> F_1 = MIMOFeedback(sys1, sys2, 1)
+        >>> pprint(F_1, use_unicode=False)
+        /    [  s      1  ]    [5  0]   \-1   [  s      1  ]
+        |    [-----    -  ]    [-  -]   |     [-----    -  ]
+        |    [1 - s    s  ]    [1  1]   |     [1 - s    s  ]
+        |I - [            ]   *[    ]   |   * [            ]
+        |    [  5    s - 1]    [0  0]   |     [  5    s - 1]
+        |    [  -    -----]    [-  -]   |     [  -    -----]
+        \    [  1      s  ]{t} [1  1]{t}/     [  1      s  ]{t}
+        >>> pprint(F_1.doit(), use_unicode=False)
+        [  -s           s - 1       ]
+        [-------     -----------    ]
+        [6*s - 1     s*(6*s - 1)    ]
+        [                           ]
+        [5*s - 5  (s - 1)*(6*s + 24)]
+        [-------  ------------------]
+        [6*s - 1     s*(6*s - 1)    ]{t}
+
+        If the user wants the resultant ``TransferFunctionMatrix`` object without
+        canceling the common factors then the ``cancel`` kwarg should be passed ``False``.
+
+        >>> pprint(F_1.doit(cancel=False), use_unicode=False)
+        [             s*(s - 1)                              s - 1               ]
+        [         -----------------                       -----------            ]
+        [         (1 - s)*(6*s - 1)                       s*(6*s - 1)            ]
+        [                                                                        ]
+        [s*(25*s - 25) + 5*(1 - s)*(6*s - 1)  s*(s - 1)*(6*s - 1) + s*(25*s - 25)]
+        [-----------------------------------  -----------------------------------]
+        [         (1 - s)*(6*s - 1)                        2                     ]
+        [                                                 s *(6*s - 1)           ]{t}
+
+        If the user wants the expanded form of the resultant transfer function matrix,
+        the ``expand`` kwarg should be passed as ``True``.
+
+        >>> pprint(F_1.doit(expand=True), use_unicode=False)
+        [  -s          s - 1      ]
+        [-------      --------    ]
+        [6*s - 1         2        ]
+        [             6*s  - s    ]
+        [                         ]
+        [            2            ]
+        [5*s - 5  6*s  + 18*s - 24]
+        [-------  ----------------]
+        [6*s - 1         2        ]
+        [             6*s  - s    ]{t}
+
+        """
+        _mat = self.sensitivity * self.sys1.doit()._expr_mat
+
+        _resultant_tfm = _to_TFM(_mat, self.var)
+
+        if cancel:
+            _resultant_tfm = _resultant_tfm.simplify()
+
+        if expand:
+            _resultant_tfm = _resultant_tfm.expand()
+
+        return _resultant_tfm
+
+    def _eval_rewrite_as_TransferFunctionMatrix(self, sys1, sys2, sign, **kwargs):
+        return self.doit()
+
+    def __neg__(self):
+        return MIMOFeedback(-self.sys1, -self.sys2, self.sign)
+
+
+def _to_TFM(mat, var):
+    """Private method to convert ImmutableMatrix to TransferFunctionMatrix efficiently"""
+    to_tf = lambda expr: TransferFunction.from_rational_expression(expr, var)
+    arg = [[to_tf(expr) for expr in row] for row in mat.tolist()]
+    return TransferFunctionMatrix(arg)
+
+
+class TransferFunctionMatrix(MIMOLinearTimeInvariant):
+    r"""
+    A class for representing the MIMO (multiple-input and multiple-output)
+    generalization of the SISO (single-input and single-output) transfer function.
+
+    It is a matrix of transfer functions (``TransferFunction``, SISO-``Series`` or SISO-``Parallel``).
+    There is only one argument, ``arg`` which is also the compulsory argument.
+    ``arg`` is expected to be strictly of the type list of lists
+    which holds the transfer functions or reducible to transfer functions.
+
+    Parameters
+    ==========
+
+    arg : Nested ``List`` (strictly).
+        Users are expected to input a nested list of ``TransferFunction``, ``Series``
+        and/or ``Parallel`` objects.
+
+    Examples
+    ========
+
+    .. note::
+        ``pprint()`` can be used for better visualization of ``TransferFunctionMatrix`` objects.
+
+    >>> from sympy.abc import s, p, a
+    >>> from sympy import pprint
+    >>> from sympy.physics.control.lti import TransferFunction, TransferFunctionMatrix, Series, Parallel
+    >>> tf_1 = TransferFunction(s + a, s**2 + s + 1, s)
+    >>> tf_2 = TransferFunction(p**4 - 3*p + 2, s + p, s)
+    >>> tf_3 = TransferFunction(3, s + 2, s)
+    >>> tf_4 = TransferFunction(-a + p, 9*s - 9, s)
+    >>> tfm_1 = TransferFunctionMatrix([[tf_1], [tf_2], [tf_3]])
+    >>> tfm_1
+    TransferFunctionMatrix(((TransferFunction(a + s, s**2 + s + 1, s),), (TransferFunction(p**4 - 3*p + 2, p + s, s),), (TransferFunction(3, s + 2, s),)))
+    >>> tfm_1.var
+    s
+    >>> tfm_1.num_inputs
+    1
+    >>> tfm_1.num_outputs
+    3
+    >>> tfm_1.shape
+    (3, 1)
+    >>> tfm_1.args
+    (((TransferFunction(a + s, s**2 + s + 1, s),), (TransferFunction(p**4 - 3*p + 2, p + s, s),), (TransferFunction(3, s + 2, s),)),)
+    >>> tfm_2 = TransferFunctionMatrix([[tf_1, -tf_3], [tf_2, -tf_1], [tf_3, -tf_2]])
+    >>> tfm_2
+    TransferFunctionMatrix(((TransferFunction(a + s, s**2 + s + 1, s), TransferFunction(-3, s + 2, s)), (TransferFunction(p**4 - 3*p + 2, p + s, s), TransferFunction(-a - s, s**2 + s + 1, s)), (TransferFunction(3, s + 2, s), TransferFunction(-p**4 + 3*p - 2, p + s, s))))
+    >>> pprint(tfm_2, use_unicode=False)  # pretty-printing for better visualization
+    [   a + s           -3       ]
+    [ ----------       -----     ]
+    [  2               s + 2     ]
+    [ s  + s + 1                 ]
+    [                            ]
+    [ 4                          ]
+    [p  - 3*p + 2      -a - s    ]
+    [------------    ----------  ]
+    [   p + s         2          ]
+    [                s  + s + 1  ]
+    [                            ]
+    [                 4          ]
+    [     3        - p  + 3*p - 2]
+    [   -----      --------------]
+    [   s + 2          p + s     ]{t}
+
+    TransferFunctionMatrix can be transposed, if user wants to switch the input and output transfer functions
+
+    >>> tfm_2.transpose()
+    TransferFunctionMatrix(((TransferFunction(a + s, s**2 + s + 1, s), TransferFunction(p**4 - 3*p + 2, p + s, s), TransferFunction(3, s + 2, s)), (TransferFunction(-3, s + 2, s), TransferFunction(-a - s, s**2 + s + 1, s), TransferFunction(-p**4 + 3*p - 2, p + s, s))))
+    >>> pprint(_, use_unicode=False)
+    [             4                          ]
+    [  a + s     p  - 3*p + 2        3       ]
+    [----------  ------------      -----     ]
+    [ 2             p + s          s + 2     ]
+    [s  + s + 1                              ]
+    [                                        ]
+    [                             4          ]
+    [   -3          -a - s     - p  + 3*p - 2]
+    [  -----      ----------   --------------]
+    [  s + 2       2               p + s     ]
+    [             s  + s + 1                 ]{t}
+
+    >>> tf_5 = TransferFunction(5, s, s)
+    >>> tf_6 = TransferFunction(5*s, (2 + s**2), s)
+    >>> tf_7 = TransferFunction(5, (s*(2 + s**2)), s)
+    >>> tf_8 = TransferFunction(5, 1, s)
+    >>> tfm_3 = TransferFunctionMatrix([[tf_5, tf_6], [tf_7, tf_8]])
+    >>> tfm_3
+    TransferFunctionMatrix(((TransferFunction(5, s, s), TransferFunction(5*s, s**2 + 2, s)), (TransferFunction(5, s*(s**2 + 2), s), TransferFunction(5, 1, s))))
+    >>> pprint(tfm_3, use_unicode=False)
+    [    5        5*s  ]
+    [    -       ------]
+    [    s        2    ]
+    [            s  + 2]
+    [                  ]
+    [    5         5   ]
+    [----------    -   ]
+    [  / 2    \    1   ]
+    [s*\s  + 2/        ]{t}
+    >>> tfm_3.var
+    s
+    >>> tfm_3.shape
+    (2, 2)
+    >>> tfm_3.num_outputs
+    2
+    >>> tfm_3.num_inputs
+    2
+    >>> tfm_3.args
+    (((TransferFunction(5, s, s), TransferFunction(5*s, s**2 + 2, s)), (TransferFunction(5, s*(s**2 + 2), s), TransferFunction(5, 1, s))),)
+
+    To access the ``TransferFunction`` at any index in the ``TransferFunctionMatrix``, use the index notation.
+
+    >>> tfm_3[1, 0]  # gives the TransferFunction present at 2nd Row and 1st Col. Similar to that in Matrix classes
+    TransferFunction(5, s*(s**2 + 2), s)
+    >>> tfm_3[0, 0]  # gives the TransferFunction present at 1st Row and 1st Col.
+    TransferFunction(5, s, s)
+    >>> tfm_3[:, 0]  # gives the first column
+    TransferFunctionMatrix(((TransferFunction(5, s, s),), (TransferFunction(5, s*(s**2 + 2), s),)))
+    >>> pprint(_, use_unicode=False)
+    [    5     ]
+    [    -     ]
+    [    s     ]
+    [          ]
+    [    5     ]
+    [----------]
+    [  / 2    \]
+    [s*\s  + 2/]{t}
+    >>> tfm_3[0, :]  # gives the first row
+    TransferFunctionMatrix(((TransferFunction(5, s, s), TransferFunction(5*s, s**2 + 2, s)),))
+    >>> pprint(_, use_unicode=False)
+    [5   5*s  ]
+    [-  ------]
+    [s   2    ]
+    [   s  + 2]{t}
+
+    To negate a transfer function matrix, ``-`` operator can be prepended:
+
+    >>> tfm_4 = TransferFunctionMatrix([[tf_2], [-tf_1], [tf_3]])
+    >>> -tfm_4
+    TransferFunctionMatrix(((TransferFunction(-p**4 + 3*p - 2, p + s, s),), (TransferFunction(a + s, s**2 + s + 1, s),), (TransferFunction(-3, s + 2, s),)))
+    >>> tfm_5 = TransferFunctionMatrix([[tf_1, tf_2], [tf_3, -tf_1]])
+    >>> -tfm_5
+    TransferFunctionMatrix(((TransferFunction(-a - s, s**2 + s + 1, s), TransferFunction(-p**4 + 3*p - 2, p + s, s)), (TransferFunction(-3, s + 2, s), TransferFunction(a + s, s**2 + s + 1, s))))
+
+    ``subs()`` returns the ``TransferFunctionMatrix`` object with the value substituted in the expression. This will not
+    mutate your original ``TransferFunctionMatrix``.
+
+    >>> tfm_2.subs(p, 2)  #  substituting p everywhere in tfm_2 with 2.
+    TransferFunctionMatrix(((TransferFunction(a + s, s**2 + s + 1, s), TransferFunction(-3, s + 2, s)), (TransferFunction(12, s + 2, s), TransferFunction(-a - s, s**2 + s + 1, s)), (TransferFunction(3, s + 2, s), TransferFunction(-12, s + 2, s))))
+    >>> pprint(_, use_unicode=False)
+    [  a + s        -3     ]
+    [----------    -----   ]
+    [ 2            s + 2   ]
+    [s  + s + 1            ]
+    [                      ]
+    [    12        -a - s  ]
+    [  -----     ----------]
+    [  s + 2      2        ]
+    [            s  + s + 1]
+    [                      ]
+    [    3          -12    ]
+    [  -----       -----   ]
+    [  s + 2       s + 2   ]{t}
+    >>> pprint(tfm_2, use_unicode=False) # State of tfm_2 is unchanged after substitution
+    [   a + s           -3       ]
+    [ ----------       -----     ]
+    [  2               s + 2     ]
+    [ s  + s + 1                 ]
+    [                            ]
+    [ 4                          ]
+    [p  - 3*p + 2      -a - s    ]
+    [------------    ----------  ]
+    [   p + s         2          ]
+    [                s  + s + 1  ]
+    [                            ]
+    [                 4          ]
+    [     3        - p  + 3*p - 2]
+    [   -----      --------------]
+    [   s + 2          p + s     ]{t}
+
+    ``subs()`` also supports multiple substitutions.
+
+    >>> tfm_2.subs({p: 2, a: 1})  # substituting p with 2 and a with 1
+    TransferFunctionMatrix(((TransferFunction(s + 1, s**2 + s + 1, s), TransferFunction(-3, s + 2, s)), (TransferFunction(12, s + 2, s), TransferFunction(-s - 1, s**2 + s + 1, s)), (TransferFunction(3, s + 2, s), TransferFunction(-12, s + 2, s))))
+    >>> pprint(_, use_unicode=False)
+    [  s + 1        -3     ]
+    [----------    -----   ]
+    [ 2            s + 2   ]
+    [s  + s + 1            ]
+    [                      ]
+    [    12        -s - 1  ]
+    [  -----     ----------]
+    [  s + 2      2        ]
+    [            s  + s + 1]
+    [                      ]
+    [    3          -12    ]
+    [  -----       -----   ]
+    [  s + 2       s + 2   ]{t}
+
+    Users can reduce the ``Series`` and ``Parallel`` elements of the matrix to ``TransferFunction`` by using
+    ``doit()``.
+
+    >>> tfm_6 = TransferFunctionMatrix([[Series(tf_3, tf_4), Parallel(tf_3, tf_4)]])
+    >>> tfm_6
+    TransferFunctionMatrix(((Series(TransferFunction(3, s + 2, s), TransferFunction(-a + p, 9*s - 9, s)), Parallel(TransferFunction(3, s + 2, s), TransferFunction(-a + p, 9*s - 9, s))),))
+    >>> pprint(tfm_6, use_unicode=False)
+    [-a + p    3    -a + p      3  ]
+    [-------*-----  ------- + -----]
+    [9*s - 9 s + 2  9*s - 9   s + 2]{t}
+    >>> tfm_6.doit()
+    TransferFunctionMatrix(((TransferFunction(-3*a + 3*p, (s + 2)*(9*s - 9), s), TransferFunction(27*s + (-a + p)*(s + 2) - 27, (s + 2)*(9*s - 9), s)),))
+    >>> pprint(_, use_unicode=False)
+    [    -3*a + 3*p     27*s + (-a + p)*(s + 2) - 27]
+    [-----------------  ----------------------------]
+    [(s + 2)*(9*s - 9)       (s + 2)*(9*s - 9)      ]{t}
+    >>> tf_9 = TransferFunction(1, s, s)
+    >>> tf_10 = TransferFunction(1, s**2, s)
+    >>> tfm_7 = TransferFunctionMatrix([[Series(tf_9, tf_10), tf_9], [tf_10, Parallel(tf_9, tf_10)]])
+    >>> tfm_7
+    TransferFunctionMatrix(((Series(TransferFunction(1, s, s), TransferFunction(1, s**2, s)), TransferFunction(1, s, s)), (TransferFunction(1, s**2, s), Parallel(TransferFunction(1, s, s), TransferFunction(1, s**2, s)))))
+    >>> pprint(tfm_7, use_unicode=False)
+    [ 1      1   ]
+    [----    -   ]
+    [   2    s   ]
+    [s*s         ]
+    [            ]
+    [ 1    1    1]
+    [ --   -- + -]
+    [  2    2   s]
+    [ s    s     ]{t}
+    >>> tfm_7.doit()
+    TransferFunctionMatrix(((TransferFunction(1, s**3, s), TransferFunction(1, s, s)), (TransferFunction(1, s**2, s), TransferFunction(s**2 + s, s**3, s))))
+    >>> pprint(_, use_unicode=False)
+    [1     1   ]
+    [--    -   ]
+    [ 3    s   ]
+    [s         ]
+    [          ]
+    [     2    ]
+    [1   s  + s]
+    [--  ------]
+    [ 2     3  ]
+    [s     s   ]{t}
+
+    Addition, subtraction, and multiplication of transfer function matrices can form
+    unevaluated ``Series`` or ``Parallel`` objects.
+
+    - For addition and subtraction:
+      All the transfer function matrices must have the same shape.
+
+    - For multiplication (C = A * B):
+      The number of inputs of the first transfer function matrix (A) must be equal to the
+      number of outputs of the second transfer function matrix (B).
+
+    Also, use pretty-printing (``pprint``) to analyse better.
+
+    >>> tfm_8 = TransferFunctionMatrix([[tf_3], [tf_2], [-tf_1]])
+    >>> tfm_9 = TransferFunctionMatrix([[-tf_3]])
+    >>> tfm_10 = TransferFunctionMatrix([[tf_1], [tf_2], [tf_4]])
+    >>> tfm_11 = TransferFunctionMatrix([[tf_4], [-tf_1]])
+    >>> tfm_12 = TransferFunctionMatrix([[tf_4, -tf_1, tf_3], [-tf_2, -tf_4, -tf_3]])
+    >>> tfm_8 + tfm_10
+    MIMOParallel(TransferFunctionMatrix(((TransferFunction(3, s + 2, s),), (TransferFunction(p**4 - 3*p + 2, p + s, s),), (TransferFunction(-a - s, s**2 + s + 1, s),))), TransferFunctionMatrix(((TransferFunction(a + s, s**2 + s + 1, s),), (TransferFunction(p**4 - 3*p + 2, p + s, s),), (TransferFunction(-a + p, 9*s - 9, s),))))
+    >>> pprint(_, use_unicode=False)
+    [     3      ]      [   a + s    ]
+    [   -----    ]      [ ---------- ]
+    [   s + 2    ]      [  2         ]
+    [            ]      [ s  + s + 1 ]
+    [ 4          ]      [            ]
+    [p  - 3*p + 2]      [ 4          ]
+    [------------]    + [p  - 3*p + 2]
+    [   p + s    ]      [------------]
+    [            ]      [   p + s    ]
+    [   -a - s   ]      [            ]
+    [ ---------- ]      [   -a + p   ]
+    [  2         ]      [  -------   ]
+    [ s  + s + 1 ]{t}   [  9*s - 9   ]{t}
+    >>> -tfm_10 - tfm_8
+    MIMOParallel(TransferFunctionMatrix(((TransferFunction(-a - s, s**2 + s + 1, s),), (TransferFunction(-p**4 + 3*p - 2, p + s, s),), (TransferFunction(a - p, 9*s - 9, s),))), TransferFunctionMatrix(((TransferFunction(-3, s + 2, s),), (TransferFunction(-p**4 + 3*p - 2, p + s, s),), (TransferFunction(a + s, s**2 + s + 1, s),))))
+    >>> pprint(_, use_unicode=False)
+    [    -a - s    ]      [     -3       ]
+    [  ----------  ]      [    -----     ]
+    [   2          ]      [    s + 2     ]
+    [  s  + s + 1  ]      [              ]
+    [              ]      [   4          ]
+    [   4          ]      [- p  + 3*p - 2]
+    [- p  + 3*p - 2]    + [--------------]
+    [--------------]      [    p + s     ]
+    [    p + s     ]      [              ]
+    [              ]      [    a + s     ]
+    [    a - p     ]      [  ----------  ]
+    [   -------    ]      [   2          ]
+    [   9*s - 9    ]{t}   [  s  + s + 1  ]{t}
+    >>> tfm_12 * tfm_8
+    MIMOSeries(TransferFunctionMatrix(((TransferFunction(3, s + 2, s),), (TransferFunction(p**4 - 3*p + 2, p + s, s),), (TransferFunction(-a - s, s**2 + s + 1, s),))), TransferFunctionMatrix(((TransferFunction(-a + p, 9*s - 9, s), TransferFunction(-a - s, s**2 + s + 1, s), TransferFunction(3, s + 2, s)), (TransferFunction(-p**4 + 3*p - 2, p + s, s), TransferFunction(a - p, 9*s - 9, s), TransferFunction(-3, s + 2, s)))))
+    >>> pprint(_, use_unicode=False)
+                                           [     3      ]
+                                           [   -----    ]
+    [    -a + p        -a - s      3  ]    [   s + 2    ]
+    [   -------      ----------  -----]    [            ]
+    [   9*s - 9       2          s + 2]    [ 4          ]
+    [                s  + s + 1       ]    [p  - 3*p + 2]
+    [                                 ]   *[------------]
+    [   4                             ]    [   p + s    ]
+    [- p  + 3*p - 2    a - p      -3  ]    [            ]
+    [--------------   -------    -----]    [   -a - s   ]
+    [    p + s        9*s - 9    s + 2]{t} [ ---------- ]
+                                           [  2         ]
+                                           [ s  + s + 1 ]{t}
+    >>> tfm_12 * tfm_8 * tfm_9
+    MIMOSeries(TransferFunctionMatrix(((TransferFunction(-3, s + 2, s),),)), TransferFunctionMatrix(((TransferFunction(3, s + 2, s),), (TransferFunction(p**4 - 3*p + 2, p + s, s),), (TransferFunction(-a - s, s**2 + s + 1, s),))), TransferFunctionMatrix(((TransferFunction(-a + p, 9*s - 9, s), TransferFunction(-a - s, s**2 + s + 1, s), TransferFunction(3, s + 2, s)), (TransferFunction(-p**4 + 3*p - 2, p + s, s), TransferFunction(a - p, 9*s - 9, s), TransferFunction(-3, s + 2, s)))))
+    >>> pprint(_, use_unicode=False)
+                                           [     3      ]
+                                           [   -----    ]
+    [    -a + p        -a - s      3  ]    [   s + 2    ]
+    [   -------      ----------  -----]    [            ]
+    [   9*s - 9       2          s + 2]    [ 4          ]
+    [                s  + s + 1       ]    [p  - 3*p + 2]    [ -3  ]
+    [                                 ]   *[------------]   *[-----]
+    [   4                             ]    [   p + s    ]    [s + 2]{t}
+    [- p  + 3*p - 2    a - p      -3  ]    [            ]
+    [--------------   -------    -----]    [   -a - s   ]
+    [    p + s        9*s - 9    s + 2]{t} [ ---------- ]
+                                           [  2         ]
+                                           [ s  + s + 1 ]{t}
+    >>> tfm_10 + tfm_8*tfm_9
+    MIMOParallel(TransferFunctionMatrix(((TransferFunction(a + s, s**2 + s + 1, s),), (TransferFunction(p**4 - 3*p + 2, p + s, s),), (TransferFunction(-a + p, 9*s - 9, s),))), MIMOSeries(TransferFunctionMatrix(((TransferFunction(-3, s + 2, s),),)), TransferFunctionMatrix(((TransferFunction(3, s + 2, s),), (TransferFunction(p**4 - 3*p + 2, p + s, s),), (TransferFunction(-a - s, s**2 + s + 1, s),)))))
+    >>> pprint(_, use_unicode=False)
+    [   a + s    ]      [     3      ]
+    [ ---------- ]      [   -----    ]
+    [  2         ]      [   s + 2    ]
+    [ s  + s + 1 ]      [            ]
+    [            ]      [ 4          ]
+    [ 4          ]      [p  - 3*p + 2]    [ -3  ]
+    [p  - 3*p + 2]    + [------------]   *[-----]
+    [------------]      [   p + s    ]    [s + 2]{t}
+    [   p + s    ]      [            ]
+    [            ]      [   -a - s   ]
+    [   -a + p   ]      [ ---------- ]
+    [  -------   ]      [  2         ]
+    [  9*s - 9   ]{t}   [ s  + s + 1 ]{t}
+
+    These unevaluated ``Series`` or ``Parallel`` objects can convert into the
+    resultant transfer function matrix using ``.doit()`` method or by
+    ``.rewrite(TransferFunctionMatrix)``.
+
+    >>> (-tfm_8 + tfm_10 + tfm_8*tfm_9).doit()
+    TransferFunctionMatrix(((TransferFunction((a + s)*(s + 2)**3 - 3*(s + 2)**2*(s**2 + s + 1) - 9*(s + 2)*(s**2 + s + 1), (s + 2)**3*(s**2 + s + 1), s),), (TransferFunction((p + s)*(-3*p**4 + 9*p - 6), (p + s)**2*(s + 2), s),), (TransferFunction((-a + p)*(s + 2)*(s**2 + s + 1)**2 + (a + s)*(s + 2)*(9*s - 9)*(s**2 + s + 1) + (3*a + 3*s)*(9*s - 9)*(s**2 + s + 1), (s + 2)*(9*s - 9)*(s**2 + s + 1)**2, s),)))
+    >>> (-tfm_12 * -tfm_8 * -tfm_9).rewrite(TransferFunctionMatrix)
+    TransferFunctionMatrix(((TransferFunction(3*(-3*a + 3*p)*(p + s)*(s + 2)*(s**2 + s + 1)**2 + 3*(-3*a - 3*s)*(p + s)*(s + 2)*(9*s - 9)*(s**2 + s + 1) + 3*(a + s)*(s + 2)**2*(9*s - 9)*(-p**4 + 3*p - 2)*(s**2 + s + 1), (p + s)*(s + 2)**3*(9*s - 9)*(s**2 + s + 1)**2, s),), (TransferFunction(3*(-a + p)*(p + s)*(s + 2)**2*(-p**4 + 3*p - 2)*(s**2 + s + 1) + 3*(3*a + 3*s)*(p + s)**2*(s + 2)*(9*s - 9) + 3*(p + s)*(s + 2)*(9*s - 9)*(-3*p**4 + 9*p - 6)*(s**2 + s + 1), (p + s)**2*(s + 2)**3*(9*s - 9)*(s**2 + s + 1), s),)))
+
+    See Also
+    ========
+
+    TransferFunction, MIMOSeries, MIMOParallel, Feedback
+
+    """
+    def __new__(cls, arg):
+
+        expr_mat_arg = []
+        try:
+            var = arg[0][0].var
+        except TypeError:
+            raise ValueError(filldedent("""
+                `arg` param in TransferFunctionMatrix should
+                strictly be a nested list containing TransferFunction
+                objects."""))
+        for row in arg:
+            temp = []
+            for element in row:
+                if not isinstance(element, SISOLinearTimeInvariant):
+                    raise TypeError(filldedent("""
+                        Each element is expected to be of
+                        type `SISOLinearTimeInvariant`."""))
+
+                if var != element.var:
+                    raise ValueError(filldedent("""
+                        Conflicting value(s) found for `var`. All TransferFunction
+                        instances in TransferFunctionMatrix should use the same
+                        complex variable in Laplace domain."""))
+
+                temp.append(element.to_expr())
+            expr_mat_arg.append(temp)
+
+        if isinstance(arg, (tuple, list, Tuple)):
+            # Making nested Tuple (sympy.core.containers.Tuple) from nested list or nested Python tuple
+            arg = Tuple(*(Tuple(*r, sympify=False) for r in arg), sympify=False)
+
+        obj = super(TransferFunctionMatrix, cls).__new__(cls, arg)
+        obj._expr_mat = ImmutableMatrix(expr_mat_arg)
+        return obj
+
+    @classmethod
+    def from_Matrix(cls, matrix, var):
+        """
+        Creates a new ``TransferFunctionMatrix`` efficiently from a SymPy Matrix of ``Expr`` objects.
+
+        Parameters
+        ==========
+
+        matrix : ``ImmutableMatrix`` having ``Expr``/``Number`` elements.
+        var : Symbol
+            Complex variable of the Laplace transform which will be used by the
+            all the ``TransferFunction`` objects in the ``TransferFunctionMatrix``.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s
+        >>> from sympy.physics.control.lti import TransferFunctionMatrix
+        >>> from sympy import Matrix, pprint
+        >>> M = Matrix([[s, 1/s], [1/(s+1), s]])
+        >>> M_tf = TransferFunctionMatrix.from_Matrix(M, s)
+        >>> pprint(M_tf, use_unicode=False)
+        [  s    1]
+        [  -    -]
+        [  1    s]
+        [        ]
+        [  1    s]
+        [-----  -]
+        [s + 1  1]{t}
+        >>> M_tf.elem_poles()
+        [[[], [0]], [[-1], []]]
+        >>> M_tf.elem_zeros()
+        [[[0], []], [[], [0]]]
+
+        """
+        return _to_TFM(matrix, var)
+
+    @property
+    def var(self):
+        """
+        Returns the complex variable used by all the transfer functions or
+        ``Series``/``Parallel`` objects in a transfer function matrix.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import p, s
+        >>> from sympy.physics.control.lti import TransferFunction, TransferFunctionMatrix, Series, Parallel
+        >>> G1 = TransferFunction(p**2 + 2*p + 4, p - 6, p)
+        >>> G2 = TransferFunction(p, 4 - p, p)
+        >>> G3 = TransferFunction(0, p**4 - 1, p)
+        >>> G4 = TransferFunction(s + 1, s**2 + s + 1, s)
+        >>> S1 = Series(G1, G2)
+        >>> S2 = Series(-G3, Parallel(G2, -G1))
+        >>> tfm1 = TransferFunctionMatrix([[G1], [G2], [G3]])
+        >>> tfm1.var
+        p
+        >>> tfm2 = TransferFunctionMatrix([[-S1, -S2], [S1, S2]])
+        >>> tfm2.var
+        p
+        >>> tfm3 = TransferFunctionMatrix([[G4]])
+        >>> tfm3.var
+        s
+
+        """
+        return self.args[0][0][0].var
+
+    @property
+    def num_inputs(self):
+        """
+        Returns the number of inputs of the system.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p
+        >>> from sympy.physics.control.lti import TransferFunction, TransferFunctionMatrix
+        >>> G1 = TransferFunction(s + 3, s**2 - 3, s)
+        >>> G2 = TransferFunction(4, s**2, s)
+        >>> G3 = TransferFunction(p**2 + s**2, p - 3, s)
+        >>> tfm_1 = TransferFunctionMatrix([[G2, -G1, G3], [-G2, -G1, -G3]])
+        >>> tfm_1.num_inputs
+        3
+
+        See Also
+        ========
+
+        num_outputs
+
+        """
+        return self._expr_mat.shape[1]
+
+    @property
+    def num_outputs(self):
+        """
+        Returns the number of outputs of the system.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s
+        >>> from sympy.physics.control.lti import TransferFunctionMatrix
+        >>> from sympy import Matrix
+        >>> M_1 = Matrix([[s], [1/s]])
+        >>> TFM = TransferFunctionMatrix.from_Matrix(M_1, s)
+        >>> print(TFM)
+        TransferFunctionMatrix(((TransferFunction(s, 1, s),), (TransferFunction(1, s, s),)))
+        >>> TFM.num_outputs
+        2
+
+        See Also
+        ========
+
+        num_inputs
+
+        """
+        return self._expr_mat.shape[0]
+
+    @property
+    def shape(self):
+        """
+        Returns the shape of the transfer function matrix, that is, ``(# of outputs, # of inputs)``.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s, p
+        >>> from sympy.physics.control.lti import TransferFunction, TransferFunctionMatrix
+        >>> tf1 = TransferFunction(p**2 - 1, s**4 + s**3 - p, p)
+        >>> tf2 = TransferFunction(1 - p, p**2 - 3*p + 7, p)
+        >>> tf3 = TransferFunction(3, 4, p)
+        >>> tfm1 = TransferFunctionMatrix([[tf1, -tf2]])
+        >>> tfm1.shape
+        (1, 2)
+        >>> tfm2 = TransferFunctionMatrix([[-tf2, tf3], [tf1, -tf1]])
+        >>> tfm2.shape
+        (2, 2)
+
+        """
+        return self._expr_mat.shape
+
+    def __neg__(self):
+        neg = -self._expr_mat
+        return _to_TFM(neg, self.var)
+
+    @_check_other_MIMO
+    def __add__(self, other):
+
+        if not isinstance(other, MIMOParallel):
+            return MIMOParallel(self, other)
+        other_arg_list = list(other.args)
+        return MIMOParallel(self, *other_arg_list)
+
+    @_check_other_MIMO
+    def __sub__(self, other):
+        return self + (-other)
+
+    @_check_other_MIMO
+    def __mul__(self, other):
+
+        if not isinstance(other, MIMOSeries):
+            return MIMOSeries(other, self)
+        other_arg_list = list(other.args)
+        return MIMOSeries(*other_arg_list, self)
+
+    def __getitem__(self, key):
+        trunc = self._expr_mat.__getitem__(key)
+        if isinstance(trunc, ImmutableMatrix):
+            return _to_TFM(trunc, self.var)
+        return TransferFunction.from_rational_expression(trunc, self.var)
+
+    def transpose(self):
+        """Returns the transpose of the ``TransferFunctionMatrix`` (switched input and output layers)."""
+        transposed_mat = self._expr_mat.transpose()
+        return _to_TFM(transposed_mat, self.var)
+
+    def elem_poles(self):
+        """
+        Returns the poles of each element of the ``TransferFunctionMatrix``.
+
+        .. note::
+            Actual poles of a MIMO system are NOT the poles of individual elements.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s
+        >>> from sympy.physics.control.lti import TransferFunction, TransferFunctionMatrix
+        >>> tf_1 = TransferFunction(3, (s + 1), s)
+        >>> tf_2 = TransferFunction(s + 6, (s + 1)*(s + 2), s)
+        >>> tf_3 = TransferFunction(s + 3, s**2 + 3*s + 2, s)
+        >>> tf_4 = TransferFunction(s + 2, s**2 + 5*s - 10, s)
+        >>> tfm_1 = TransferFunctionMatrix([[tf_1, tf_2], [tf_3, tf_4]])
+        >>> tfm_1
+        TransferFunctionMatrix(((TransferFunction(3, s + 1, s), TransferFunction(s + 6, (s + 1)*(s + 2), s)), (TransferFunction(s + 3, s**2 + 3*s + 2, s), TransferFunction(s + 2, s**2 + 5*s - 10, s))))
+        >>> tfm_1.elem_poles()
+        [[[-1], [-2, -1]], [[-2, -1], [-5/2 + sqrt(65)/2, -sqrt(65)/2 - 5/2]]]
+
+        See Also
+        ========
+
+        elem_zeros
+
+        """
+        return [[element.poles() for element in row] for row in self.doit().args[0]]
+
+    def elem_zeros(self):
+        """
+        Returns the zeros of each element of the ``TransferFunctionMatrix``.
+
+        .. note::
+            Actual zeros of a MIMO system are NOT the zeros of individual elements.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s
+        >>> from sympy.physics.control.lti import TransferFunction, TransferFunctionMatrix
+        >>> tf_1 = TransferFunction(3, (s + 1), s)
+        >>> tf_2 = TransferFunction(s + 6, (s + 1)*(s + 2), s)
+        >>> tf_3 = TransferFunction(s + 3, s**2 + 3*s + 2, s)
+        >>> tf_4 = TransferFunction(s**2 - 9*s + 20, s**2 + 5*s - 10, s)
+        >>> tfm_1 = TransferFunctionMatrix([[tf_1, tf_2], [tf_3, tf_4]])
+        >>> tfm_1
+        TransferFunctionMatrix(((TransferFunction(3, s + 1, s), TransferFunction(s + 6, (s + 1)*(s + 2), s)), (TransferFunction(s + 3, s**2 + 3*s + 2, s), TransferFunction(s**2 - 9*s + 20, s**2 + 5*s - 10, s))))
+        >>> tfm_1.elem_zeros()
+        [[[], [-6]], [[-3], [4, 5]]]
+
+        See Also
+        ========
+
+        elem_poles
+
+        """
+        return [[element.zeros() for element in row] for row in self.doit().args[0]]
+
+    def eval_frequency(self, other):
+        """
+        Evaluates system response of each transfer function in the ``TransferFunctionMatrix`` at any point in the real or complex plane.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import s
+        >>> from sympy.physics.control.lti import TransferFunction, TransferFunctionMatrix
+        >>> from sympy import I
+        >>> tf_1 = TransferFunction(3, (s + 1), s)
+        >>> tf_2 = TransferFunction(s + 6, (s + 1)*(s + 2), s)
+        >>> tf_3 = TransferFunction(s + 3, s**2 + 3*s + 2, s)
+        >>> tf_4 = TransferFunction(s**2 - 9*s + 20, s**2 + 5*s - 10, s)
+        >>> tfm_1 = TransferFunctionMatrix([[tf_1, tf_2], [tf_3, tf_4]])
+        >>> tfm_1
+        TransferFunctionMatrix(((TransferFunction(3, s + 1, s), TransferFunction(s + 6, (s + 1)*(s + 2), s)), (TransferFunction(s + 3, s**2 + 3*s + 2, s), TransferFunction(s**2 - 9*s + 20, s**2 + 5*s - 10, s))))
+        >>> tfm_1.eval_frequency(2)
+        Matrix([
+        [   1, 2/3],
+        [5/12, 3/2]])
+        >>> tfm_1.eval_frequency(I*2)
+        Matrix([
+        [   3/5 - 6*I/5,                -I],
+        [3/20 - 11*I/20, -101/74 + 23*I/74]])
+        """
+        mat = self._expr_mat.subs(self.var, other)
+        return mat.expand()
+
+    def _flat(self):
+        """Returns flattened list of args in TransferFunctionMatrix"""
+        return [elem for tup in self.args[0] for elem in tup]
+
+    def _eval_evalf(self, prec):
+        """Calls evalf() on each transfer function in the transfer function matrix"""
+        dps = prec_to_dps(prec)
+        mat = self._expr_mat.applyfunc(lambda a: a.evalf(n=dps))
+        return _to_TFM(mat, self.var)
+
+    def _eval_simplify(self, **kwargs):
+        """Simplifies the transfer function matrix"""
+        simp_mat = self._expr_mat.applyfunc(lambda a: cancel(a, expand=False))
+        return _to_TFM(simp_mat, self.var)
+
+    def expand(self, **hints):
+        """Expands the transfer function matrix"""
+        expand_mat = self._expr_mat.expand(**hints)
+        return _to_TFM(expand_mat, self.var)
+
+class StateSpace(LinearTimeInvariant):
+    r"""
+    State space model (ssm) of a linear, time invariant control system.
+
+    Represents the standard state-space model with A, B, C, D as state-space matrices.
+    This makes the linear control system:
+        (1) x'(t) = A * x(t) + B * u(t);    x in R^n , u in R^k
+        (2) y(t)  = C * x(t) + D * u(t);    y in R^m
+    where u(t) is any input signal, y(t) the corresponding output, and x(t) the system's state.
+
+    Parameters
+    ==========
+
+    A : Matrix
+        The State matrix of the state space model.
+    B : Matrix
+        The Input-to-State matrix of the state space model.
+    C : Matrix
+        The State-to-Output matrix of the state space model.
+    D : Matrix
+        The Feedthrough matrix of the state space model.
+
+    Examples
+    ========
+
+    >>> from sympy import Matrix
+    >>> from sympy.physics.control import StateSpace
+
+    The easiest way to create a StateSpaceModel is via four matrices:
+
+    >>> A = Matrix([[1, 2], [1, 0]])
+    >>> B = Matrix([1, 1])
+    >>> C = Matrix([[0, 1]])
+    >>> D = Matrix([0])
+    >>> StateSpace(A, B, C, D)
+    StateSpace(Matrix([
+    [1, 2],
+    [1, 0]]), Matrix([
+    [1],
+    [1]]), Matrix([[0, 1]]), Matrix([[0]]))
+
+
+    One can use less matrices. The rest will be filled with a minimum of zeros:
+
+    >>> StateSpace(A, B)
+    StateSpace(Matrix([
+    [1, 2],
+    [1, 0]]), Matrix([
+    [1],
+    [1]]), Matrix([[0, 0]]), Matrix([[0]]))
+
+
+    See Also
+    ========
+
+    TransferFunction, TransferFunctionMatrix
+
+    References
+    ==========
+    .. [1] https://en.wikipedia.org/wiki/State-space_representation
+    .. [2] https://in.mathworks.com/help/control/ref/ss.html
+
+    """
+    def __new__(cls, A=None, B=None, C=None, D=None):
+        if A is None:
+            A = zeros(1)
+        if B is None:
+            B = zeros(A.rows, 1)
+        if C is None:
+            C = zeros(1, A.cols)
+        if D is None:
+            D = zeros(C.rows, B.cols)
+
+        A = _sympify(A)
+        B = _sympify(B)
+        C = _sympify(C)
+        D = _sympify(D)
+
+        if (isinstance(A, ImmutableDenseMatrix) and isinstance(B, ImmutableDenseMatrix) and
+            isinstance(C, ImmutableDenseMatrix) and isinstance(D, ImmutableDenseMatrix)):
+            # Check State Matrix is square
+            if A.rows != A.cols:
+                raise ShapeError("Matrix A must be a square matrix.")
+
+            # Check State and Input matrices have same rows
+            if A.rows != B.rows:
+                raise ShapeError("Matrices A and B must have the same number of rows.")
+
+            # Check Ouput and Feedthrough matrices have same rows
+            if C.rows != D.rows:
+                raise ShapeError("Matrices C and D must have the same number of rows.")
+
+            # Check State and Ouput matrices have same columns
+            if A.cols != C.cols:
+                raise ShapeError("Matrices A and C must have the same number of columns.")
+
+            # Check Input and Feedthrough matrices have same columns
+            if B.cols != D.cols:
+                raise ShapeError("Matrices B and D must have the same number of columns.")
+
+            obj = super(StateSpace, cls).__new__(cls, A, B, C, D)
+            obj._A = A
+            obj._B = B
+            obj._C = C
+            obj._D = D
+
+            # Determine if the system is SISO or MIMO
+            num_outputs = D.rows
+            num_inputs = D.cols
+            if num_inputs == 1 and num_outputs == 1:
+                obj._is_SISO = True
+                obj._clstype = SISOLinearTimeInvariant
+            else:
+                obj._is_SISO = False
+                obj._clstype = MIMOLinearTimeInvariant
+
+            return obj
+
+        else:
+            raise TypeError("A, B, C and D inputs must all be sympy Matrices.")
+
+    @property
+    def state_matrix(self):
+        """
+        Returns the state matrix of the model.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A = Matrix([[1, 2], [1, 0]])
+        >>> B = Matrix([1, 1])
+        >>> C = Matrix([[0, 1]])
+        >>> D = Matrix([0])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> ss.state_matrix
+        Matrix([
+        [1, 2],
+        [1, 0]])
+
+        """
+        return self._A
+
+    @property
+    def input_matrix(self):
+        """
+        Returns the input matrix of the model.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A = Matrix([[1, 2], [1, 0]])
+        >>> B = Matrix([1, 1])
+        >>> C = Matrix([[0, 1]])
+        >>> D = Matrix([0])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> ss.input_matrix
+        Matrix([
+        [1],
+        [1]])
+
+        """
+        return self._B
+
+    @property
+    def output_matrix(self):
+        """
+        Returns the output matrix of the model.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A = Matrix([[1, 2], [1, 0]])
+        >>> B = Matrix([1, 1])
+        >>> C = Matrix([[0, 1]])
+        >>> D = Matrix([0])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> ss.output_matrix
+        Matrix([[0, 1]])
+
+        """
+        return self._C
+
+    @property
+    def feedforward_matrix(self):
+        """
+        Returns the feedforward matrix of the model.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A = Matrix([[1, 2], [1, 0]])
+        >>> B = Matrix([1, 1])
+        >>> C = Matrix([[0, 1]])
+        >>> D = Matrix([0])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> ss.feedforward_matrix
+        Matrix([[0]])
+
+        """
+        return self._D
+
+    @property
+    def num_states(self):
+        """
+        Returns the number of states of the model.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A = Matrix([[1, 2], [1, 0]])
+        >>> B = Matrix([1, 1])
+        >>> C = Matrix([[0, 1]])
+        >>> D = Matrix([0])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> ss.num_states
+        2
+
+        """
+        return self._A.rows
+
+    @property
+    def num_inputs(self):
+        """
+        Returns the number of inputs of the model.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A = Matrix([[1, 2], [1, 0]])
+        >>> B = Matrix([1, 1])
+        >>> C = Matrix([[0, 1]])
+        >>> D = Matrix([0])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> ss.num_inputs
+        1
+
+        """
+        return self._D.cols
+
+    @property
+    def num_outputs(self):
+        """
+        Returns the number of outputs of the model.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A = Matrix([[1, 2], [1, 0]])
+        >>> B = Matrix([1, 1])
+        >>> C = Matrix([[0, 1]])
+        >>> D = Matrix([0])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> ss.num_outputs
+        1
+
+        """
+        return self._D.rows
+
+    def _eval_evalf(self, prec):
+        """
+        Returns state space model where numerical expressions are evaluated into floating point numbers.
+        """
+        dps = prec_to_dps(prec)
+        return StateSpace(
+            self._A.evalf(n = dps),
+            self._B.evalf(n = dps),
+            self._C.evalf(n = dps),
+            self._D.evalf(n = dps))
+
+    def _eval_rewrite_as_TransferFunction(self, *args):
+        """
+        Returns the equivalent Transfer Function of the state space model.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import TransferFunction, StateSpace
+        >>> A = Matrix([[-5, -1], [3, -1]])
+        >>> B = Matrix([2, 5])
+        >>> C = Matrix([[1, 2]])
+        >>> D = Matrix([0])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> ss.rewrite(TransferFunction)
+        [[TransferFunction(12*s + 59, s**2 + 6*s + 8, s)]]
+
+        """
+        s = Symbol('s')
+        n = self._A.shape[0]
+        I = eye(n)
+        G = self._C*(s*I - self._A).solve(self._B) + self._D
+        G = G.simplify()
+        to_tf = lambda expr: TransferFunction.from_rational_expression(expr, s)
+        tf_mat = [[to_tf(expr) for expr in sublist] for sublist in G.tolist()]
+        return tf_mat
+
+    def __add__(self, other):
+        """
+        Add two State Space systems (parallel connection).
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A1 = Matrix([[1]])
+        >>> B1 = Matrix([[2]])
+        >>> C1 = Matrix([[-1]])
+        >>> D1 = Matrix([[-2]])
+        >>> A2 = Matrix([[-1]])
+        >>> B2 = Matrix([[-2]])
+        >>> C2 = Matrix([[1]])
+        >>> D2 = Matrix([[2]])
+        >>> ss1 = StateSpace(A1, B1, C1, D1)
+        >>> ss2 = StateSpace(A2, B2, C2, D2)
+        >>> ss1 + ss2
+        StateSpace(Matrix([
+        [1,  0],
+        [0, -1]]), Matrix([
+        [ 2],
+        [-2]]), Matrix([[-1, 1]]), Matrix([[0]]))
+
+        """
+        # Check for scalars
+        if isinstance(other, (int, float, complex, Symbol)):
+            A = self._A
+            B = self._B
+            C = self._C
+            D = self._D.applyfunc(lambda element: element + other)
+
+        else:
+            # Check nature of system
+            if not isinstance(other, StateSpace):
+                raise ValueError("Addition is only supported for 2 State Space models.")
+            # Check dimensions of system
+            elif ((self.num_inputs != other.num_inputs) or (self.num_outputs != other.num_outputs)):
+                raise ShapeError("Systems with incompatible inputs and outputs cannot be added.")
+
+            m1 = (self._A).row_join(zeros(self._A.shape[0], other._A.shape[-1]))
+            m2 = zeros(other._A.shape[0], self._A.shape[-1]).row_join(other._A)
+
+            A = m1.col_join(m2)
+            B = self._B.col_join(other._B)
+            C = self._C.row_join(other._C)
+            D = self._D + other._D
+
+        return StateSpace(A, B, C, D)
+
+    def __radd__(self, other):
+        """
+        Right add two State Space systems.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.control import StateSpace
+        >>> s = StateSpace()
+        >>> 5 + s
+        StateSpace(Matrix([[0]]), Matrix([[0]]), Matrix([[0]]), Matrix([[5]]))
+
+        """
+        return self + other
+
+    def __sub__(self, other):
+        """
+        Subtract two State Space systems.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A1 = Matrix([[1]])
+        >>> B1 = Matrix([[2]])
+        >>> C1 = Matrix([[-1]])
+        >>> D1 = Matrix([[-2]])
+        >>> A2 = Matrix([[-1]])
+        >>> B2 = Matrix([[-2]])
+        >>> C2 = Matrix([[1]])
+        >>> D2 = Matrix([[2]])
+        >>> ss1 = StateSpace(A1, B1, C1, D1)
+        >>> ss2 = StateSpace(A2, B2, C2, D2)
+        >>> ss1 - ss2
+        StateSpace(Matrix([
+        [1,  0],
+        [0, -1]]), Matrix([
+        [ 2],
+        [-2]]), Matrix([[-1, -1]]), Matrix([[-4]]))
+
+        """
+        return self + (-other)
+
+    def __rsub__(self, other):
+        """
+        Right subtract two tate Space systems.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.control import StateSpace
+        >>> s = StateSpace()
+        >>> 5 - s
+        StateSpace(Matrix([[0]]), Matrix([[0]]), Matrix([[0]]), Matrix([[5]]))
+
+        """
+        return other + (-self)
+
+    def __neg__(self):
+        """
+        Returns the negation of the state space model.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A = Matrix([[-5, -1], [3, -1]])
+        >>> B = Matrix([2, 5])
+        >>> C = Matrix([[1, 2]])
+        >>> D = Matrix([0])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> -ss
+        StateSpace(Matrix([
+        [-5, -1],
+        [ 3, -1]]), Matrix([
+        [2],
+        [5]]), Matrix([[-1, -2]]), Matrix([[0]]))
+
+        """
+        return StateSpace(self._A, self._B, -self._C, -self._D)
+
+    def __mul__(self, other):
+        """
+        Multiplication of two State Space systems (serial connection).
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A = Matrix([[-5, -1], [3, -1]])
+        >>> B = Matrix([2, 5])
+        >>> C = Matrix([[1, 2]])
+        >>> D = Matrix([0])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> ss*5
+        StateSpace(Matrix([
+        [-5, -1],
+        [ 3, -1]]), Matrix([
+        [2],
+        [5]]), Matrix([[5, 10]]), Matrix([[0]]))
+
+        """
+        # Check for scalars
+        if isinstance(other, (int, float, complex, Symbol)):
+            A = self._A
+            B = self._B
+            C = self._C.applyfunc(lambda element: element*other)
+            D = self._D.applyfunc(lambda element: element*other)
+
+        else:
+            # Check nature of system
+            if not isinstance(other, StateSpace):
+                raise ValueError("Multiplication is only supported for 2 State Space models.")
+            # Check dimensions of system
+            elif self.num_inputs != other.num_outputs:
+                raise ShapeError("Systems with incompatible inputs and outputs cannot be multiplied.")
+
+            m1 = (other._A).row_join(zeros(other._A.shape[0], self._A.shape[1]))
+            m2 = (self._B * other._C).row_join(self._A)
+
+            A = m1.col_join(m2)
+            B = (other._B).col_join(self._B * other._D)
+            C = (self._D * other._C).row_join(self._C)
+            D = self._D * other._D
+
+        return StateSpace(A, B, C, D)
+
+    def __rmul__(self, other):
+        """
+        Right multiply two tate Space systems.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A = Matrix([[-5, -1], [3, -1]])
+        >>> B = Matrix([2, 5])
+        >>> C = Matrix([[1, 2]])
+        >>> D = Matrix([0])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> 5*ss
+        StateSpace(Matrix([
+        [-5, -1],
+        [ 3, -1]]), Matrix([
+        [10],
+        [25]]), Matrix([[1, 2]]), Matrix([[0]]))
+
+        """
+        if isinstance(other, (int, float, complex, Symbol)):
+            A = self._A
+            C = self._C
+            B = self._B.applyfunc(lambda element: element*other)
+            D = self._D.applyfunc(lambda element: element*other)
+            return StateSpace(A, B, C, D)
+        else:
+            return self*other
+
+    def __repr__(self):
+        A_str = self._A.__repr__()
+        B_str = self._B.__repr__()
+        C_str = self._C.__repr__()
+        D_str = self._D.__repr__()
+
+        return f"StateSpace(\n{A_str},\n\n{B_str},\n\n{C_str},\n\n{D_str})"
+
+
+    def append(self, other):
+        """
+        Returns the first model appended with the second model. The order is preserved.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A1 = Matrix([[1]])
+        >>> B1 = Matrix([[2]])
+        >>> C1 = Matrix([[-1]])
+        >>> D1 = Matrix([[-2]])
+        >>> A2 = Matrix([[-1]])
+        >>> B2 = Matrix([[-2]])
+        >>> C2 = Matrix([[1]])
+        >>> D2 = Matrix([[2]])
+        >>> ss1 = StateSpace(A1, B1, C1, D1)
+        >>> ss2 = StateSpace(A2, B2, C2, D2)
+        >>> ss1.append(ss2)
+        StateSpace(Matrix([
+        [1,  0],
+        [0, -1]]), Matrix([
+        [2,  0],
+        [0, -2]]), Matrix([
+        [-1, 0],
+        [ 0, 1]]), Matrix([
+        [-2, 0],
+        [ 0, 2]]))
+
+        """
+        n = self.num_states + other.num_states
+        m = self.num_inputs + other.num_inputs
+        p = self.num_outputs + other.num_outputs
+
+        A = zeros(n, n)
+        B = zeros(n, m)
+        C = zeros(p, n)
+        D = zeros(p, m)
+
+        A[:self.num_states, :self.num_states] = self._A
+        A[self.num_states:, self.num_states:] = other._A
+        B[:self.num_states, :self.num_inputs] = self._B
+        B[self.num_states:, self.num_inputs:] = other._B
+        C[:self.num_outputs, :self.num_states] = self._C
+        C[self.num_outputs:, self.num_states:] = other._C
+        D[:self.num_outputs, :self.num_inputs] = self._D
+        D[self.num_outputs:, self.num_inputs:] = other._D
+        return StateSpace(A, B, C, D)
+
+    def observability_matrix(self):
+        """
+        Returns the observability matrix of the state space model:
+            [C, C * A^1, C * A^2, .. , C * A^(n-1)]; A in R^(n x n), C in R^(m x k)
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A = Matrix([[-1.5, -2], [1, 0]])
+        >>> B = Matrix([0.5, 0])
+        >>> C = Matrix([[0, 1]])
+        >>> D = Matrix([1])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> ob = ss.observability_matrix()
+        >>> ob
+        Matrix([
+        [0, 1],
+        [1, 0]])
+
+        References
+        ==========
+        .. [1] https://in.mathworks.com/help/control/ref/statespacemodel.obsv.html
+
+        """
+        n = self.num_states
+        ob = self._C
+        for i in range(1,n):
+            ob = ob.col_join(self._C * self._A**i)
+
+        return ob
+
+    def observable_subspace(self):
+        """
+        Returns the observable subspace of the state space model.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A = Matrix([[-1.5, -2], [1, 0]])
+        >>> B = Matrix([0.5, 0])
+        >>> C = Matrix([[0, 1]])
+        >>> D = Matrix([1])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> ob_subspace = ss.observable_subspace()
+        >>> ob_subspace
+        [Matrix([
+        [0],
+        [1]]), Matrix([
+        [1],
+        [0]])]
+
+        """
+        return self.observability_matrix().columnspace()
+
+    def is_observable(self):
+        """
+        Returns if the state space model is observable.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A = Matrix([[-1.5, -2], [1, 0]])
+        >>> B = Matrix([0.5, 0])
+        >>> C = Matrix([[0, 1]])
+        >>> D = Matrix([1])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> ss.is_observable()
+        True
+
+        """
+        return self.observability_matrix().rank() == self.num_states
+
+    def controllability_matrix(self):
+        """
+        Returns the controllability matrix of the system:
+            [B, A * B, A^2 * B, .. , A^(n-1) * B]; A in R^(n x n), B in R^(n x m)
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A = Matrix([[-1.5, -2], [1, 0]])
+        >>> B = Matrix([0.5, 0])
+        >>> C = Matrix([[0, 1]])
+        >>> D = Matrix([1])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> ss.controllability_matrix()
+        Matrix([
+        [0.5, -0.75],
+        [  0,   0.5]])
+
+        References
+        ==========
+        .. [1] https://in.mathworks.com/help/control/ref/statespacemodel.ctrb.html
+
+        """
+        co = self._B
+        n = self._A.shape[0]
+        for i in range(1, n):
+            co = co.row_join(((self._A)**i) * self._B)
+
+        return co
+
+    def controllable_subspace(self):
+        """
+        Returns the controllable subspace of the state space model.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A = Matrix([[-1.5, -2], [1, 0]])
+        >>> B = Matrix([0.5, 0])
+        >>> C = Matrix([[0, 1]])
+        >>> D = Matrix([1])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> co_subspace = ss.controllable_subspace()
+        >>> co_subspace
+        [Matrix([
+        [0.5],
+        [  0]]), Matrix([
+        [-0.75],
+        [  0.5]])]
+
+        """
+        return self.controllability_matrix().columnspace()
+
+    def is_controllable(self):
+        """
+        Returns if the state space model is controllable.
+
+        Examples
+        ========
+
+        >>> from sympy import Matrix
+        >>> from sympy.physics.control import StateSpace
+        >>> A = Matrix([[-1.5, -2], [1, 0]])
+        >>> B = Matrix([0.5, 0])
+        >>> C = Matrix([[0, 1]])
+        >>> D = Matrix([1])
+        >>> ss = StateSpace(A, B, C, D)
+        >>> ss.is_controllable()
+        True
+
+        """
+        return self.controllability_matrix().rank() == self.num_states
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--- /dev/null
+++ b/parrot/lib/python3.10/site-packages/sympy/physics/control/tests/test_control_plots.py
@@ -0,0 +1,299 @@
+from math import isclose
+from sympy.core.numbers import I
+from sympy.core.symbol import Dummy
+from sympy.functions.elementary.complexes import (Abs, arg)
+from sympy.functions.elementary.exponential import log
+from sympy.abc import s, p, a
+from sympy.external import import_module
+from sympy.physics.control.control_plots import \
+    (pole_zero_numerical_data, pole_zero_plot, step_response_numerical_data,
+    step_response_plot, impulse_response_numerical_data,
+    impulse_response_plot, ramp_response_numerical_data,
+    ramp_response_plot, bode_magnitude_numerical_data,
+    bode_phase_numerical_data, bode_plot)
+from sympy.physics.control.lti import (TransferFunction,
+    Series, Parallel, TransferFunctionMatrix)
+from sympy.testing.pytest import raises, skip
+
+matplotlib = import_module(
+        'matplotlib', import_kwargs={'fromlist': ['pyplot']},
+        catch=(RuntimeError,))
+
+numpy = import_module('numpy')
+
+tf1 = TransferFunction(1, p**2 + 0.5*p + 2, p)
+tf2 = TransferFunction(p, 6*p**2 + 3*p + 1, p)
+tf3 = TransferFunction(p, p**3 - 1, p)
+tf4 = TransferFunction(10, p**3, p)
+tf5 = TransferFunction(5, s**2 + 2*s + 10, s)
+tf6 = TransferFunction(1, 1, s)
+tf7 = TransferFunction(4*s*3 + 9*s**2 + 0.1*s + 11, 8*s**6 + 9*s**4 + 11, s)
+tf8 = TransferFunction(5, s**2 + (2+I)*s + 10, s)
+
+ser1 = Series(tf4, TransferFunction(1, p - 5, p))
+ser2 = Series(tf3, TransferFunction(p, p + 2, p))
+
+par1 = Parallel(tf1, tf2)
+
+
+def _to_tuple(a, b):
+    return tuple(a), tuple(b)
+
+def _trim_tuple(a, b):
+    a, b = _to_tuple(a, b)
+    return tuple(a[0: 2] + a[len(a)//2 : len(a)//2 + 1] + a[-2:]), \
+        tuple(b[0: 2] + b[len(b)//2 : len(b)//2 + 1] + b[-2:])
+
+def y_coordinate_equality(plot_data_func, evalf_func, system):
+    """Checks whether the y-coordinate value of the plotted
+    data point is equal to the value of the function at a
+    particular x."""
+    x, y = plot_data_func(system)
+    x, y = _trim_tuple(x, y)
+    y_exp = tuple(evalf_func(system, x_i) for x_i in x)
+    return all(Abs(y_exp_i - y_i) < 1e-8 for y_exp_i, y_i in zip(y_exp, y))
+
+
+def test_errors():
+    if not matplotlib:
+        skip("Matplotlib not the default backend")
+
+    # Invalid `system` check
+    tfm = TransferFunctionMatrix([[tf6, tf5], [tf5, tf6]])
+    expr = 1/(s**2 - 1)
+    raises(NotImplementedError, lambda: pole_zero_plot(tfm))
+    raises(NotImplementedError, lambda: pole_zero_numerical_data(expr))
+    raises(NotImplementedError, lambda: impulse_response_plot(expr))
+    raises(NotImplementedError, lambda: impulse_response_numerical_data(tfm))
+    raises(NotImplementedError, lambda: step_response_plot(tfm))
+    raises(NotImplementedError, lambda: step_response_numerical_data(expr))
+    raises(NotImplementedError, lambda: ramp_response_plot(expr))
+    raises(NotImplementedError, lambda: ramp_response_numerical_data(tfm))
+    raises(NotImplementedError, lambda: bode_plot(tfm))
+
+    # More than 1 variables
+    tf_a = TransferFunction(a, s + 1, s)
+    raises(ValueError, lambda: pole_zero_plot(tf_a))
+    raises(ValueError, lambda: pole_zero_numerical_data(tf_a))
+    raises(ValueError, lambda: impulse_response_plot(tf_a))
+    raises(ValueError, lambda: impulse_response_numerical_data(tf_a))
+    raises(ValueError, lambda: step_response_plot(tf_a))
+    raises(ValueError, lambda: step_response_numerical_data(tf_a))
+    raises(ValueError, lambda: ramp_response_plot(tf_a))
+    raises(ValueError, lambda: ramp_response_numerical_data(tf_a))
+    raises(ValueError, lambda: bode_plot(tf_a))
+
+    # lower_limit > 0 for response plots
+    raises(ValueError, lambda: impulse_response_plot(tf1, lower_limit=-1))
+    raises(ValueError, lambda: step_response_plot(tf1, lower_limit=-0.1))
+    raises(ValueError, lambda: ramp_response_plot(tf1, lower_limit=-4/3))
+
+    # slope in ramp_response_plot() is negative
+    raises(ValueError, lambda: ramp_response_plot(tf1, slope=-0.1))
+
+    # incorrect frequency or phase unit
+    raises(ValueError, lambda: bode_plot(tf1,freq_unit = 'hz'))
+    raises(ValueError, lambda: bode_plot(tf1,phase_unit = 'degree'))
+
+
+def test_pole_zero():
+    if not numpy:
+        skip("NumPy is required for this test")
+
+    def pz_tester(sys, expected_value):
+        z, p = pole_zero_numerical_data(sys)
+        z_check = numpy.allclose(z, expected_value[0])
+        p_check = numpy.allclose(p, expected_value[1])
+        return p_check and z_check
+
+    exp1 = [[], [-0.24999999999999994+1.3919410907075054j, -0.24999999999999994-1.3919410907075054j]]
+    exp2 = [[0.0], [-0.25+0.3227486121839514j, -0.25-0.3227486121839514j]]
+    exp3 = [[0.0], [-0.5000000000000004+0.8660254037844395j,
+        -0.5000000000000004-0.8660254037844395j, 0.9999999999999998+0j]]
+    exp4 = [[], [5.0, 0.0, 0.0, 0.0]]
+    exp5 = [[-5.645751311064592, -0.5000000000000008, -0.3542486889354093],
+        [-0.24999999999999986+1.3919410907075052j,
+        -0.24999999999999986-1.3919410907075052j, -0.2499999999999998+0.32274861218395134j,
+        -0.2499999999999998-0.32274861218395134j]]
+    exp6 = [[], [-1.1641600331447917-3.545808351896439j,
+          -0.8358399668552097+2.5458083518964383j]]
+
+    assert pz_tester(tf1, exp1)
+    assert pz_tester(tf2, exp2)
+    assert pz_tester(tf3, exp3)
+    assert pz_tester(ser1, exp4)
+    assert pz_tester(par1, exp5)
+    assert pz_tester(tf8, exp6)
+
+
+def test_bode():
+    if not numpy:
+        skip("NumPy is required for this test")
+
+    def bode_phase_evalf(system, point):
+        expr = system.to_expr()
+        _w = Dummy("w", real=True)
+        w_expr = expr.subs({system.var: I*_w})
+        return arg(w_expr).subs({_w: point}).evalf()
+
+    def bode_mag_evalf(system, point):
+        expr = system.to_expr()
+        _w = Dummy("w", real=True)
+        w_expr = expr.subs({system.var: I*_w})
+        return 20*log(Abs(w_expr), 10).subs({_w: point}).evalf()
+
+    def test_bode_data(sys):
+        return y_coordinate_equality(bode_magnitude_numerical_data, bode_mag_evalf, sys) \
+            and y_coordinate_equality(bode_phase_numerical_data, bode_phase_evalf, sys)
+
+    assert test_bode_data(tf1)
+    assert test_bode_data(tf2)
+    assert test_bode_data(tf3)
+    assert test_bode_data(tf4)
+    assert test_bode_data(tf5)
+
+
+def check_point_accuracy(a, b):
+    return all(isclose(*_, rel_tol=1e-1, abs_tol=1e-6
+        ) for _ in zip(a, b))
+
+
+def test_impulse_response():
+    if not numpy:
+        skip("NumPy is required for this test")
+
+    def impulse_res_tester(sys, expected_value):
+        x, y = _to_tuple(*impulse_response_numerical_data(sys,
+            adaptive=False, n=10))
+        x_check = check_point_accuracy(x, expected_value[0])
+        y_check = check_point_accuracy(y, expected_value[1])
+        return x_check and y_check
+
+    exp1 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445,
+        5.555555555555555, 6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0),
+        (0.0, 0.544019738507865, 0.01993849743234938, -0.31140243360893216, -0.022852779906491996, 0.1778306498155759,
+        0.01962941084328499, -0.1013115194573652, -0.014975541213105696, 0.0575789724730714))
+    exp2 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445, 5.555555555555555,
+        6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0), (0.1666666675, 0.08389223412935855,
+        0.02338051973475047, -0.014966807776379383, -0.034645954223054234, -0.040560075735512804,
+        -0.037658628907103885, -0.030149507719590022, -0.021162090730736834, -0.012721292737437523))
+    exp3 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445, 5.555555555555555,
+        6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0), (4.369893391586999e-09, 1.1750333000630964,
+        3.2922404058312473, 9.432290008148343, 28.37098083007151, 86.18577464367974, 261.90356653762115,
+        795.6538758627842, 2416.9920942096983, 7342.159505206647))
+    exp4 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445, 5.555555555555555,
+        6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0), (0.0, 6.17283950617284, 24.69135802469136,
+        55.555555555555564, 98.76543209876544, 154.320987654321, 222.22222222222226, 302.46913580246917,
+        395.0617283950618, 500.0))
+    exp5 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445, 5.555555555555555,
+        6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0), (0.0, -0.10455606138085417,
+        0.06757671513476461, -0.03234567568833768, 0.013582514927757873, -0.005273419510705473,
+        0.0019364083003354075, -0.000680070134067832, 0.00022969845960406913, -7.476094359583917e-05))
+    exp6 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445,
+        5.555555555555555, 6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0),
+        (-6.016699583000218e-09, 0.35039802056107394, 3.3728423827689884, 12.119846079276684,
+        25.86101014293389, 29.352480635282088, -30.49475907497664, -273.8717189554019, -863.2381702029659,
+        -1747.0262164682233))
+    exp7 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335,
+        4.444444444444445, 5.555555555555555, 6.666666666666667, 7.777777777777779,
+        8.88888888888889, 10.0), (0.0, 18.934638095560974, 5346.93244680907, 1384609.8718249386,
+        358161126.65801865, 92645770015.70108, 23964739753087.42, 6198974342083139.0, 1.603492601616059e+18,
+        4.147764422869658e+20))
+
+    assert impulse_res_tester(tf1, exp1)
+    assert impulse_res_tester(tf2, exp2)
+    assert impulse_res_tester(tf3, exp3)
+    assert impulse_res_tester(tf4, exp4)
+    assert impulse_res_tester(tf5, exp5)
+    assert impulse_res_tester(tf7, exp6)
+    assert impulse_res_tester(ser1, exp7)
+
+
+def test_step_response():
+    if not numpy:
+        skip("NumPy is required for this test")
+
+    def step_res_tester(sys, expected_value):
+        x, y = _to_tuple(*step_response_numerical_data(sys,
+            adaptive=False, n=10))
+        x_check = check_point_accuracy(x, expected_value[0])
+        y_check = check_point_accuracy(y, expected_value[1])
+        return x_check and y_check
+
+    exp1 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445,
+        5.555555555555555, 6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0),
+        (-1.9193285738516863e-08, 0.42283495488246126, 0.7840485977945262, 0.5546841805655717,
+        0.33903033806932087, 0.4627251747410237, 0.5909907598988051, 0.5247213989553071,
+        0.4486997874319281, 0.4839358435839171))
+    exp2 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445,
+        5.555555555555555, 6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0),
+        (0.0, 0.13728409095645816, 0.19474559355325086, 0.1974909129243011, 0.16841657696573073,
+        0.12559777736159378, 0.08153828016664713, 0.04360471317348958, 0.015072994568868221,
+        -0.003636420058445484))
+    exp3 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445,
+        5.555555555555555, 6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0),
+        (0.0, 0.6314542141914303, 2.9356520038101035, 9.37731009663807, 28.452300356688376,
+        86.25721933273988, 261.9236645044672, 795.6435410577224, 2416.9786984578764, 7342.154119725917))
+    exp4 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445,
+        5.555555555555555, 6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0),
+        (0.0, 2.286236899862826, 18.28989519890261, 61.72839629629631, 146.31916159122088, 285.7796124828532,
+        493.8271703703705, 784.1792566529494, 1170.553292729767, 1666.6667))
+    exp5 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445,
+        5.555555555555555, 6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0),
+        (-3.999999997894577e-09, 0.6720357068882895, 0.4429938256137113, 0.5182010838004518,
+        0.4944139147159695, 0.5016379853883338, 0.4995466896527733, 0.5001154784851325,
+        0.49997448824584123, 0.5000039745919259))
+    exp6 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445,
+        5.555555555555555, 6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0),
+        (-1.5433688493882158e-09, 0.3428705539937336, 1.1253619102202777, 3.1849962651016517,
+        9.47532757182671, 28.727231099148135, 87.29426924860557, 265.2138681048606, 805.6636260007757,
+        2447.387582370878))
+
+    assert step_res_tester(tf1, exp1)
+    assert step_res_tester(tf2, exp2)
+    assert step_res_tester(tf3, exp3)
+    assert step_res_tester(tf4, exp4)
+    assert step_res_tester(tf5, exp5)
+    assert step_res_tester(ser2, exp6)
+
+
+def test_ramp_response():
+    if not numpy:
+        skip("NumPy is required for this test")
+
+    def ramp_res_tester(sys, num_points, expected_value, slope=1):
+        x, y = _to_tuple(*ramp_response_numerical_data(sys,
+            slope=slope, adaptive=False, n=num_points))
+        x_check = check_point_accuracy(x, expected_value[0])
+        y_check = check_point_accuracy(y, expected_value[1])
+        return x_check and y_check
+
+    exp1 = ((0.0, 2.0, 4.0, 6.0, 8.0, 10.0), (0.0, 0.7324667795033895, 1.9909720978650398,
+        2.7956587704217783, 3.9224897567931514, 4.85022655284895))
+    exp2 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445,
+        5.555555555555555, 6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0),
+        (2.4360213402019326e-08, 0.10175320182493253, 0.33057612497658406, 0.5967937263298935,
+        0.8431511866718248, 1.0398805391471613, 1.1776043125035738, 1.2600994825747305, 1.2981042689274653,
+        1.304684417610106))
+    exp3 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445, 5.555555555555555,
+        6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0), (-3.9329040468771836e-08,
+        0.34686634635794555, 2.9998828170537903, 12.33303690737476, 40.993913948137795, 127.84145222317912,
+        391.41713691996, 1192.0006858708389, 3623.9808672503405, 11011.728034546572))
+    exp4 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445, 5.555555555555555,
+        6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0), (0.0, 1.9051973784484078, 30.483158055174524,
+        154.32098765432104, 487.7305288827924, 1190.7483615302544, 2469.1358024691367, 4574.3789056546275,
+        7803.688462124678, 12500.0))
+    exp5 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445, 5.555555555555555,
+        6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0), (0.0, 3.8844361856975635, 9.141792069209865,
+        14.096349157657231, 19.09783068994694, 24.10179770390321, 29.09907319114121, 34.10040420185154,
+        39.09983919254265, 44.10006013058409))
+    exp6 = ((0.0, 1.1111111111111112, 2.2222222222222223, 3.3333333333333335, 4.444444444444445, 5.555555555555555,
+        6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0), (0.0, 1.1111111111111112, 2.2222222222222223,
+        3.3333333333333335, 4.444444444444445, 5.555555555555555, 6.666666666666667, 7.777777777777779, 8.88888888888889, 10.0))
+
+    assert ramp_res_tester(tf1, 6, exp1)
+    assert ramp_res_tester(tf2, 10, exp2, 1.2)
+    assert ramp_res_tester(tf3, 10, exp3, 1.5)
+    assert ramp_res_tester(tf4, 10, exp4, 3)
+    assert ramp_res_tester(tf5, 10, exp5, 9)
+    assert ramp_res_tester(tf6, 10, exp6)
diff --git a/parrot/lib/python3.10/site-packages/sympy/physics/control/tests/test_lti.py b/parrot/lib/python3.10/site-packages/sympy/physics/control/tests/test_lti.py
new file mode 100644
index 0000000000000000000000000000000000000000..9a3f599cbe240827cf24c7473782f7b71ad9a562
--- /dev/null
+++ b/parrot/lib/python3.10/site-packages/sympy/physics/control/tests/test_lti.py
@@ -0,0 +1,1750 @@
+from sympy.core.add import Add
+from sympy.core.function import Function
+from sympy.core.mul import Mul
+from sympy.core.numbers import (I, pi, Rational, oo)
+from sympy.core.power import Pow
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import atan
+from sympy.matrices.dense import eye
+from sympy.polys.polytools import factor
+from sympy.polys.rootoftools import CRootOf
+from sympy.simplify.simplify import simplify
+from sympy.core.containers import Tuple
+from sympy.matrices import ImmutableMatrix, Matrix, ShapeError
+from sympy.physics.control import (TransferFunction, Series, Parallel,
+    Feedback, TransferFunctionMatrix, MIMOSeries, MIMOParallel, MIMOFeedback,
+    StateSpace, gbt, bilinear, forward_diff, backward_diff, phase_margin, gain_margin)
+from sympy.testing.pytest import raises
+
+a, x, b, c, s, g, d, p, k, tau, zeta, wn, T = symbols('a, x, b, c, s, g, d, p, k,\
+    tau, zeta, wn, T')
+a0, a1, a2, a3, b0, b1, b2, b3, c0, c1, c2, c3, d0, d1, d2, d3 = symbols('a0:4,\
+    b0:4, c0:4, d0:4')
+TF1 = TransferFunction(1, s**2 + 2*zeta*wn*s + wn**2, s)
+TF2 = TransferFunction(k, 1, s)
+TF3 = TransferFunction(a2*p - s, a2*s + p, s)
+
+
+def test_TransferFunction_construction():
+    tf = TransferFunction(s + 1, s**2 + s + 1, s)
+    assert tf.num == (s + 1)
+    assert tf.den == (s**2 + s + 1)
+    assert tf.args == (s + 1, s**2 + s + 1, s)
+
+    tf1 = TransferFunction(s + 4, s - 5, s)
+    assert tf1.num == (s + 4)
+    assert tf1.den == (s - 5)
+    assert tf1.args == (s + 4, s - 5, s)
+
+    # using different polynomial variables.
+    tf2 = TransferFunction(p + 3, p**2 - 9, p)
+    assert tf2.num == (p + 3)
+    assert tf2.den == (p**2 - 9)
+    assert tf2.args == (p + 3, p**2 - 9, p)
+
+    tf3 = TransferFunction(p**3 + 5*p**2 + 4, p**4 + 3*p + 1, p)
+    assert tf3.args == (p**3 + 5*p**2 + 4, p**4 + 3*p + 1, p)
+
+    # no pole-zero cancellation on its own.
+    tf4 = TransferFunction((s + 3)*(s - 1), (s - 1)*(s + 5), s)
+    assert tf4.den == (s - 1)*(s + 5)
+    assert tf4.args == ((s + 3)*(s - 1), (s - 1)*(s + 5), s)
+
+    tf4_ = TransferFunction(p + 2, p + 2, p)
+    assert tf4_.args == (p + 2, p + 2, p)
+
+    tf5 = TransferFunction(s - 1, 4 - p, s)
+    assert tf5.args == (s - 1, 4 - p, s)
+
+    tf5_ = TransferFunction(s - 1, s - 1, s)
+    assert tf5_.args == (s - 1, s - 1, s)
+
+    tf6 = TransferFunction(5, 6, s)
+    assert tf6.num == 5
+    assert tf6.den == 6
+    assert tf6.args == (5, 6, s)
+
+    tf6_ = TransferFunction(1/2, 4, s)
+    assert tf6_.num == 0.5
+    assert tf6_.den == 4
+    assert tf6_.args == (0.500000000000000, 4, s)
+
+    tf7 = TransferFunction(3*s**2 + 2*p + 4*s, 8*p**2 + 7*s, s)
+    tf8 = TransferFunction(3*s**2 + 2*p + 4*s, 8*p**2 + 7*s, p)
+    assert not tf7 == tf8
+
+    tf7_ = TransferFunction(a0*s + a1*s**2 + a2*s**3, b0*p - b1*s, s)
+    tf8_ = TransferFunction(a0*s + a1*s**2 + a2*s**3, b0*p - b1*s, s)
+    assert tf7_ == tf8_
+    assert -(-tf7_) == tf7_ == -(-(-(-tf7_)))
+
+    tf9 = TransferFunction(a*s**3 + b*s**2 + g*s + d, d*p + g*p**2 + g*s, s)
+    assert tf9.args == (a*s**3 + b*s**2 + d + g*s, d*p + g*p**2 + g*s, s)
+
+    tf10 = TransferFunction(p**3 + d, g*s**2 + d*s + a, p)
+    tf10_ = TransferFunction(p**3 + d, g*s**2 + d*s + a, p)
+    assert tf10.args == (d + p**3, a + d*s + g*s**2, p)
+    assert tf10_ == tf10
+
+    tf11 = TransferFunction(a1*s + a0, b2*s**2 + b1*s + b0, s)
+    assert tf11.num == (a0 + a1*s)
+    assert tf11.den == (b0 + b1*s + b2*s**2)
+    assert tf11.args == (a0 + a1*s, b0 + b1*s + b2*s**2, s)
+
+    # when just the numerator is 0, leave the denominator alone.
+    tf12 = TransferFunction(0, p**2 - p + 1, p)
+    assert tf12.args == (0, p**2 - p + 1, p)
+
+    tf13 = TransferFunction(0, 1, s)
+    assert tf13.args == (0, 1, s)
+
+    # float exponents
+    tf14 = TransferFunction(a0*s**0.5 + a2*s**0.6 - a1, a1*p**(-8.7), s)
+    assert tf14.args == (a0*s**0.5 - a1 + a2*s**0.6, a1*p**(-8.7), s)
+
+    tf15 = TransferFunction(a2**2*p**(1/4) + a1*s**(-4/5), a0*s - p, p)
+    assert tf15.args == (a1*s**(-0.8) + a2**2*p**0.25, a0*s - p, p)
+
+    omega_o, k_p, k_o, k_i = symbols('omega_o, k_p, k_o, k_i')
+    tf18 = TransferFunction((k_p + k_o*s + k_i/s), s**2 + 2*omega_o*s + omega_o**2, s)
+    assert tf18.num == k_i/s + k_o*s + k_p
+    assert tf18.args == (k_i/s + k_o*s + k_p, omega_o**2 + 2*omega_o*s + s**2, s)
+
+    # ValueError when denominator is zero.
+    raises(ValueError, lambda: TransferFunction(4, 0, s))
+    raises(ValueError, lambda: TransferFunction(s, 0, s))
+    raises(ValueError, lambda: TransferFunction(0, 0, s))
+
+    raises(TypeError, lambda: TransferFunction(Matrix([1, 2, 3]), s, s))
+
+    raises(TypeError, lambda: TransferFunction(s**2 + 2*s - 1, s + 3, 3))
+    raises(TypeError, lambda: TransferFunction(p + 1, 5 - p, 4))
+    raises(TypeError, lambda: TransferFunction(3, 4, 8))
+
+
+def test_TransferFunction_functions():
+    # classmethod from_rational_expression
+    expr_1 = Mul(0, Pow(s, -1, evaluate=False), evaluate=False)
+    expr_2 = s/0
+    expr_3 = (p*s**2 + 5*s)/(s + 1)**3
+    expr_4 = 6
+    expr_5 = ((2 + 3*s)*(5 + 2*s))/((9 + 3*s)*(5 + 2*s**2))
+    expr_6 = (9*s**4 + 4*s**2 + 8)/((s + 1)*(s + 9))
+    tf = TransferFunction(s + 1, s**2 + 2, s)
+    delay = exp(-s/tau)
+    expr_7 = delay*tf.to_expr()
+    H1 = TransferFunction.from_rational_expression(expr_7, s)
+    H2 = TransferFunction(s + 1, (s**2 + 2)*exp(s/tau), s)
+    expr_8 = Add(2,  3*s/(s**2 + 1), evaluate=False)
+
+    assert TransferFunction.from_rational_expression(expr_1) == TransferFunction(0, s, s)
+    raises(ZeroDivisionError, lambda: TransferFunction.from_rational_expression(expr_2))
+    raises(ValueError, lambda: TransferFunction.from_rational_expression(expr_3))
+    assert TransferFunction.from_rational_expression(expr_3, s) == TransferFunction((p*s**2 + 5*s), (s + 1)**3, s)
+    assert TransferFunction.from_rational_expression(expr_3, p) == TransferFunction((p*s**2 + 5*s), (s + 1)**3, p)
+    raises(ValueError, lambda: TransferFunction.from_rational_expression(expr_4))
+    assert TransferFunction.from_rational_expression(expr_4, s) == TransferFunction(6, 1, s)
+    assert TransferFunction.from_rational_expression(expr_5, s) == \
+        TransferFunction((2 + 3*s)*(5 + 2*s), (9 + 3*s)*(5 + 2*s**2), s)
+    assert TransferFunction.from_rational_expression(expr_6, s) == \
+        TransferFunction((9*s**4 + 4*s**2 + 8), (s + 1)*(s + 9), s)
+    assert H1 == H2
+    assert TransferFunction.from_rational_expression(expr_8, s) == \
+        TransferFunction(2*s**2 + 3*s + 2, s**2 + 1, s)
+
+    # classmethod from_coeff_lists
+    tf1 = TransferFunction.from_coeff_lists([1, 2], [3, 4, 5], s)
+    num2 = [p**2, 2*p]
+    den2 = [p**3, p + 1, 4]
+    tf2 = TransferFunction.from_coeff_lists(num2, den2, s)
+    num3 = [1, 2, 3]
+    den3 = [0, 0]
+
+    assert tf1 == TransferFunction(s + 2, 3*s**2 + 4*s + 5, s)
+    assert tf2 == TransferFunction(p**2*s + 2*p, p**3*s**2 + s*(p + 1) + 4, s)
+    raises(ZeroDivisionError, lambda: TransferFunction.from_coeff_lists(num3, den3, s))
+
+    # classmethod from_zpk
+    zeros = [4]
+    poles = [-1+2j, -1-2j]
+    gain = 3
+    tf1 = TransferFunction.from_zpk(zeros, poles, gain, s)
+
+    assert tf1 == TransferFunction(3*s - 12, (s + 1.0 - 2.0*I)*(s + 1.0 + 2.0*I), s)
+
+    # explicitly cancel poles and zeros.
+    tf0 = TransferFunction(s**5 + s**3 + s, s - s**2, s)
+    a = TransferFunction(-(s**4 + s**2 + 1), s - 1, s)
+    assert tf0.simplify() == simplify(tf0) == a
+
+    tf1 = TransferFunction((p + 3)*(p - 1), (p - 1)*(p + 5), p)
+    b = TransferFunction(p + 3, p + 5, p)
+    assert tf1.simplify() == simplify(tf1) == b
+
+    # expand the numerator and the denominator.
+    G1 = TransferFunction((1 - s)**2, (s**2 + 1)**2, s)
+    G2 = TransferFunction(1, -3, p)
+    c = (a2*s**p + a1*s**s + a0*p**p)*(p**s + s**p)
+    d = (b0*s**s + b1*p**s)*(b2*s*p + p**p)
+    e = a0*p**p*p**s + a0*p**p*s**p + a1*p**s*s**s + a1*s**p*s**s + a2*p**s*s**p + a2*s**(2*p)
+    f = b0*b2*p*s*s**s + b0*p**p*s**s + b1*b2*p*p**s*s + b1*p**p*p**s
+    g = a1*a2*s*s**p + a1*p*s + a2*b1*p*s*s**p + b1*p**2*s
+    G3 = TransferFunction(c, d, s)
+    G4 = TransferFunction(a0*s**s - b0*p**p, (a1*s + b1*s*p)*(a2*s**p + p), p)
+
+    assert G1.expand() == TransferFunction(s**2 - 2*s + 1, s**4 + 2*s**2 + 1, s)
+    assert tf1.expand() == TransferFunction(p**2 + 2*p - 3, p**2 + 4*p - 5, p)
+    assert G2.expand() == G2
+    assert G3.expand() == TransferFunction(e, f, s)
+    assert G4.expand() == TransferFunction(a0*s**s - b0*p**p, g, p)
+
+    # purely symbolic polynomials.
+    p1 = a1*s + a0
+    p2 = b2*s**2 + b1*s + b0
+    SP1 = TransferFunction(p1, p2, s)
+    expect1 = TransferFunction(2.0*s + 1.0, 5.0*s**2 + 4.0*s + 3.0, s)
+    expect1_ = TransferFunction(2*s + 1, 5*s**2 + 4*s + 3, s)
+    assert SP1.subs({a0: 1, a1: 2, b0: 3, b1: 4, b2: 5}) == expect1_
+    assert SP1.subs({a0: 1, a1: 2, b0: 3, b1: 4, b2: 5}).evalf() == expect1
+    assert expect1_.evalf() == expect1
+
+    c1, d0, d1, d2 = symbols('c1, d0:3')
+    p3, p4 = c1*p, d2*p**3 + d1*p**2 - d0
+    SP2 = TransferFunction(p3, p4, p)
+    expect2 = TransferFunction(2.0*p, 5.0*p**3 + 2.0*p**2 - 3.0, p)
+    expect2_ = TransferFunction(2*p, 5*p**3 + 2*p**2 - 3, p)
+    assert SP2.subs({c1: 2, d0: 3, d1: 2, d2: 5}) == expect2_
+    assert SP2.subs({c1: 2, d0: 3, d1: 2, d2: 5}).evalf() == expect2
+    assert expect2_.evalf() == expect2
+
+    SP3 = TransferFunction(a0*p**3 + a1*s**2 - b0*s + b1, a1*s + p, s)
+    expect3 = TransferFunction(2.0*p**3 + 4.0*s**2 - s + 5.0, p + 4.0*s, s)
+    expect3_ = TransferFunction(2*p**3 + 4*s**2 - s + 5, p + 4*s, s)
+    assert SP3.subs({a0: 2, a1: 4, b0: 1, b1: 5}) == expect3_
+    assert SP3.subs({a0: 2, a1: 4, b0: 1, b1: 5}).evalf() == expect3
+    assert expect3_.evalf() == expect3
+
+    SP4 = TransferFunction(s - a1*p**3, a0*s + p, p)
+    expect4 = TransferFunction(7.0*p**3 + s, p - s, p)
+    expect4_ = TransferFunction(7*p**3 + s, p - s, p)
+    assert SP4.subs({a0: -1, a1: -7}) == expect4_
+    assert SP4.subs({a0: -1, a1: -7}).evalf() == expect4
+    assert expect4_.evalf() == expect4
+
+    # evaluate the transfer function at particular frequencies.
+    assert tf1.eval_frequency(wn) == wn**2/(wn**2 + 4*wn - 5) + 2*wn/(wn**2 + 4*wn - 5) - 3/(wn**2 + 4*wn - 5)
+    assert G1.eval_frequency(1 + I) == S(3)/25 + S(4)*I/25
+    assert G4.eval_frequency(S(5)/3) == \
+        a0*s**s/(a1*a2*s**(S(8)/3) + S(5)*a1*s/3 + 5*a2*b1*s**(S(8)/3)/3 + S(25)*b1*s/9) - 5*3**(S(1)/3)*5**(S(2)/3)*b0/(9*a1*a2*s**(S(8)/3) + 15*a1*s + 15*a2*b1*s**(S(8)/3) + 25*b1*s)
+
+    # Low-frequency (or DC) gain.
+    assert tf0.dc_gain() == 1
+    assert tf1.dc_gain() == Rational(3, 5)
+    assert SP2.dc_gain() == 0
+    assert expect4.dc_gain() == -1
+    assert expect2_.dc_gain() == 0
+    assert TransferFunction(1, s, s).dc_gain() == oo
+
+    # Poles of a transfer function.
+    tf_ = TransferFunction(x**3 - k, k, x)
+    _tf = TransferFunction(k, x**4 - k, x)
+    TF_ = TransferFunction(x**2, x**10 + x + x**2, x)
+    _TF = TransferFunction(x**10 + x + x**2, x**2, x)
+    assert G1.poles() == [I, I, -I, -I]
+    assert G2.poles() == []
+    assert tf1.poles() == [-5, 1]
+    assert expect4_.poles() == [s]
+    assert SP4.poles() == [-a0*s]
+    assert expect3.poles() == [-0.25*p]
+    assert str(expect2.poles()) == str([0.729001428685125, -0.564500714342563 - 0.710198984796332*I, -0.564500714342563 + 0.710198984796332*I])
+    assert str(expect1.poles()) == str([-0.4 - 0.66332495807108*I, -0.4 + 0.66332495807108*I])
+    assert _tf.poles() == [k**(Rational(1, 4)), -k**(Rational(1, 4)), I*k**(Rational(1, 4)), -I*k**(Rational(1, 4))]
+    assert TF_.poles() == [CRootOf(x**9 + x + 1, 0), 0, CRootOf(x**9 + x + 1, 1), CRootOf(x**9 + x + 1, 2),
+        CRootOf(x**9 + x + 1, 3), CRootOf(x**9 + x + 1, 4), CRootOf(x**9 + x + 1, 5), CRootOf(x**9 + x + 1, 6),
+        CRootOf(x**9 + x + 1, 7), CRootOf(x**9 + x + 1, 8)]
+    raises(NotImplementedError, lambda: TransferFunction(x**2, a0*x**10 + x + x**2, x).poles())
+
+    # Stability of a transfer function.
+    q, r = symbols('q, r', negative=True)
+    t = symbols('t', positive=True)
+    TF_ = TransferFunction(s**2 + a0 - a1*p, q*s - r, s)
+    stable_tf = TransferFunction(s**2 + a0 - a1*p, q*s - 1, s)
+    stable_tf_ = TransferFunction(s**2 + a0 - a1*p, q*s - t, s)
+
+    assert G1.is_stable() is False
+    assert G2.is_stable() is True
+    assert tf1.is_stable() is False   # as one pole is +ve, and the other is -ve.
+    assert expect2.is_stable() is False
+    assert expect1.is_stable() is True
+    assert stable_tf.is_stable() is True
+    assert stable_tf_.is_stable() is True
+    assert TF_.is_stable() is False
+    assert expect4_.is_stable() is None   # no assumption provided for the only pole 's'.
+    assert SP4.is_stable() is None
+
+    # Zeros of a transfer function.
+    assert G1.zeros() == [1, 1]
+    assert G2.zeros() == []
+    assert tf1.zeros() == [-3, 1]
+    assert expect4_.zeros() == [7**(Rational(2, 3))*(-s)**(Rational(1, 3))/7, -7**(Rational(2, 3))*(-s)**(Rational(1, 3))/14 -
+        sqrt(3)*7**(Rational(2, 3))*I*(-s)**(Rational(1, 3))/14, -7**(Rational(2, 3))*(-s)**(Rational(1, 3))/14 + sqrt(3)*7**(Rational(2, 3))*I*(-s)**(Rational(1, 3))/14]
+    assert SP4.zeros() == [(s/a1)**(Rational(1, 3)), -(s/a1)**(Rational(1, 3))/2 - sqrt(3)*I*(s/a1)**(Rational(1, 3))/2,
+        -(s/a1)**(Rational(1, 3))/2 + sqrt(3)*I*(s/a1)**(Rational(1, 3))/2]
+    assert str(expect3.zeros()) == str([0.125 - 1.11102430216445*sqrt(-0.405063291139241*p**3 - 1.0),
+        1.11102430216445*sqrt(-0.405063291139241*p**3 - 1.0) + 0.125])
+    assert tf_.zeros() == [k**(Rational(1, 3)), -k**(Rational(1, 3))/2 - sqrt(3)*I*k**(Rational(1, 3))/2,
+        -k**(Rational(1, 3))/2 + sqrt(3)*I*k**(Rational(1, 3))/2]
+    assert _TF.zeros() == [CRootOf(x**9 + x + 1, 0), 0, CRootOf(x**9 + x + 1, 1), CRootOf(x**9 + x + 1, 2),
+        CRootOf(x**9 + x + 1, 3), CRootOf(x**9 + x + 1, 4), CRootOf(x**9 + x + 1, 5), CRootOf(x**9 + x + 1, 6),
+        CRootOf(x**9 + x + 1, 7), CRootOf(x**9 + x + 1, 8)]
+    raises(NotImplementedError, lambda: TransferFunction(a0*x**10 + x + x**2, x**2, x).zeros())
+
+    # negation of TF.
+    tf2 = TransferFunction(s + 3, s**2 - s**3 + 9, s)
+    tf3 = TransferFunction(-3*p + 3, 1 - p, p)
+    assert -tf2 == TransferFunction(-s - 3, s**2 - s**3 + 9, s)
+    assert -tf3 == TransferFunction(3*p - 3, 1 - p, p)
+
+    # taking power of a TF.
+    tf4 = TransferFunction(p + 4, p - 3, p)
+    tf5 = TransferFunction(s**2 + 1, 1 - s, s)
+    expect2 = TransferFunction((s**2 + 1)**3, (1 - s)**3, s)
+    expect1 = TransferFunction((p + 4)**2, (p - 3)**2, p)
+    assert (tf4*tf4).doit() == tf4**2 == pow(tf4, 2) == expect1
+    assert (tf5*tf5*tf5).doit() == tf5**3 == pow(tf5, 3) == expect2
+    assert tf5**0 == pow(tf5, 0) == TransferFunction(1, 1, s)
+    assert Series(tf4).doit()**-1 == tf4**-1 == pow(tf4, -1) == TransferFunction(p - 3, p + 4, p)
+    assert (tf5*tf5).doit()**-1 == tf5**-2 == pow(tf5, -2) == TransferFunction((1 - s)**2, (s**2 + 1)**2, s)
+
+    raises(ValueError, lambda: tf4**(s**2 + s - 1))
+    raises(ValueError, lambda: tf5**s)
+    raises(ValueError, lambda: tf4**tf5)
+
+    # SymPy's own functions.
+    tf = TransferFunction(s - 1, s**2 - 2*s + 1, s)
+    tf6 = TransferFunction(s + p, p**2 - 5, s)
+    assert factor(tf) == TransferFunction(s - 1, (s - 1)**2, s)
+    assert tf.num.subs(s, 2) == tf.den.subs(s, 2) == 1
+    # subs & xreplace
+    assert tf.subs(s, 2) == TransferFunction(s - 1, s**2 - 2*s + 1, s)
+    assert tf6.subs(p, 3) == TransferFunction(s + 3, 4, s)
+    assert tf3.xreplace({p: s}) == TransferFunction(-3*s + 3, 1 - s, s)
+    raises(TypeError, lambda: tf3.xreplace({p: exp(2)}))
+    assert tf3.subs(p, exp(2)) == tf3
+
+    tf7 = TransferFunction(a0*s**p + a1*p**s, a2*p - s, s)
+    assert tf7.xreplace({s: k}) == TransferFunction(a0*k**p + a1*p**k, a2*p - k, k)
+    assert tf7.subs(s, k) == TransferFunction(a0*s**p + a1*p**s, a2*p - s, s)
+
+    # Conversion to Expr with to_expr()
+    tf8 = TransferFunction(a0*s**5 + 5*s**2 + 3, s**6 - 3, s)
+    tf9 = TransferFunction((5 + s), (5 + s)*(6 + s), s)
+    tf10 = TransferFunction(0, 1, s)
+    tf11 = TransferFunction(1, 1, s)
+    assert tf8.to_expr() == Mul((a0*s**5 + 5*s**2 + 3), Pow((s**6 - 3), -1, evaluate=False), evaluate=False)
+    assert tf9.to_expr() == Mul((s + 5), Pow((5 + s)*(6 + s), -1, evaluate=False), evaluate=False)
+    assert tf10.to_expr() == Mul(S(0), Pow(1, -1, evaluate=False), evaluate=False)
+    assert tf11.to_expr() == Pow(1, -1, evaluate=False)
+
+def test_TransferFunction_addition_and_subtraction():
+    tf1 = TransferFunction(s + 6, s - 5, s)
+    tf2 = TransferFunction(s + 3, s + 1, s)
+    tf3 = TransferFunction(s + 1, s**2 + s + 1, s)
+    tf4 = TransferFunction(p, 2 - p, p)
+
+    # addition
+    assert tf1 + tf2 == Parallel(tf1, tf2)
+    assert tf3 + tf1 == Parallel(tf3, tf1)
+    assert -tf1 + tf2 + tf3 == Parallel(-tf1, tf2, tf3)
+    assert tf1 + (tf2 + tf3) == Parallel(tf1, tf2, tf3)
+
+    c = symbols("c", commutative=False)
+    raises(ValueError, lambda: tf1 + Matrix([1, 2, 3]))
+    raises(ValueError, lambda: tf2 + c)
+    raises(ValueError, lambda: tf3 + tf4)
+    raises(ValueError, lambda: tf1 + (s - 1))
+    raises(ValueError, lambda: tf1 + 8)
+    raises(ValueError, lambda: (1 - p**3) + tf1)
+
+    # subtraction
+    assert tf1 - tf2 == Parallel(tf1, -tf2)
+    assert tf3 - tf2 == Parallel(tf3, -tf2)
+    assert -tf1 - tf3 == Parallel(-tf1, -tf3)
+    assert tf1 - tf2 + tf3 == Parallel(tf1, -tf2, tf3)
+
+    raises(ValueError, lambda: tf1 - Matrix([1, 2, 3]))
+    raises(ValueError, lambda: tf3 - tf4)
+    raises(ValueError, lambda: tf1 - (s - 1))
+    raises(ValueError, lambda: tf1 - 8)
+    raises(ValueError, lambda: (s + 5) - tf2)
+    raises(ValueError, lambda: (1 + p**4) - tf1)
+
+
+def test_TransferFunction_multiplication_and_division():
+    G1 = TransferFunction(s + 3, -s**3 + 9, s)
+    G2 = TransferFunction(s + 1, s - 5, s)
+    G3 = TransferFunction(p, p**4 - 6, p)
+    G4 = TransferFunction(p + 4, p - 5, p)
+    G5 = TransferFunction(s + 6, s - 5, s)
+    G6 = TransferFunction(s + 3, s + 1, s)
+    G7 = TransferFunction(1, 1, s)
+
+    # multiplication
+    assert G1*G2 == Series(G1, G2)
+    assert -G1*G5 == Series(-G1, G5)
+    assert -G2*G5*-G6 == Series(-G2, G5, -G6)
+    assert -G1*-G2*-G5*-G6 == Series(-G1, -G2, -G5, -G6)
+    assert G3*G4 == Series(G3, G4)
+    assert (G1*G2)*-(G5*G6) == \
+        Series(G1, G2, TransferFunction(-1, 1, s), Series(G5, G6))
+    assert G1*G2*(G5 + G6) == Series(G1, G2, Parallel(G5, G6))
+
+    # division - See ``test_Feedback_functions()`` for division by Parallel objects.
+    assert G5/G6 == Series(G5, pow(G6, -1))
+    assert -G3/G4 == Series(-G3, pow(G4, -1))
+    assert (G5*G6)/G7 == Series(G5, G6, pow(G7, -1))
+
+    c = symbols("c", commutative=False)
+    raises(ValueError, lambda: G3 * Matrix([1, 2, 3]))
+    raises(ValueError, lambda: G1 * c)
+    raises(ValueError, lambda: G3 * G5)
+    raises(ValueError, lambda: G5 * (s - 1))
+    raises(ValueError, lambda: 9 * G5)
+
+    raises(ValueError, lambda: G3 / Matrix([1, 2, 3]))
+    raises(ValueError, lambda: G6 / 0)
+    raises(ValueError, lambda: G3 / G5)
+    raises(ValueError, lambda: G5 / 2)
+    raises(ValueError, lambda: G5 / s**2)
+    raises(ValueError, lambda: (s - 4*s**2) / G2)
+    raises(ValueError, lambda: 0 / G4)
+    raises(ValueError, lambda: G7 / (1 + G6))
+    raises(ValueError, lambda: G7 / (G5 * G6))
+    raises(ValueError, lambda: G7 / (G7 + (G5 + G6)))
+
+
+def test_TransferFunction_is_proper():
+    omega_o, zeta, tau = symbols('omega_o, zeta, tau')
+    G1 = TransferFunction(omega_o**2, s**2 + p*omega_o*zeta*s + omega_o**2, omega_o)
+    G2 = TransferFunction(tau - s**3, tau + p**4, tau)
+    G3 = TransferFunction(a*b*s**3 + s**2 - a*p + s, b - s*p**2, p)
+    G4 = TransferFunction(b*s**2 + p**2 - a*p + s, b - p**2, s)
+    assert G1.is_proper
+    assert G2.is_proper
+    assert G3.is_proper
+    assert not G4.is_proper
+
+
+def test_TransferFunction_is_strictly_proper():
+    omega_o, zeta, tau = symbols('omega_o, zeta, tau')
+    tf1 = TransferFunction(omega_o**2, s**2 + p*omega_o*zeta*s + omega_o**2, omega_o)
+    tf2 = TransferFunction(tau - s**3, tau + p**4, tau)
+    tf3 = TransferFunction(a*b*s**3 + s**2 - a*p + s, b - s*p**2, p)
+    tf4 = TransferFunction(b*s**2 + p**2 - a*p + s, b - p**2, s)
+    assert not tf1.is_strictly_proper
+    assert not tf2.is_strictly_proper
+    assert tf3.is_strictly_proper
+    assert not tf4.is_strictly_proper
+
+
+def test_TransferFunction_is_biproper():
+    tau, omega_o, zeta = symbols('tau, omega_o, zeta')
+    tf1 = TransferFunction(omega_o**2, s**2 + p*omega_o*zeta*s + omega_o**2, omega_o)
+    tf2 = TransferFunction(tau - s**3, tau + p**4, tau)
+    tf3 = TransferFunction(a*b*s**3 + s**2 - a*p + s, b - s*p**2, p)
+    tf4 = TransferFunction(b*s**2 + p**2 - a*p + s, b - p**2, s)
+    assert tf1.is_biproper
+    assert tf2.is_biproper
+    assert not tf3.is_biproper
+    assert not tf4.is_biproper
+
+
+def test_Series_construction():
+    tf = TransferFunction(a0*s**3 + a1*s**2 - a2*s, b0*p**4 + b1*p**3 - b2*s*p, s)
+    tf2 = TransferFunction(a2*p - s, a2*s + p, s)
+    tf3 = TransferFunction(a0*p + p**a1 - s, p, p)
+    tf4 = TransferFunction(1, s**2 + 2*zeta*wn*s + wn**2, s)
+    inp = Function('X_d')(s)
+    out = Function('X')(s)
+
+    s0 = Series(tf, tf2)
+    assert s0.args == (tf, tf2)
+    assert s0.var == s
+
+    s1 = Series(Parallel(tf, -tf2), tf2)
+    assert s1.args == (Parallel(tf, -tf2), tf2)
+    assert s1.var == s
+
+    tf3_ = TransferFunction(inp, 1, s)
+    tf4_ = TransferFunction(-out, 1, s)
+    s2 = Series(tf, Parallel(tf3_, tf4_), tf2)
+    assert s2.args == (tf, Parallel(tf3_, tf4_), tf2)
+
+    s3 = Series(tf, tf2, tf4)
+    assert s3.args == (tf, tf2, tf4)
+
+    s4 = Series(tf3_, tf4_)
+    assert s4.args == (tf3_, tf4_)
+    assert s4.var == s
+
+    s6 = Series(tf2, tf4, Parallel(tf2, -tf), tf4)
+    assert s6.args == (tf2, tf4, Parallel(tf2, -tf), tf4)
+
+    s7 = Series(tf, tf2)
+    assert s0 == s7
+    assert not s0 == s2
+
+    raises(ValueError, lambda: Series(tf, tf3))
+    raises(ValueError, lambda: Series(tf, tf2, tf3, tf4))
+    raises(ValueError, lambda: Series(-tf3, tf2))
+    raises(TypeError, lambda: Series(2, tf, tf4))
+    raises(TypeError, lambda: Series(s**2 + p*s, tf3, tf2))
+    raises(TypeError, lambda: Series(tf3, Matrix([1, 2, 3, 4])))
+
+
+def test_MIMOSeries_construction():
+    tf_1 = TransferFunction(a0*s**3 + a1*s**2 - a2*s, b0*p**4 + b1*p**3 - b2*s*p, s)
+    tf_2 = TransferFunction(a2*p - s, a2*s + p, s)
+    tf_3 = TransferFunction(1, s**2 + 2*zeta*wn*s + wn**2, s)
+
+    tfm_1 = TransferFunctionMatrix([[tf_1, tf_2, tf_3], [-tf_3, -tf_2, tf_1]])
+    tfm_2 = TransferFunctionMatrix([[-tf_2], [-tf_2], [-tf_3]])
+    tfm_3 = TransferFunctionMatrix([[-tf_3]])
+    tfm_4 = TransferFunctionMatrix([[TF3], [TF2], [-TF1]])
+    tfm_5 = TransferFunctionMatrix.from_Matrix(Matrix([1/p]), p)
+
+    s8 = MIMOSeries(tfm_2, tfm_1)
+    assert s8.args == (tfm_2, tfm_1)
+    assert s8.var == s
+    assert s8.shape == (s8.num_outputs, s8.num_inputs) == (2, 1)
+
+    s9 = MIMOSeries(tfm_3, tfm_2, tfm_1)
+    assert s9.args == (tfm_3, tfm_2, tfm_1)
+    assert s9.var == s
+    assert s9.shape == (s9.num_outputs, s9.num_inputs) == (2, 1)
+
+    s11 = MIMOSeries(tfm_3, MIMOParallel(-tfm_2, -tfm_4), tfm_1)
+    assert s11.args == (tfm_3, MIMOParallel(-tfm_2, -tfm_4), tfm_1)
+    assert s11.shape == (s11.num_outputs, s11.num_inputs) == (2, 1)
+
+    # arg cannot be empty tuple.
+    raises(ValueError, lambda: MIMOSeries())
+
+    # arg cannot contain SISO as well as MIMO systems.
+    raises(TypeError, lambda: MIMOSeries(tfm_1, tf_1))
+
+    # for all the adjacent transfer function matrices:
+    # no. of inputs of first TFM must be equal to the no. of outputs of the second TFM.
+    raises(ValueError, lambda: MIMOSeries(tfm_1, tfm_2, -tfm_1))
+
+    # all the TFMs must use the same complex variable.
+    raises(ValueError, lambda: MIMOSeries(tfm_3, tfm_5))
+
+    # Number or expression not allowed in the arguments.
+    raises(TypeError, lambda: MIMOSeries(2, tfm_2, tfm_3))
+    raises(TypeError, lambda: MIMOSeries(s**2 + p*s, -tfm_2, tfm_3))
+    raises(TypeError, lambda: MIMOSeries(Matrix([1/p]), tfm_3))
+
+
+def test_Series_functions():
+    tf1 = TransferFunction(1, s**2 + 2*zeta*wn*s + wn**2, s)
+    tf2 = TransferFunction(k, 1, s)
+    tf3 = TransferFunction(a2*p - s, a2*s + p, s)
+    tf4 = TransferFunction(a0*p + p**a1 - s, p, p)
+    tf5 = TransferFunction(a1*s**2 + a2*s - a0, s + a0, s)
+
+    assert tf1*tf2*tf3 == Series(tf1, tf2, tf3) == Series(Series(tf1, tf2), tf3) \
+        == Series(tf1, Series(tf2, tf3))
+    assert tf1*(tf2 + tf3) == Series(tf1, Parallel(tf2, tf3))
+    assert tf1*tf2 + tf5 == Parallel(Series(tf1, tf2), tf5)
+    assert tf1*tf2 - tf5 == Parallel(Series(tf1, tf2), -tf5)
+    assert tf1*tf2 + tf3 + tf5 == Parallel(Series(tf1, tf2), tf3, tf5)
+    assert tf1*tf2 - tf3 - tf5 == Parallel(Series(tf1, tf2), -tf3, -tf5)
+    assert tf1*tf2 - tf3 + tf5 == Parallel(Series(tf1, tf2), -tf3, tf5)
+    assert tf1*tf2 + tf3*tf5 == Parallel(Series(tf1, tf2), Series(tf3, tf5))
+    assert tf1*tf2 - tf3*tf5 == Parallel(Series(tf1, tf2), Series(TransferFunction(-1, 1, s), Series(tf3, tf5)))
+    assert tf2*tf3*(tf2 - tf1)*tf3 == Series(tf2, tf3, Parallel(tf2, -tf1), tf3)
+    assert -tf1*tf2 == Series(-tf1, tf2)
+    assert -(tf1*tf2) == Series(TransferFunction(-1, 1, s), Series(tf1, tf2))
+    raises(ValueError, lambda: tf1*tf2*tf4)
+    raises(ValueError, lambda: tf1*(tf2 - tf4))
+    raises(ValueError, lambda: tf3*Matrix([1, 2, 3]))
+
+    # evaluate=True -> doit()
+    assert Series(tf1, tf2, evaluate=True) == Series(tf1, tf2).doit() == \
+        TransferFunction(k, s**2 + 2*s*wn*zeta + wn**2, s)
+    assert Series(tf1, tf2, Parallel(tf1, -tf3), evaluate=True) == Series(tf1, tf2, Parallel(tf1, -tf3)).doit() == \
+        TransferFunction(k*(a2*s + p + (-a2*p + s)*(s**2 + 2*s*wn*zeta + wn**2)), (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2)**2, s)
+    assert Series(tf2, tf1, -tf3, evaluate=True) == Series(tf2, tf1, -tf3).doit() == \
+        TransferFunction(k*(-a2*p + s), (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), s)
+    assert not Series(tf1, -tf2, evaluate=False) == Series(tf1, -tf2).doit()
+
+    assert Series(Parallel(tf1, tf2), Parallel(tf2, -tf3)).doit() == \
+        TransferFunction((k*(s**2 + 2*s*wn*zeta + wn**2) + 1)*(-a2*p + k*(a2*s + p) + s), (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), s)
+    assert Series(-tf1, -tf2, -tf3).doit() == \
+        TransferFunction(k*(-a2*p + s), (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), s)
+    assert -Series(tf1, tf2, tf3).doit() == \
+        TransferFunction(-k*(a2*p - s), (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), s)
+    assert Series(tf2, tf3, Parallel(tf2, -tf1), tf3).doit() == \
+        TransferFunction(k*(a2*p - s)**2*(k*(s**2 + 2*s*wn*zeta + wn**2) - 1), (a2*s + p)**2*(s**2 + 2*s*wn*zeta + wn**2), s)
+
+    assert Series(tf1, tf2).rewrite(TransferFunction) == TransferFunction(k, s**2 + 2*s*wn*zeta + wn**2, s)
+    assert Series(tf2, tf1, -tf3).rewrite(TransferFunction) == \
+        TransferFunction(k*(-a2*p + s), (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), s)
+
+    S1 = Series(Parallel(tf1, tf2), Parallel(tf2, -tf3))
+    assert S1.is_proper
+    assert not S1.is_strictly_proper
+    assert S1.is_biproper
+
+    S2 = Series(tf1, tf2, tf3)
+    assert S2.is_proper
+    assert S2.is_strictly_proper
+    assert not S2.is_biproper
+
+    S3 = Series(tf1, -tf2, Parallel(tf1, -tf3))
+    assert S3.is_proper
+    assert S3.is_strictly_proper
+    assert not S3.is_biproper
+
+
+def test_MIMOSeries_functions():
+    tfm1 = TransferFunctionMatrix([[TF1, TF2, TF3], [-TF3, -TF2, TF1]])
+    tfm2 = TransferFunctionMatrix([[-TF1], [-TF2], [-TF3]])
+    tfm3 = TransferFunctionMatrix([[-TF1]])
+    tfm4 = TransferFunctionMatrix([[-TF2, -TF3], [-TF1, TF2]])
+    tfm5 = TransferFunctionMatrix([[TF2, -TF2], [-TF3, -TF2]])
+    tfm6 = TransferFunctionMatrix([[-TF3], [TF1]])
+    tfm7 = TransferFunctionMatrix([[TF1], [-TF2]])
+
+    assert tfm1*tfm2 + tfm6 == MIMOParallel(MIMOSeries(tfm2, tfm1), tfm6)
+    assert tfm1*tfm2 + tfm7 + tfm6 == MIMOParallel(MIMOSeries(tfm2, tfm1), tfm7, tfm6)
+    assert tfm1*tfm2 - tfm6 - tfm7 == MIMOParallel(MIMOSeries(tfm2, tfm1), -tfm6, -tfm7)
+    assert tfm4*tfm5 + (tfm4 - tfm5) == MIMOParallel(MIMOSeries(tfm5, tfm4), tfm4, -tfm5)
+    assert tfm4*-tfm6 + (-tfm4*tfm6) == MIMOParallel(MIMOSeries(-tfm6, tfm4), MIMOSeries(tfm6, -tfm4))
+
+    raises(ValueError, lambda: tfm1*tfm2 + TF1)
+    raises(TypeError, lambda: tfm1*tfm2 + a0)
+    raises(TypeError, lambda: tfm4*tfm6 - (s - 1))
+    raises(TypeError, lambda: tfm4*-tfm6 - 8)
+    raises(TypeError, lambda: (-1 + p**5) + tfm1*tfm2)
+
+    # Shape criteria.
+
+    raises(TypeError, lambda: -tfm1*tfm2 + tfm4)
+    raises(TypeError, lambda: tfm1*tfm2 - tfm4 + tfm5)
+    raises(TypeError, lambda: tfm1*tfm2 - tfm4*tfm5)
+
+    assert tfm1*tfm2*-tfm3 == MIMOSeries(-tfm3, tfm2, tfm1)
+    assert (tfm1*-tfm2)*tfm3 == MIMOSeries(tfm3, -tfm2, tfm1)
+
+    # Multiplication of a Series object with a SISO TF not allowed.
+
+    raises(ValueError, lambda: tfm4*tfm5*TF1)
+    raises(TypeError, lambda: tfm4*tfm5*a1)
+    raises(TypeError, lambda: tfm4*-tfm5*(s - 2))
+    raises(TypeError, lambda: tfm5*tfm4*9)
+    raises(TypeError, lambda: (-p**3 + 1)*tfm5*tfm4)
+
+    # Transfer function matrix in the arguments.
+    assert (MIMOSeries(tfm2, tfm1, evaluate=True) == MIMOSeries(tfm2, tfm1).doit()
+        == TransferFunctionMatrix(((TransferFunction(-k**2*(a2*s + p)**2*(s**2 + 2*s*wn*zeta + wn**2)**2 + (-a2*p + s)*(a2*p - s)*(s**2 + 2*s*wn*zeta + wn**2)**2 - (a2*s + p)**2,
+        (a2*s + p)**2*(s**2 + 2*s*wn*zeta + wn**2)**2, s),),
+        (TransferFunction(k**2*(a2*s + p)**2*(s**2 + 2*s*wn*zeta + wn**2)**2 + (-a2*p + s)*(a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2) + (a2*p - s)*(a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2),
+        (a2*s + p)**2*(s**2 + 2*s*wn*zeta + wn**2)**2, s),))))
+
+    # doit() should not cancel poles and zeros.
+    mat_1 = Matrix([[1/(1+s), (1+s)/(1+s**2+2*s)**3]])
+    mat_2 = Matrix([[(1+s)], [(1+s**2+2*s)**3/(1+s)]])
+    tm_1, tm_2 = TransferFunctionMatrix.from_Matrix(mat_1, s), TransferFunctionMatrix.from_Matrix(mat_2, s)
+    assert (MIMOSeries(tm_2, tm_1).doit()
+        == TransferFunctionMatrix(((TransferFunction(2*(s + 1)**2*(s**2 + 2*s + 1)**3, (s + 1)**2*(s**2 + 2*s + 1)**3, s),),)))
+    assert MIMOSeries(tm_2, tm_1).doit().simplify() == TransferFunctionMatrix(((TransferFunction(2, 1, s),),))
+
+    # calling doit() will expand the internal Series and Parallel objects.
+    assert (MIMOSeries(-tfm3, -tfm2, tfm1, evaluate=True)
+        == MIMOSeries(-tfm3, -tfm2, tfm1).doit()
+        == TransferFunctionMatrix(((TransferFunction(k**2*(a2*s + p)**2*(s**2 + 2*s*wn*zeta + wn**2)**2 + (a2*p - s)**2*(s**2 + 2*s*wn*zeta + wn**2)**2 + (a2*s + p)**2,
+        (a2*s + p)**2*(s**2 + 2*s*wn*zeta + wn**2)**3, s),),
+        (TransferFunction(-k**2*(a2*s + p)**2*(s**2 + 2*s*wn*zeta + wn**2)**2 + (-a2*p + s)*(a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2) + (a2*p - s)*(a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2),
+        (a2*s + p)**2*(s**2 + 2*s*wn*zeta + wn**2)**3, s),))))
+    assert (MIMOSeries(MIMOParallel(tfm4, tfm5), tfm5, evaluate=True)
+        == MIMOSeries(MIMOParallel(tfm4, tfm5), tfm5).doit()
+        == TransferFunctionMatrix(((TransferFunction(-k*(-a2*s - p + (-a2*p + s)*(s**2 + 2*s*wn*zeta + wn**2)), (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), s), TransferFunction(k*(-a2*p - \
+            k*(a2*s + p) + s), a2*s + p, s)), (TransferFunction(-k*(-a2*s - p + (-a2*p + s)*(s**2 + 2*s*wn*zeta + wn**2)), (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), s), \
+            TransferFunction((-a2*p + s)*(-a2*p - k*(a2*s + p) + s), (a2*s + p)**2, s)))) == MIMOSeries(MIMOParallel(tfm4, tfm5), tfm5).rewrite(TransferFunctionMatrix))
+
+
+def test_Parallel_construction():
+    tf = TransferFunction(a0*s**3 + a1*s**2 - a2*s, b0*p**4 + b1*p**3 - b2*s*p, s)
+    tf2 = TransferFunction(a2*p - s, a2*s + p, s)
+    tf3 = TransferFunction(a0*p + p**a1 - s, p, p)
+    tf4 = TransferFunction(1, s**2 + 2*zeta*wn*s + wn**2, s)
+    inp = Function('X_d')(s)
+    out = Function('X')(s)
+
+    p0 = Parallel(tf, tf2)
+    assert p0.args == (tf, tf2)
+    assert p0.var == s
+
+    p1 = Parallel(Series(tf, -tf2), tf2)
+    assert p1.args == (Series(tf, -tf2), tf2)
+    assert p1.var == s
+
+    tf3_ = TransferFunction(inp, 1, s)
+    tf4_ = TransferFunction(-out, 1, s)
+    p2 = Parallel(tf, Series(tf3_, -tf4_), tf2)
+    assert p2.args == (tf, Series(tf3_, -tf4_), tf2)
+
+    p3 = Parallel(tf, tf2, tf4)
+    assert p3.args == (tf, tf2, tf4)
+
+    p4 = Parallel(tf3_, tf4_)
+    assert p4.args == (tf3_, tf4_)
+    assert p4.var == s
+
+    p5 = Parallel(tf, tf2)
+    assert p0 == p5
+    assert not p0 == p1
+
+    p6 = Parallel(tf2, tf4, Series(tf2, -tf4))
+    assert p6.args == (tf2, tf4, Series(tf2, -tf4))
+
+    p7 = Parallel(tf2, tf4, Series(tf2, -tf), tf4)
+    assert p7.args == (tf2, tf4, Series(tf2, -tf), tf4)
+
+    raises(ValueError, lambda: Parallel(tf, tf3))
+    raises(ValueError, lambda: Parallel(tf, tf2, tf3, tf4))
+    raises(ValueError, lambda: Parallel(-tf3, tf4))
+    raises(TypeError, lambda: Parallel(2, tf, tf4))
+    raises(TypeError, lambda: Parallel(s**2 + p*s, tf3, tf2))
+    raises(TypeError, lambda: Parallel(tf3, Matrix([1, 2, 3, 4])))
+
+
+def test_MIMOParallel_construction():
+    tfm1 = TransferFunctionMatrix([[TF1], [TF2], [TF3]])
+    tfm2 = TransferFunctionMatrix([[-TF3], [TF2], [TF1]])
+    tfm3 = TransferFunctionMatrix([[TF1]])
+    tfm4 = TransferFunctionMatrix([[TF2], [TF1], [TF3]])
+    tfm5 = TransferFunctionMatrix([[TF1, TF2], [TF2, TF1]])
+    tfm6 = TransferFunctionMatrix([[TF2, TF1], [TF1, TF2]])
+    tfm7 = TransferFunctionMatrix.from_Matrix(Matrix([[1/p]]), p)
+
+    p8 = MIMOParallel(tfm1, tfm2)
+    assert p8.args == (tfm1, tfm2)
+    assert p8.var == s
+    assert p8.shape == (p8.num_outputs, p8.num_inputs) == (3, 1)
+
+    p9 = MIMOParallel(MIMOSeries(tfm3, tfm1), tfm2)
+    assert p9.args == (MIMOSeries(tfm3, tfm1), tfm2)
+    assert p9.var == s
+    assert p9.shape == (p9.num_outputs, p9.num_inputs) == (3, 1)
+
+    p10 = MIMOParallel(tfm1, MIMOSeries(tfm3, tfm4), tfm2)
+    assert p10.args == (tfm1, MIMOSeries(tfm3, tfm4), tfm2)
+    assert p10.var == s
+    assert p10.shape == (p10.num_outputs, p10.num_inputs) == (3, 1)
+
+    p11 = MIMOParallel(tfm2, tfm1, tfm4)
+    assert p11.args == (tfm2, tfm1, tfm4)
+    assert p11.shape == (p11.num_outputs, p11.num_inputs) == (3, 1)
+
+    p12 = MIMOParallel(tfm6, tfm5)
+    assert p12.args == (tfm6, tfm5)
+    assert p12.shape == (p12.num_outputs, p12.num_inputs) == (2, 2)
+
+    p13 = MIMOParallel(tfm2, tfm4, MIMOSeries(-tfm3, tfm4), -tfm4)
+    assert p13.args == (tfm2, tfm4, MIMOSeries(-tfm3, tfm4), -tfm4)
+    assert p13.shape == (p13.num_outputs, p13.num_inputs) == (3, 1)
+
+    # arg cannot be empty tuple.
+    raises(TypeError, lambda: MIMOParallel(()))
+
+    # arg cannot contain SISO as well as MIMO systems.
+    raises(TypeError, lambda: MIMOParallel(tfm1, tfm2, TF1))
+
+    # all TFMs must have same shapes.
+    raises(TypeError, lambda: MIMOParallel(tfm1, tfm3, tfm4))
+
+    # all TFMs must be using the same complex variable.
+    raises(ValueError, lambda: MIMOParallel(tfm3, tfm7))
+
+    # Number or expression not allowed in the arguments.
+    raises(TypeError, lambda: MIMOParallel(2, tfm1, tfm4))
+    raises(TypeError, lambda: MIMOParallel(s**2 + p*s, -tfm4, tfm2))
+
+
+def test_Parallel_functions():
+    tf1 = TransferFunction(1, s**2 + 2*zeta*wn*s + wn**2, s)
+    tf2 = TransferFunction(k, 1, s)
+    tf3 = TransferFunction(a2*p - s, a2*s + p, s)
+    tf4 = TransferFunction(a0*p + p**a1 - s, p, p)
+    tf5 = TransferFunction(a1*s**2 + a2*s - a0, s + a0, s)
+
+    assert tf1 + tf2 + tf3 == Parallel(tf1, tf2, tf3)
+    assert tf1 + tf2 + tf3 + tf5 == Parallel(tf1, tf2, tf3, tf5)
+    assert tf1 + tf2 - tf3 - tf5 == Parallel(tf1, tf2, -tf3, -tf5)
+    assert tf1 + tf2*tf3 == Parallel(tf1, Series(tf2, tf3))
+    assert tf1 - tf2*tf3 == Parallel(tf1, -Series(tf2,tf3))
+    assert -tf1 - tf2 == Parallel(-tf1, -tf2)
+    assert -(tf1 + tf2) == Series(TransferFunction(-1, 1, s), Parallel(tf1, tf2))
+    assert (tf2 + tf3)*tf1 == Series(Parallel(tf2, tf3), tf1)
+    assert (tf1 + tf2)*(tf3*tf5) == Series(Parallel(tf1, tf2), tf3, tf5)
+    assert -(tf2 + tf3)*-tf5 == Series(TransferFunction(-1, 1, s), Parallel(tf2, tf3), -tf5)
+    assert tf2 + tf3 + tf2*tf1 + tf5 == Parallel(tf2, tf3, Series(tf2, tf1), tf5)
+    assert tf2 + tf3 + tf2*tf1 - tf3 == Parallel(tf2, tf3, Series(tf2, tf1), -tf3)
+    assert (tf1 + tf2 + tf5)*(tf3 + tf5) == Series(Parallel(tf1, tf2, tf5), Parallel(tf3, tf5))
+    raises(ValueError, lambda: tf1 + tf2 + tf4)
+    raises(ValueError, lambda: tf1 - tf2*tf4)
+    raises(ValueError, lambda: tf3 + Matrix([1, 2, 3]))
+
+    # evaluate=True -> doit()
+    assert Parallel(tf1, tf2, evaluate=True) == Parallel(tf1, tf2).doit() == \
+        TransferFunction(k*(s**2 + 2*s*wn*zeta + wn**2) + 1, s**2 + 2*s*wn*zeta + wn**2, s)
+    assert Parallel(tf1, tf2, Series(-tf1, tf3), evaluate=True) == \
+        Parallel(tf1, tf2, Series(-tf1, tf3)).doit() == TransferFunction(k*(a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2)**2 + \
+            (-a2*p + s)*(s**2 + 2*s*wn*zeta + wn**2) + (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), (a2*s + p)*(s**2 + \
+                2*s*wn*zeta + wn**2)**2, s)
+    assert Parallel(tf2, tf1, -tf3, evaluate=True) == Parallel(tf2, tf1, -tf3).doit() == \
+        TransferFunction(a2*s + k*(a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2) + p + (-a2*p + s)*(s**2 + 2*s*wn*zeta + wn**2) \
+            , (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), s)
+    assert not Parallel(tf1, -tf2, evaluate=False) == Parallel(tf1, -tf2).doit()
+
+    assert Parallel(Series(tf1, tf2), Series(tf2, tf3)).doit() == \
+        TransferFunction(k*(a2*p - s)*(s**2 + 2*s*wn*zeta + wn**2) + k*(a2*s + p), (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), s)
+    assert Parallel(-tf1, -tf2, -tf3).doit() == \
+        TransferFunction(-a2*s - k*(a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2) - p + (-a2*p + s)*(s**2 + 2*s*wn*zeta + wn**2), \
+            (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), s)
+    assert -Parallel(tf1, tf2, tf3).doit() == \
+        TransferFunction(-a2*s - k*(a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2) - p - (a2*p - s)*(s**2 + 2*s*wn*zeta + wn**2), \
+            (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), s)
+    assert Parallel(tf2, tf3, Series(tf2, -tf1), tf3).doit() == \
+        TransferFunction(k*(a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2) - k*(a2*s + p) + (2*a2*p - 2*s)*(s**2 + 2*s*wn*zeta \
+            + wn**2), (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), s)
+
+    assert Parallel(tf1, tf2).rewrite(TransferFunction) == \
+        TransferFunction(k*(s**2 + 2*s*wn*zeta + wn**2) + 1, s**2 + 2*s*wn*zeta + wn**2, s)
+    assert Parallel(tf2, tf1, -tf3).rewrite(TransferFunction) == \
+        TransferFunction(a2*s + k*(a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2) + p + (-a2*p + s)*(s**2 + 2*s*wn*zeta + \
+             wn**2), (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), s)
+
+    assert Parallel(tf1, Parallel(tf2, tf3)) == Parallel(tf1, tf2, tf3) == Parallel(Parallel(tf1, tf2), tf3)
+
+    P1 = Parallel(Series(tf1, tf2), Series(tf2, tf3))
+    assert P1.is_proper
+    assert not P1.is_strictly_proper
+    assert P1.is_biproper
+
+    P2 = Parallel(tf1, -tf2, -tf3)
+    assert P2.is_proper
+    assert not P2.is_strictly_proper
+    assert P2.is_biproper
+
+    P3 = Parallel(tf1, -tf2, Series(tf1, tf3))
+    assert P3.is_proper
+    assert not P3.is_strictly_proper
+    assert P3.is_biproper
+
+
+def test_MIMOParallel_functions():
+    tf4 = TransferFunction(a0*p + p**a1 - s, p, p)
+    tf5 = TransferFunction(a1*s**2 + a2*s - a0, s + a0, s)
+
+    tfm1 = TransferFunctionMatrix([[TF1], [TF2], [TF3]])
+    tfm2 = TransferFunctionMatrix([[-TF2], [tf5], [-TF1]])
+    tfm3 = TransferFunctionMatrix([[tf5], [-tf5], [TF2]])
+    tfm4 = TransferFunctionMatrix([[TF2, -tf5], [TF1, tf5]])
+    tfm5 = TransferFunctionMatrix([[TF1, TF2], [TF3, -tf5]])
+    tfm6 = TransferFunctionMatrix([[-TF2]])
+    tfm7 = TransferFunctionMatrix([[tf4], [-tf4], [tf4]])
+
+    assert tfm1 + tfm2 + tfm3 == MIMOParallel(tfm1, tfm2, tfm3) == MIMOParallel(MIMOParallel(tfm1, tfm2), tfm3)
+    assert tfm2 - tfm1 - tfm3 == MIMOParallel(tfm2, -tfm1, -tfm3)
+    assert tfm2 - tfm3 + (-tfm1*tfm6*-tfm6) == MIMOParallel(tfm2, -tfm3, MIMOSeries(-tfm6, tfm6, -tfm1))
+    assert tfm1 + tfm1 - (-tfm1*tfm6) == MIMOParallel(tfm1, tfm1, -MIMOSeries(tfm6, -tfm1))
+    assert tfm2 - tfm3 - tfm1 + tfm2 == MIMOParallel(tfm2, -tfm3, -tfm1, tfm2)
+    assert tfm1 + tfm2 - tfm3 - tfm1 == MIMOParallel(tfm1, tfm2, -tfm3, -tfm1)
+    raises(ValueError, lambda: tfm1 + tfm2 + TF2)
+    raises(TypeError, lambda: tfm1 - tfm2 - a1)
+    raises(TypeError, lambda: tfm2 - tfm3 - (s - 1))
+    raises(TypeError, lambda: -tfm3 - tfm2 - 9)
+    raises(TypeError, lambda: (1 - p**3) - tfm3 - tfm2)
+    # All TFMs must use the same complex var. tfm7 uses 'p'.
+    raises(ValueError, lambda: tfm3 - tfm2 - tfm7)
+    raises(ValueError, lambda: tfm2 - tfm1 + tfm7)
+    # (tfm1 +/- tfm2) has (3, 1) shape while tfm4 has (2, 2) shape.
+    raises(TypeError, lambda: tfm1 + tfm2 + tfm4)
+    raises(TypeError, lambda: (tfm1 - tfm2) - tfm4)
+
+    assert (tfm1 + tfm2)*tfm6 == MIMOSeries(tfm6, MIMOParallel(tfm1, tfm2))
+    assert (tfm2 - tfm3)*tfm6*-tfm6 == MIMOSeries(-tfm6, tfm6, MIMOParallel(tfm2, -tfm3))
+    assert (tfm2 - tfm1 - tfm3)*(tfm6 + tfm6) == MIMOSeries(MIMOParallel(tfm6, tfm6), MIMOParallel(tfm2, -tfm1, -tfm3))
+    raises(ValueError, lambda: (tfm4 + tfm5)*TF1)
+    raises(TypeError, lambda: (tfm2 - tfm3)*a2)
+    raises(TypeError, lambda: (tfm3 + tfm2)*(s - 6))
+    raises(TypeError, lambda: (tfm1 + tfm2 + tfm3)*0)
+    raises(TypeError, lambda: (1 - p**3)*(tfm1 + tfm3))
+
+    # (tfm3 - tfm2) has (3, 1) shape while tfm4*tfm5 has (2, 2) shape.
+    raises(ValueError, lambda: (tfm3 - tfm2)*tfm4*tfm5)
+    # (tfm1 - tfm2) has (3, 1) shape while tfm5 has (2, 2) shape.
+    raises(ValueError, lambda: (tfm1 - tfm2)*tfm5)
+
+    # TFM in the arguments.
+    assert (MIMOParallel(tfm1, tfm2, evaluate=True) == MIMOParallel(tfm1, tfm2).doit()
+    == MIMOParallel(tfm1, tfm2).rewrite(TransferFunctionMatrix)
+    == TransferFunctionMatrix(((TransferFunction(-k*(s**2 + 2*s*wn*zeta + wn**2) + 1, s**2 + 2*s*wn*zeta + wn**2, s),), \
+        (TransferFunction(-a0 + a1*s**2 + a2*s + k*(a0 + s), a0 + s, s),), (TransferFunction(-a2*s - p + (a2*p - s)* \
+        (s**2 + 2*s*wn*zeta + wn**2), (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), s),))))
+
+
+def test_Feedback_construction():
+    tf1 = TransferFunction(1, s**2 + 2*zeta*wn*s + wn**2, s)
+    tf2 = TransferFunction(k, 1, s)
+    tf3 = TransferFunction(a2*p - s, a2*s + p, s)
+    tf4 = TransferFunction(a0*p + p**a1 - s, p, p)
+    tf5 = TransferFunction(a1*s**2 + a2*s - a0, s + a0, s)
+    tf6 = TransferFunction(s - p, p + s, p)
+
+    f1 = Feedback(TransferFunction(1, 1, s), tf1*tf2*tf3)
+    assert f1.args == (TransferFunction(1, 1, s), Series(tf1, tf2, tf3), -1)
+    assert f1.sys1 == TransferFunction(1, 1, s)
+    assert f1.sys2 == Series(tf1, tf2, tf3)
+    assert f1.var == s
+
+    f2 = Feedback(tf1, tf2*tf3)
+    assert f2.args == (tf1, Series(tf2, tf3), -1)
+    assert f2.sys1 == tf1
+    assert f2.sys2 == Series(tf2, tf3)
+    assert f2.var == s
+
+    f3 = Feedback(tf1*tf2, tf5)
+    assert f3.args == (Series(tf1, tf2), tf5, -1)
+    assert f3.sys1 == Series(tf1, tf2)
+
+    f4 = Feedback(tf4, tf6)
+    assert f4.args == (tf4, tf6, -1)
+    assert f4.sys1 == tf4
+    assert f4.var == p
+
+    f5 = Feedback(tf5, TransferFunction(1, 1, s))
+    assert f5.args == (tf5, TransferFunction(1, 1, s), -1)
+    assert f5.var == s
+    assert f5 == Feedback(tf5)  # When sys2 is not passed explicitly, it is assumed to be unit tf.
+
+    f6 = Feedback(TransferFunction(1, 1, p), tf4)
+    assert f6.args == (TransferFunction(1, 1, p), tf4, -1)
+    assert f6.var == p
+
+    f7 = -Feedback(tf4*tf6, TransferFunction(1, 1, p))
+    assert f7.args == (Series(TransferFunction(-1, 1, p), Series(tf4, tf6)), -TransferFunction(1, 1, p), -1)
+    assert f7.sys1 == Series(TransferFunction(-1, 1, p), Series(tf4, tf6))
+
+    # denominator can't be a Parallel instance
+    raises(TypeError, lambda: Feedback(tf1, tf2 + tf3))
+    raises(TypeError, lambda: Feedback(tf1, Matrix([1, 2, 3])))
+    raises(TypeError, lambda: Feedback(TransferFunction(1, 1, s), s - 1))
+    raises(TypeError, lambda: Feedback(1, 1))
+    # raises(ValueError, lambda: Feedback(TransferFunction(1, 1, s), TransferFunction(1, 1, s)))
+    raises(ValueError, lambda: Feedback(tf2, tf4*tf5))
+    raises(ValueError, lambda: Feedback(tf2, tf1, 1.5))  # `sign` can only be -1 or 1
+    raises(ValueError, lambda: Feedback(tf1, -tf1**-1))  # denominator can't be zero
+    raises(ValueError, lambda: Feedback(tf4, tf5))  # Both systems should use the same `var`
+
+
+def test_Feedback_functions():
+    tf = TransferFunction(1, 1, s)
+    tf1 = TransferFunction(1, s**2 + 2*zeta*wn*s + wn**2, s)
+    tf2 = TransferFunction(k, 1, s)
+    tf3 = TransferFunction(a2*p - s, a2*s + p, s)
+    tf4 = TransferFunction(a0*p + p**a1 - s, p, p)
+    tf5 = TransferFunction(a1*s**2 + a2*s - a0, s + a0, s)
+    tf6 = TransferFunction(s - p, p + s, p)
+
+    assert (tf1*tf2*tf3 / tf3*tf5) == Series(tf1, tf2, tf3, pow(tf3, -1), tf5)
+    assert (tf1*tf2*tf3) / (tf3*tf5) == Series((tf1*tf2*tf3).doit(), pow((tf3*tf5).doit(),-1))
+    assert tf / (tf + tf1) == Feedback(tf, tf1)
+    assert tf / (tf + tf1*tf2*tf3) == Feedback(tf, tf1*tf2*tf3)
+    assert tf1 / (tf + tf1*tf2*tf3) == Feedback(tf1, tf2*tf3)
+    assert (tf1*tf2) / (tf + tf1*tf2) == Feedback(tf1*tf2, tf)
+    assert (tf1*tf2) / (tf + tf1*tf2*tf5) == Feedback(tf1*tf2, tf5)
+    assert (tf1*tf2) / (tf + tf1*tf2*tf5*tf3) in (Feedback(tf1*tf2, tf5*tf3), Feedback(tf1*tf2, tf3*tf5))
+    assert tf4 / (TransferFunction(1, 1, p) + tf4*tf6) == Feedback(tf4, tf6)
+    assert tf5 / (tf + tf5) == Feedback(tf5, tf)
+
+    raises(TypeError, lambda: tf1*tf2*tf3 / (1 + tf1*tf2*tf3))
+    raises(ValueError, lambda: tf2*tf3 / (tf + tf2*tf3*tf4))
+
+    assert Feedback(tf, tf1*tf2*tf3).doit() == \
+        TransferFunction((a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), k*(a2*p - s) + \
+        (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), s)
+    assert Feedback(tf, tf1*tf2*tf3).sensitivity == \
+        1/(k*(a2*p - s)/((a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2)) + 1)
+    assert Feedback(tf1, tf2*tf3).doit() == \
+        TransferFunction((a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2), (k*(a2*p - s) + \
+        (a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2))*(s**2 + 2*s*wn*zeta + wn**2), s)
+    assert Feedback(tf1, tf2*tf3).sensitivity == \
+        1/(k*(a2*p - s)/((a2*s + p)*(s**2 + 2*s*wn*zeta + wn**2)) + 1)
+    assert Feedback(tf1*tf2, tf5).doit() == \
+        TransferFunction(k*(a0 + s)*(s**2 + 2*s*wn*zeta + wn**2), (k*(-a0 + a1*s**2 + a2*s) + \
+        (a0 + s)*(s**2 + 2*s*wn*zeta + wn**2))*(s**2 + 2*s*wn*zeta + wn**2), s)
+    assert Feedback(tf1*tf2, tf5, 1).sensitivity == \
+        1/(-k*(-a0 + a1*s**2 + a2*s)/((a0 + s)*(s**2 + 2*s*wn*zeta + wn**2)) + 1)
+    assert Feedback(tf4, tf6).doit() == \
+        TransferFunction(p*(p + s)*(a0*p + p**a1 - s), p*(p*(p + s) + (-p + s)*(a0*p + p**a1 - s)), p)
+    assert -Feedback(tf4*tf6, TransferFunction(1, 1, p)).doit() == \
+        TransferFunction(-p*(-p + s)*(p + s)*(a0*p + p**a1 - s), p*(p + s)*(p*(p + s) + (-p + s)*(a0*p + p**a1 - s)), p)
+    assert Feedback(tf, tf).doit() == TransferFunction(1, 2, s)
+
+    assert Feedback(tf1, tf2*tf5).rewrite(TransferFunction) == \
+        TransferFunction((a0 + s)*(s**2 + 2*s*wn*zeta + wn**2), (k*(-a0 + a1*s**2 + a2*s) + \
+        (a0 + s)*(s**2 + 2*s*wn*zeta + wn**2))*(s**2 + 2*s*wn*zeta + wn**2), s)
+    assert Feedback(TransferFunction(1, 1, p), tf4).rewrite(TransferFunction) == \
+        TransferFunction(p, a0*p + p + p**a1 - s, p)
+
+
+def test_Feedback_as_TransferFunction():
+    # Solves issue https://github.com/sympy/sympy/issues/26161
+    tf1 = TransferFunction(s+1, 1, s)
+    tf2 = TransferFunction(s+2, 1, s)
+    fd1 = Feedback(tf1, tf2, -1) # Negative Feedback system
+    fd2 = Feedback(tf1, tf2, 1) # Positive Feedback system
+    unit = TransferFunction(1, 1, s)
+
+    # Checking the type
+    assert isinstance(fd1, TransferFunction)
+    assert isinstance(fd1, Feedback)
+
+    # Testing the numerator and denominator
+    assert fd1.num == tf1
+    assert fd2.num == tf1
+    assert fd1.den == Parallel(unit, Series(tf2, tf1))
+    assert fd2.den == Parallel(unit, -Series(tf2, tf1))
+
+    # Testing the Series and Parallel Combination with Feedback and TransferFunction
+    s1 = Series(tf1, fd1)
+    p1 = Parallel(tf1, fd1)
+    assert tf1 * fd1 == s1
+    assert tf1 + fd1 == p1
+    assert s1.doit() == TransferFunction((s + 1)**2, (s + 1)*(s + 2) + 1, s)
+    assert p1.doit() == TransferFunction(s + (s + 1)*((s + 1)*(s + 2) + 1) + 1, (s + 1)*(s + 2) + 1, s)
+
+    # Testing the use of Feedback and TransferFunction with Feedback
+    fd3 = Feedback(tf1*fd1, tf2, -1)
+    assert fd3 == Feedback(Series(tf1, fd1), tf2)
+    assert fd3.num == tf1 * fd1
+    assert fd3.den == Parallel(unit, Series(tf2, Series(tf1, fd1)))
+
+    # Testing the use of Feedback and TransferFunction with TransferFunction
+    tf3 = TransferFunction(tf1*fd1, tf2, s)
+    assert tf3 == TransferFunction(Series(tf1, fd1), tf2, s)
+    assert tf3.num == tf1*fd1
+
+def test_issue_26161():
+    # Issue https://github.com/sympy/sympy/issues/26161
+    Ib, Is, m, h, l2, l1 = symbols('I_b, I_s, m, h, l2, l1',
+                                            real=True, nonnegative=True)
+    KD, KP, v = symbols('K_D, K_P, v', real=True)
+
+    tau1_sq = (Ib + m * h ** 2) / m / g / h
+    tau2 = l2 / v
+    tau3 = v / (l1 + l2)
+    K = v ** 2 / g / (l1 + l2)
+
+    Gtheta = TransferFunction(-K * (tau2 * s + 1), tau1_sq * s ** 2 - 1, s)
+    Gdelta = TransferFunction(1, Is * s ** 2 + c * s, s)
+    Gpsi = TransferFunction(1, tau3 * s, s)
+    Dcont = TransferFunction(KD * s, 1, s)
+    PIcont = TransferFunction(KP, s, s)
+    Gunity = TransferFunction(1, 1, s)
+
+    Ginner = Feedback(Dcont * Gdelta, Gtheta)
+    Gouter = Feedback(PIcont * Ginner * Gpsi, Gunity)
+    assert Gouter == Feedback(Series(PIcont, Series(Ginner, Gpsi)), Gunity)
+    assert Gouter.num == Series(PIcont, Series(Ginner, Gpsi))
+    assert Gouter.den == Parallel(Gunity, Series(Gunity, Series(PIcont, Series(Ginner, Gpsi))))
+    expr = (KD*KP*g*s**3*v**2*(l1 + l2)*(Is*s**2 + c*s)**2*(-g*h*m + s**2*(Ib + h**2*m))*(-KD*g*h*m*s*v**2*(l2*s + v) + \
+            g*v*(l1 + l2)*(Is*s**2 + c*s)*(-g*h*m + s**2*(Ib + h**2*m))))/((s**2*v*(Is*s**2 + c*s)*(-KD*g*h*m*s*v**2* \
+            (l2*s + v) + g*v*(l1 + l2)*(Is*s**2 + c*s)*(-g*h*m + s**2*(Ib + h**2*m)))*(KD*KP*g*s*v*(l1 + l2)**2* \
+            (Is*s**2 + c*s)*(-g*h*m + s**2*(Ib + h**2*m)) + s**2*v*(Is*s**2 + c*s)*(-KD*g*h*m*s*v**2*(l2*s + v) + \
+            g*v*(l1 + l2)*(Is*s**2 + c*s)*(-g*h*m + s**2*(Ib + h**2*m))))/(l1 + l2)))
+
+    assert (Gouter.to_expr() - expr).simplify() == 0
+
+
+def test_MIMOFeedback_construction():
+    tf1 = TransferFunction(1, s, s)
+    tf2 = TransferFunction(s, s**3 - 1, s)
+    tf3 = TransferFunction(s, s + 1, s)
+    tf4 = TransferFunction(s, s**2 + 1, s)
+
+    tfm_1 = TransferFunctionMatrix([[tf1, tf2], [tf3, tf4]])
+    tfm_2 = TransferFunctionMatrix([[tf2, tf3], [tf4, tf1]])
+    tfm_3 = TransferFunctionMatrix([[tf3, tf4], [tf1, tf2]])
+
+    f1 = MIMOFeedback(tfm_1, tfm_2)
+    assert f1.args == (tfm_1, tfm_2, -1)
+    assert f1.sys1 == tfm_1
+    assert f1.sys2 == tfm_2
+    assert f1.var == s
+    assert f1.sign == -1
+    assert -(-f1) == f1
+
+    f2 = MIMOFeedback(tfm_2, tfm_1, 1)
+    assert f2.args == (tfm_2, tfm_1, 1)
+    assert f2.sys1 == tfm_2
+    assert f2.sys2 == tfm_1
+    assert f2.var == s
+    assert f2.sign == 1
+
+    f3 = MIMOFeedback(tfm_1, MIMOSeries(tfm_3, tfm_2))
+    assert f3.args == (tfm_1, MIMOSeries(tfm_3, tfm_2), -1)
+    assert f3.sys1 == tfm_1
+    assert f3.sys2 == MIMOSeries(tfm_3, tfm_2)
+    assert f3.var == s
+    assert f3.sign == -1
+
+    mat = Matrix([[1, 1/s], [0, 1]])
+    sys1 = controller = TransferFunctionMatrix.from_Matrix(mat, s)
+    f4 = MIMOFeedback(sys1, controller)
+    assert f4.args == (sys1, controller, -1)
+    assert f4.sys1 == f4.sys2 == sys1
+
+
+def test_MIMOFeedback_errors():
+    tf1 = TransferFunction(1, s, s)
+    tf2 = TransferFunction(s, s**3 - 1, s)
+    tf3 = TransferFunction(s, s - 1, s)
+    tf4 = TransferFunction(s, s**2 + 1, s)
+    tf5 = TransferFunction(1, 1, s)
+    tf6 = TransferFunction(-1, s - 1, s)
+
+    tfm_1 = TransferFunctionMatrix([[tf1, tf2], [tf3, tf4]])
+    tfm_2 = TransferFunctionMatrix([[tf2, tf3], [tf4, tf1]])
+    tfm_3 = TransferFunctionMatrix.from_Matrix(eye(2), var=s)
+    tfm_4 = TransferFunctionMatrix([[tf1, tf5], [tf5, tf5]])
+    tfm_5 = TransferFunctionMatrix([[-tf3, tf3], [tf3, tf6]])
+    # tfm_4 is inverse of tfm_5. Therefore tfm_5*tfm_4 = I
+    tfm_6 = TransferFunctionMatrix([[-tf3]])
+    tfm_7 = TransferFunctionMatrix([[tf3, tf4]])
+
+    # Unsupported Types
+    raises(TypeError, lambda: MIMOFeedback(tf1, tf2))
+    raises(TypeError, lambda: MIMOFeedback(MIMOParallel(tfm_1, tfm_2), tfm_3))
+    # Shape Errors
+    raises(ValueError, lambda: MIMOFeedback(tfm_1, tfm_6, 1))
+    raises(ValueError, lambda: MIMOFeedback(tfm_7, tfm_7))
+    # sign not 1/-1
+    raises(ValueError, lambda: MIMOFeedback(tfm_1, tfm_2, -2))
+    # Non-Invertible Systems
+    raises(ValueError, lambda: MIMOFeedback(tfm_5, tfm_4, 1))
+    raises(ValueError, lambda: MIMOFeedback(tfm_4, -tfm_5))
+    raises(ValueError, lambda: MIMOFeedback(tfm_3, tfm_3, 1))
+    # Variable not same in both the systems
+    tfm_8 = TransferFunctionMatrix.from_Matrix(eye(2), var=p)
+    raises(ValueError, lambda: MIMOFeedback(tfm_1, tfm_8, 1))
+
+
+def test_MIMOFeedback_functions():
+    tf1 = TransferFunction(1, s, s)
+    tf2 = TransferFunction(s, s - 1, s)
+    tf3 = TransferFunction(1, 1, s)
+    tf4 = TransferFunction(-1, s - 1, s)
+
+    tfm_1 = TransferFunctionMatrix.from_Matrix(eye(2), var=s)
+    tfm_2 = TransferFunctionMatrix([[tf1, tf3], [tf3, tf3]])
+    tfm_3 = TransferFunctionMatrix([[-tf2, tf2], [tf2, tf4]])
+    tfm_4 = TransferFunctionMatrix([[tf1, tf2], [-tf2, tf1]])
+
+    # sensitivity, doit(), rewrite()
+    F_1 = MIMOFeedback(tfm_2, tfm_3)
+    F_2 = MIMOFeedback(tfm_2, MIMOSeries(tfm_4, -tfm_1), 1)
+
+    assert F_1.sensitivity == Matrix([[S.Half, 0], [0, S.Half]])
+    assert F_2.sensitivity == Matrix([[(-2*s**4 + s**2)/(s**2 - s + 1),
+        (2*s**3 - s**2)/(s**2 - s + 1)], [-s**2, s]])
+
+    assert F_1.doit() == \
+        TransferFunctionMatrix(((TransferFunction(1, 2*s, s),
+        TransferFunction(1, 2, s)), (TransferFunction(1, 2, s),
+        TransferFunction(1, 2, s)))) == F_1.rewrite(TransferFunctionMatrix)
+    assert F_2.doit(cancel=False, expand=True) == \
+        TransferFunctionMatrix(((TransferFunction(-s**5 + 2*s**4 - 2*s**3 + s**2, s**5 - 2*s**4 + 3*s**3 - 2*s**2 + s, s),
+        TransferFunction(-2*s**4 + 2*s**3, s**2 - s + 1, s)), (TransferFunction(0, 1, s), TransferFunction(-s**2 + s, 1, s))))
+    assert F_2.doit(cancel=False) == \
+        TransferFunctionMatrix(((TransferFunction(s*(2*s**3 - s**2)*(s**2 - s + 1) + \
+        (-2*s**4 + s**2)*(s**2 - s + 1), s*(s**2 - s + 1)**2, s), TransferFunction(-2*s**4 + 2*s**3, s**2 - s + 1, s)),
+        (TransferFunction(0, 1, s), TransferFunction(-s**2 + s, 1, s))))
+    assert F_2.doit() == \
+        TransferFunctionMatrix(((TransferFunction(s*(-2*s**2 + s*(2*s - 1) + 1), s**2 - s + 1, s),
+        TransferFunction(-2*s**3*(s - 1), s**2 - s + 1, s)), (TransferFunction(0, 1, s), TransferFunction(s*(1 - s), 1, s))))
+    assert F_2.doit(expand=True) == \
+        TransferFunctionMatrix(((TransferFunction(-s**2 + s, s**2 - s + 1, s), TransferFunction(-2*s**4 + 2*s**3, s**2 - s + 1, s)),
+        (TransferFunction(0, 1, s), TransferFunction(-s**2 + s, 1, s))))
+
+    assert -(F_1.doit()) == (-F_1).doit()  # First negating then calculating vs calculating then negating.
+
+
+def test_TransferFunctionMatrix_construction():
+    tf5 = TransferFunction(a1*s**2 + a2*s - a0, s + a0, s)
+    tf4 = TransferFunction(a0*p + p**a1 - s, p, p)
+
+    tfm3_ = TransferFunctionMatrix([[-TF3]])
+    assert tfm3_.shape == (tfm3_.num_outputs, tfm3_.num_inputs) == (1, 1)
+    assert tfm3_.args == Tuple(Tuple(Tuple(-TF3)))
+    assert tfm3_.var == s
+
+    tfm5 = TransferFunctionMatrix([[TF1, -TF2], [TF3, tf5]])
+    assert tfm5.shape == (tfm5.num_outputs, tfm5.num_inputs) == (2, 2)
+    assert tfm5.args == Tuple(Tuple(Tuple(TF1, -TF2), Tuple(TF3, tf5)))
+    assert tfm5.var == s
+
+    tfm7 = TransferFunctionMatrix([[TF1, TF2], [TF3, -tf5], [-tf5, TF2]])
+    assert tfm7.shape == (tfm7.num_outputs, tfm7.num_inputs) == (3, 2)
+    assert tfm7.args == Tuple(Tuple(Tuple(TF1, TF2), Tuple(TF3, -tf5), Tuple(-tf5, TF2)))
+    assert tfm7.var == s
+
+    # all transfer functions will use the same complex variable. tf4 uses 'p'.
+    raises(ValueError, lambda: TransferFunctionMatrix([[TF1], [TF2], [tf4]]))
+    raises(ValueError, lambda: TransferFunctionMatrix([[TF1, tf4], [TF3, tf5]]))
+
+    # length of all the lists in the TFM should be equal.
+    raises(ValueError, lambda: TransferFunctionMatrix([[TF1], [TF3, tf5]]))
+    raises(ValueError, lambda: TransferFunctionMatrix([[TF1, TF3], [tf5]]))
+
+    # lists should only support transfer functions in them.
+    raises(TypeError, lambda: TransferFunctionMatrix([[TF1, TF2], [TF3, Matrix([1, 2])]]))
+    raises(TypeError, lambda: TransferFunctionMatrix([[TF1, Matrix([1, 2])], [TF3, TF2]]))
+
+    # `arg` should strictly be nested list of TransferFunction
+    raises(ValueError, lambda: TransferFunctionMatrix([TF1, TF2, tf5]))
+    raises(ValueError, lambda: TransferFunctionMatrix([TF1]))
+
+def test_TransferFunctionMatrix_functions():
+    tf5 = TransferFunction(a1*s**2 + a2*s - a0, s + a0, s)
+
+    #  Classmethod (from_matrix)
+
+    mat_1 = ImmutableMatrix([
+        [s*(s + 1)*(s - 3)/(s**4 + 1), 2],
+        [p, p*(s + 1)/(s*(s**1 + 1))]
+        ])
+    mat_2 = ImmutableMatrix([[(2*s + 1)/(s**2 - 9)]])
+    mat_3 = ImmutableMatrix([[1, 2], [3, 4]])
+    assert TransferFunctionMatrix.from_Matrix(mat_1, s) == \
+        TransferFunctionMatrix([[TransferFunction(s*(s - 3)*(s + 1), s**4 + 1, s), TransferFunction(2, 1, s)],
+        [TransferFunction(p, 1, s), TransferFunction(p, s, s)]])
+    assert TransferFunctionMatrix.from_Matrix(mat_2, s) == \
+        TransferFunctionMatrix([[TransferFunction(2*s + 1, s**2 - 9, s)]])
+    assert TransferFunctionMatrix.from_Matrix(mat_3, p) == \
+        TransferFunctionMatrix([[TransferFunction(1, 1, p), TransferFunction(2, 1, p)],
+        [TransferFunction(3, 1, p), TransferFunction(4, 1, p)]])
+
+    #  Negating a TFM
+
+    tfm1 = TransferFunctionMatrix([[TF1], [TF2]])
+    assert -tfm1 == TransferFunctionMatrix([[-TF1], [-TF2]])
+
+    tfm2 = TransferFunctionMatrix([[TF1, TF2, TF3], [tf5, -TF1, -TF3]])
+    assert -tfm2 == TransferFunctionMatrix([[-TF1, -TF2, -TF3], [-tf5, TF1, TF3]])
+
+    # subs()
+
+    H_1 = TransferFunctionMatrix.from_Matrix(mat_1, s)
+    H_2 = TransferFunctionMatrix([[TransferFunction(a*p*s, k*s**2, s), TransferFunction(p*s, k*(s**2 - a), s)]])
+    assert H_1.subs(p, 1) == TransferFunctionMatrix([[TransferFunction(s*(s - 3)*(s + 1), s**4 + 1, s), TransferFunction(2, 1, s)], [TransferFunction(1, 1, s), TransferFunction(1, s, s)]])
+    assert H_1.subs({p: 1}) == TransferFunctionMatrix([[TransferFunction(s*(s - 3)*(s + 1), s**4 + 1, s), TransferFunction(2, 1, s)], [TransferFunction(1, 1, s), TransferFunction(1, s, s)]])
+    assert H_1.subs({p: 1, s: 1}) == TransferFunctionMatrix([[TransferFunction(s*(s - 3)*(s + 1), s**4 + 1, s), TransferFunction(2, 1, s)], [TransferFunction(1, 1, s), TransferFunction(1, s, s)]]) # This should ignore `s` as it is `var`
+    assert H_2.subs(p, 2) == TransferFunctionMatrix([[TransferFunction(2*a*s, k*s**2, s), TransferFunction(2*s, k*(-a + s**2), s)]])
+    assert H_2.subs(k, 1) == TransferFunctionMatrix([[TransferFunction(a*p*s, s**2, s), TransferFunction(p*s, -a + s**2, s)]])
+    assert H_2.subs(a, 0) == TransferFunctionMatrix([[TransferFunction(0, k*s**2, s), TransferFunction(p*s, k*s**2, s)]])
+    assert H_2.subs({p: 1, k: 1, a: a0}) == TransferFunctionMatrix([[TransferFunction(a0*s, s**2, s), TransferFunction(s, -a0 + s**2, s)]])
+
+    # eval_frequency()
+    assert H_2.eval_frequency(S(1)/2 + I) == Matrix([[2*a*p/(5*k) - 4*I*a*p/(5*k), I*p/(-a*k - 3*k/4 + I*k) + p/(-2*a*k - 3*k/2 + 2*I*k)]])
+
+    # transpose()
+
+    assert H_1.transpose() == TransferFunctionMatrix([[TransferFunction(s*(s - 3)*(s + 1), s**4 + 1, s), TransferFunction(p, 1, s)], [TransferFunction(2, 1, s), TransferFunction(p, s, s)]])
+    assert H_2.transpose() == TransferFunctionMatrix([[TransferFunction(a*p*s, k*s**2, s)], [TransferFunction(p*s, k*(-a + s**2), s)]])
+    assert H_1.transpose().transpose() == H_1
+    assert H_2.transpose().transpose() == H_2
+
+    # elem_poles()
+
+    assert H_1.elem_poles() == [[[-sqrt(2)/2 - sqrt(2)*I/2, -sqrt(2)/2 + sqrt(2)*I/2, sqrt(2)/2 - sqrt(2)*I/2, sqrt(2)/2 + sqrt(2)*I/2], []],
+        [[], [0]]]
+    assert H_2.elem_poles() == [[[0, 0], [sqrt(a), -sqrt(a)]]]
+    assert tfm2.elem_poles() == [[[wn*(-zeta + sqrt((zeta - 1)*(zeta + 1))), wn*(-zeta - sqrt((zeta - 1)*(zeta + 1)))], [], [-p/a2]],
+        [[-a0], [wn*(-zeta + sqrt((zeta - 1)*(zeta + 1))), wn*(-zeta - sqrt((zeta - 1)*(zeta + 1)))], [-p/a2]]]
+
+    # elem_zeros()
+
+    assert H_1.elem_zeros() == [[[-1, 0, 3], []], [[], []]]
+    assert H_2.elem_zeros() == [[[0], [0]]]
+    assert tfm2.elem_zeros() == [[[], [], [a2*p]],
+        [[-a2/(2*a1) - sqrt(4*a0*a1 + a2**2)/(2*a1), -a2/(2*a1) + sqrt(4*a0*a1 + a2**2)/(2*a1)], [], [a2*p]]]
+
+    # doit()
+
+    H_3 = TransferFunctionMatrix([[Series(TransferFunction(1, s**3 - 3, s), TransferFunction(s**2 - 2*s + 5, 1, s), TransferFunction(1, s, s))]])
+    H_4 = TransferFunctionMatrix([[Parallel(TransferFunction(s**3 - 3, 4*s**4 - s**2 - 2*s + 5, s), TransferFunction(4 - s**3, 4*s**4 - s**2 - 2*s + 5, s))]])
+
+    assert H_3.doit() == TransferFunctionMatrix([[TransferFunction(s**2 - 2*s + 5, s*(s**3 - 3), s)]])
+    assert H_4.doit() == TransferFunctionMatrix([[TransferFunction(1, 4*s**4 - s**2 - 2*s + 5, s)]])
+
+    # _flat()
+
+    assert H_1._flat() == [TransferFunction(s*(s - 3)*(s + 1), s**4 + 1, s), TransferFunction(2, 1, s), TransferFunction(p, 1, s), TransferFunction(p, s, s)]
+    assert H_2._flat() == [TransferFunction(a*p*s, k*s**2, s), TransferFunction(p*s, k*(-a + s**2), s)]
+    assert H_3._flat() == [Series(TransferFunction(1, s**3 - 3, s), TransferFunction(s**2 - 2*s + 5, 1, s), TransferFunction(1, s, s))]
+    assert H_4._flat() == [Parallel(TransferFunction(s**3 - 3, 4*s**4 - s**2 - 2*s + 5, s), TransferFunction(4 - s**3, 4*s**4 - s**2 - 2*s + 5, s))]
+
+    # evalf()
+
+    assert H_1.evalf() == \
+        TransferFunctionMatrix(((TransferFunction(s*(s - 3.0)*(s + 1.0), s**4 + 1.0, s), TransferFunction(2.0, 1, s)), (TransferFunction(1.0*p, 1, s), TransferFunction(p, s, s))))
+    assert H_2.subs({a:3.141, p:2.88, k:2}).evalf() == \
+        TransferFunctionMatrix(((TransferFunction(4.5230399999999999494093572138808667659759521484375, s, s),
+        TransferFunction(2.87999999999999989341858963598497211933135986328125*s, 2.0*s**2 - 6.282000000000000028421709430404007434844970703125, s)),))
+
+    # simplify()
+
+    H_5 = TransferFunctionMatrix([[TransferFunction(s**5 + s**3 + s, s - s**2, s),
+        TransferFunction((s + 3)*(s - 1), (s - 1)*(s + 5), s)]])
+
+    assert H_5.simplify() == simplify(H_5) == \
+        TransferFunctionMatrix(((TransferFunction(-s**4 - s**2 - 1, s - 1, s), TransferFunction(s + 3, s + 5, s)),))
+
+    # expand()
+
+    assert (H_1.expand()
+            == TransferFunctionMatrix(((TransferFunction(s**3 - 2*s**2 - 3*s, s**4 + 1, s), TransferFunction(2, 1, s)),
+            (TransferFunction(p, 1, s), TransferFunction(p, s, s)))))
+    assert H_5.expand() == \
+        TransferFunctionMatrix(((TransferFunction(s**5 + s**3 + s, -s**2 + s, s), TransferFunction(s**2 + 2*s - 3, s**2 + 4*s - 5, s)),))
+
+def test_TransferFunction_gbt():
+    # simple transfer function, e.g. ohms law
+    tf = TransferFunction(1, a*s+b, s)
+    numZ, denZ = gbt(tf, T, 0.5)
+    # discretized transfer function with coefs from tf.gbt()
+    tf_test_bilinear = TransferFunction(s * numZ[0] + numZ[1], s * denZ[0] + denZ[1], s)
+    # corresponding tf with manually calculated coefs
+    tf_test_manual = TransferFunction(s * T/(2*(a + b*T/2)) + T/(2*(a + b*T/2)), s + (-a + b*T/2)/(a + b*T/2), s)
+
+    assert S.Zero == (tf_test_bilinear.simplify()-tf_test_manual.simplify()).simplify().num
+
+    tf = TransferFunction(1, a*s+b, s)
+    numZ, denZ = gbt(tf, T, 0)
+    # discretized transfer function with coefs from tf.gbt()
+    tf_test_forward = TransferFunction(numZ[0], s*denZ[0]+denZ[1], s)
+    # corresponding tf with manually calculated coefs
+    tf_test_manual = TransferFunction(T/a, s + (-a + b*T)/a, s)
+
+    assert S.Zero == (tf_test_forward.simplify()-tf_test_manual.simplify()).simplify().num
+
+    tf = TransferFunction(1, a*s+b, s)
+    numZ, denZ = gbt(tf, T, 1)
+    # discretized transfer function with coefs from tf.gbt()
+    tf_test_backward = TransferFunction(s*numZ[0], s*denZ[0]+denZ[1], s)
+    # corresponding tf with manually calculated coefs
+    tf_test_manual = TransferFunction(s * T/(a + b*T), s - a/(a + b*T), s)
+
+    assert S.Zero == (tf_test_backward.simplify()-tf_test_manual.simplify()).simplify().num
+
+    tf = TransferFunction(1, a*s+b, s)
+    numZ, denZ = gbt(tf, T, 0.3)
+    # discretized transfer function with coefs from tf.gbt()
+    tf_test_gbt = TransferFunction(s*numZ[0]+numZ[1], s*denZ[0]+denZ[1], s)
+    # corresponding tf with manually calculated coefs
+    tf_test_manual = TransferFunction(s*3*T/(10*(a + 3*b*T/10)) + 7*T/(10*(a + 3*b*T/10)), s + (-a + 7*b*T/10)/(a + 3*b*T/10), s)
+
+    assert S.Zero == (tf_test_gbt.simplify()-tf_test_manual.simplify()).simplify().num
+
+def test_TransferFunction_bilinear():
+    # simple transfer function, e.g. ohms law
+    tf = TransferFunction(1, a*s+b, s)
+    numZ, denZ = bilinear(tf, T)
+    # discretized transfer function with coefs from tf.bilinear()
+    tf_test_bilinear = TransferFunction(s*numZ[0]+numZ[1], s*denZ[0]+denZ[1], s)
+    # corresponding tf with manually calculated coefs
+    tf_test_manual = TransferFunction(s * T/(2*(a + b*T/2)) + T/(2*(a + b*T/2)), s + (-a + b*T/2)/(a + b*T/2), s)
+
+    assert S.Zero == (tf_test_bilinear.simplify()-tf_test_manual.simplify()).simplify().num
+
+def test_TransferFunction_forward_diff():
+    # simple transfer function, e.g. ohms law
+    tf = TransferFunction(1, a*s+b, s)
+    numZ, denZ = forward_diff(tf, T)
+    # discretized transfer function with coefs from tf.forward_diff()
+    tf_test_forward = TransferFunction(numZ[0], s*denZ[0]+denZ[1], s)
+    # corresponding tf with manually calculated coefs
+    tf_test_manual = TransferFunction(T/a, s + (-a + b*T)/a, s)
+
+    assert S.Zero == (tf_test_forward.simplify()-tf_test_manual.simplify()).simplify().num
+
+def test_TransferFunction_backward_diff():
+    # simple transfer function, e.g. ohms law
+    tf = TransferFunction(1, a*s+b, s)
+    numZ, denZ = backward_diff(tf, T)
+    # discretized transfer function with coefs from tf.backward_diff()
+    tf_test_backward = TransferFunction(s*numZ[0]+numZ[1], s*denZ[0]+denZ[1], s)
+    # corresponding tf with manually calculated coefs
+    tf_test_manual = TransferFunction(s * T/(a + b*T), s - a/(a + b*T), s)
+
+    assert S.Zero == (tf_test_backward.simplify()-tf_test_manual.simplify()).simplify().num
+
+def test_TransferFunction_phase_margin():
+    # Test for phase margin
+    tf1 = TransferFunction(10, p**3 + 1, p)
+    tf2 = TransferFunction(s**2, 10, s)
+    tf3 = TransferFunction(1, a*s+b, s)
+    tf4 = TransferFunction((s + 1)*exp(s/tau), s**2 + 2, s)
+    tf_m = TransferFunctionMatrix([[tf2],[tf3]])
+
+    assert phase_margin(tf1) == -180 + 180*atan(3*sqrt(11))/pi
+    assert phase_margin(tf2) == 0
+
+    raises(NotImplementedError, lambda: phase_margin(tf4))
+    raises(ValueError, lambda: phase_margin(tf3))
+    raises(ValueError, lambda: phase_margin(MIMOSeries(tf_m)))
+
+def test_TransferFunction_gain_margin():
+    # Test for gain margin
+    tf1 = TransferFunction(s**2, 5*(s+1)*(s-5)*(s-10), s)
+    tf2 = TransferFunction(s**2 + 2*s + 1, 1, s)
+    tf3 = TransferFunction(1, a*s+b, s)
+    tf4 = TransferFunction((s + 1)*exp(s/tau), s**2 + 2, s)
+    tf_m = TransferFunctionMatrix([[tf2],[tf3]])
+
+    assert gain_margin(tf1) == -20*log(S(7)/540)/log(10)
+    assert gain_margin(tf2) == oo
+
+    raises(NotImplementedError, lambda: gain_margin(tf4))
+    raises(ValueError, lambda: gain_margin(tf3))
+    raises(ValueError, lambda: gain_margin(MIMOSeries(tf_m)))
+
+
+def test_StateSpace_construction():
+    # using different numbers for a SISO system.
+    A1 = Matrix([[0, 1], [1, 0]])
+    B1 = Matrix([1, 0])
+    C1 = Matrix([[0, 1]])
+    D1 = Matrix([0])
+    ss1 = StateSpace(A1, B1, C1, D1)
+
+    assert ss1.state_matrix == Matrix([[0, 1], [1, 0]])
+    assert ss1.input_matrix == Matrix([1, 0])
+    assert ss1.output_matrix == Matrix([[0, 1]])
+    assert ss1.feedforward_matrix == Matrix([0])
+    assert ss1.args == (Matrix([[0, 1], [1, 0]]), Matrix([[1], [0]]), Matrix([[0, 1]]), Matrix([[0]]))
+
+    # using different symbols for a SISO system.
+    ss2 = StateSpace(Matrix([a0]), Matrix([a1]),
+                    Matrix([a2]), Matrix([a3]))
+
+    assert ss2.state_matrix == Matrix([[a0]])
+    assert ss2.input_matrix == Matrix([[a1]])
+    assert ss2.output_matrix == Matrix([[a2]])
+    assert ss2.feedforward_matrix == Matrix([[a3]])
+    assert ss2.args == (Matrix([[a0]]), Matrix([[a1]]), Matrix([[a2]]), Matrix([[a3]]))
+
+    # using different numbers for a MIMO system.
+    ss3 = StateSpace(Matrix([[-1.5, -2], [1, 0]]),
+                    Matrix([[0.5, 0], [0, 1]]),
+                    Matrix([[0, 1], [0, 2]]),
+                    Matrix([[2, 2], [1, 1]]))
+
+    assert ss3.state_matrix == Matrix([[-1.5, -2], [1,  0]])
+    assert ss3.input_matrix == Matrix([[0.5, 0], [0, 1]])
+    assert ss3.output_matrix == Matrix([[0, 1], [0, 2]])
+    assert ss3.feedforward_matrix == Matrix([[2, 2], [1, 1]])
+    assert ss3.args == (Matrix([[-1.5, -2],
+                                [1,  0]]),
+                        Matrix([[0.5, 0],
+                                [0, 1]]),
+                        Matrix([[0, 1],
+                                [0, 2]]),
+                        Matrix([[2, 2],
+                                [1, 1]]))
+
+    # using different symbols for a MIMO system.
+    A4 = Matrix([[a0, a1], [a2, a3]])
+    B4 = Matrix([[b0, b1], [b2, b3]])
+    C4 = Matrix([[c0, c1], [c2, c3]])
+    D4 = Matrix([[d0, d1], [d2, d3]])
+    ss4 = StateSpace(A4, B4, C4, D4)
+
+    assert ss4.state_matrix == Matrix([[a0, a1], [a2, a3]])
+    assert ss4.input_matrix == Matrix([[b0, b1], [b2, b3]])
+    assert ss4.output_matrix == Matrix([[c0, c1], [c2, c3]])
+    assert ss4.feedforward_matrix == Matrix([[d0, d1], [d2, d3]])
+    assert ss4.args == (Matrix([[a0, a1],
+                                [a2, a3]]),
+                        Matrix([[b0, b1],
+                                [b2, b3]]),
+                        Matrix([[c0, c1],
+                                [c2, c3]]),
+                        Matrix([[d0, d1],
+                                [d2, d3]]))
+
+    # using less matrices. Rest will be filled with a minimum of zeros.
+    ss5 = StateSpace()
+    assert ss5.args == (Matrix([[0]]), Matrix([[0]]), Matrix([[0]]), Matrix([[0]]))
+
+    A6 = Matrix([[0, 1], [1, 0]])
+    B6 = Matrix([1, 1])
+    ss6 = StateSpace(A6, B6)
+
+    assert ss6.state_matrix == Matrix([[0, 1], [1, 0]])
+    assert ss6.input_matrix ==  Matrix([1, 1])
+    assert ss6.output_matrix == Matrix([[0, 0]])
+    assert ss6.feedforward_matrix == Matrix([[0]])
+    assert ss6.args == (Matrix([[0, 1],
+                                [1, 0]]),
+                        Matrix([[1],
+                                [1]]),
+                        Matrix([[0, 0]]),
+                        Matrix([[0]]))
+
+    # Check if the system is SISO or MIMO.
+    # If system is not SISO, then it is definitely MIMO.
+
+    assert ss1.is_SISO == True
+    assert ss2.is_SISO == True
+    assert ss3.is_SISO == False
+    assert ss4.is_SISO == False
+    assert ss5.is_SISO == True
+    assert ss6.is_SISO == True
+
+    # ShapeError if matrices do not fit.
+    raises(ShapeError, lambda: StateSpace(Matrix([s, (s+1)**2]), Matrix([s+1]),
+                                          Matrix([s**2 - 1]), Matrix([2*s])))
+    raises(ShapeError, lambda: StateSpace(Matrix([s]), Matrix([s+1, s**3 + 1]),
+                                          Matrix([s**2 - 1]), Matrix([2*s])))
+    raises(ShapeError, lambda: StateSpace(Matrix([s]), Matrix([s+1]),
+                                          Matrix([[s**2 - 1], [s**2 + 2*s + 1]]), Matrix([2*s])))
+    raises(ShapeError, lambda: StateSpace(Matrix([[-s, -s], [s, 0]]),
+                                                Matrix([[s/2, 0], [0, s]]),
+                                                Matrix([[0, s]]),
+                                                Matrix([[2*s, 2*s], [s, s]])))
+
+    # TypeError if arguments are not sympy matrices.
+    raises(TypeError, lambda: StateSpace(s**2, s+1, 2*s, 1))
+    raises(TypeError, lambda: StateSpace(Matrix([2, 0.5]), Matrix([-1]),
+                                         Matrix([1]), 0))
+def test_StateSpace_add():
+    A1 = Matrix([[4, 1],[2, -3]])
+    B1 = Matrix([[5, 2],[-3, -3]])
+    C1 = Matrix([[2, -4],[0, 1]])
+    D1 = Matrix([[3, 2],[1, -1]])
+    ss1 = StateSpace(A1, B1, C1, D1)
+
+    A2 = Matrix([[-3, 4, 2],[-1, -3, 0],[2, 5, 3]])
+    B2 = Matrix([[1, 4],[-3, -3],[-2, 1]])
+    C2 = Matrix([[4, 2, -3],[1, 4, 3]])
+    D2 = Matrix([[-2, 4],[0, 1]])
+    ss2 = StateSpace(A2, B2, C2, D2)
+    ss3 = StateSpace()
+    ss4 = StateSpace(Matrix([1]), Matrix([2]), Matrix([3]), Matrix([4]))
+
+    expected_add = \
+        StateSpace(
+        Matrix([
+        [4,  1,  0,  0, 0],
+        [2, -3,  0,  0, 0],
+        [0,  0, -3,  4, 2],
+        [0,  0, -1, -3, 0],
+        [0,  0,  2,  5, 3]]),
+        Matrix([
+        [ 5,  2],
+        [-3, -3],
+        [ 1,  4],
+        [-3, -3],
+        [-2,  1]]),
+        Matrix([
+        [2, -4, 4, 2, -3],
+        [0,  1, 1, 4,  3]]),
+        Matrix([
+        [1, 6],
+        [1, 0]]))
+
+    expected_mul = \
+        StateSpace(
+        Matrix([
+        [ -3,   4,  2, 0,  0],
+        [ -1,  -3,  0, 0,  0],
+        [  2,   5,  3, 0,  0],
+        [ 22,  18, -9, 4,  1],
+        [-15, -18,  0, 2, -3]]),
+        Matrix([
+        [  1,   4],
+        [ -3,  -3],
+        [ -2,   1],
+        [-10,  22],
+        [  6, -15]]),
+        Matrix([
+        [14, 14, -3, 2, -4],
+        [ 3, -2, -6, 0,  1]]),
+        Matrix([
+        [-6, 14],
+        [-2,  3]]))
+
+    assert ss1 + ss2 == expected_add
+    assert ss1*ss2 == expected_mul
+    assert ss3 + 1/2 == StateSpace(Matrix([[0]]), Matrix([[0]]), Matrix([[0]]), Matrix([[0.5]]))
+    assert ss4*1.5 == StateSpace(Matrix([[1]]), Matrix([[2]]), Matrix([[4.5]]), Matrix([[6.0]]))
+    assert 1.5*ss4 == StateSpace(Matrix([[1]]), Matrix([[3.0]]), Matrix([[3]]), Matrix([[6.0]]))
+    raises(ShapeError, lambda: ss1 + ss3)
+    raises(ShapeError, lambda: ss2*ss4)
+
+def test_StateSpace_negation():
+    A = Matrix([[a0, a1], [a2, a3]])
+    B = Matrix([[b0, b1], [b2, b3]])
+    C = Matrix([[c0, c1], [c1, c2], [c2, c3]])
+    D = Matrix([[d0, d1], [d1, d2], [d2, d3]])
+    SS = StateSpace(A, B, C, D)
+    SS_neg = -SS
+
+    state_mat = Matrix([[-1, 1], [1, -1]])
+    input_mat = Matrix([1, -1])
+    output_mat = Matrix([[-1, 1]])
+    feedforward_mat = Matrix([1])
+    system = StateSpace(state_mat, input_mat, output_mat, feedforward_mat)
+
+    assert SS_neg == \
+        StateSpace(Matrix([[a0, a1],
+                           [a2, a3]]),
+                   Matrix([[b0, b1],
+                           [b2, b3]]),
+                   Matrix([[-c0, -c1],
+                           [-c1, -c2],
+                           [-c2, -c3]]),
+                   Matrix([[-d0, -d1],
+                           [-d1, -d2],
+                           [-d2, -d3]]))
+    assert -system == \
+        StateSpace(Matrix([[-1,  1],
+                           [ 1, -1]]),
+                   Matrix([[ 1],[-1]]),
+                   Matrix([[1, -1]]),
+                   Matrix([[-1]]))
+    assert -SS_neg == SS
+    assert -(-(-(-system))) == system
+
+def test_SymPy_substitution_functions():
+    # subs
+    ss1 = StateSpace(Matrix([s]), Matrix([(s + 1)**2]), Matrix([s**2 - 1]), Matrix([2*s]))
+    ss2 = StateSpace(Matrix([s + p]), Matrix([(s + 1)*(p - 1)]), Matrix([p**3 - s**3]), Matrix([s - p]))
+
+    assert ss1.subs({s:5}) == StateSpace(Matrix([[5]]), Matrix([[36]]), Matrix([[24]]), Matrix([[10]]))
+    assert ss2.subs({p:1}) == StateSpace(Matrix([[s + 1]]), Matrix([[0]]), Matrix([[1 - s**3]]), Matrix([[s - 1]]))
+
+    # xreplace
+    assert ss1.xreplace({s:p}) == \
+        StateSpace(Matrix([[p]]), Matrix([[(p + 1)**2]]), Matrix([[p**2 - 1]]), Matrix([[2*p]]))
+    assert ss2.xreplace({s:a, p:b}) == \
+        StateSpace(Matrix([[a + b]]), Matrix([[(a + 1)*(b - 1)]]), Matrix([[-a**3 + b**3]]), Matrix([[a - b]]))
+
+    # evalf
+    p1 = a1*s + a0
+    p2 = b2*s**2 + b1*s + b0
+    G = StateSpace(Matrix([p1]), Matrix([p2]))
+    expect = StateSpace(Matrix([[2*s + 1]]), Matrix([[5*s**2 + 4*s + 3]]), Matrix([[0]]), Matrix([[0]]))
+    expect_ = StateSpace(Matrix([[2.0*s + 1.0]]), Matrix([[5.0*s**2 + 4.0*s + 3.0]]), Matrix([[0]]), Matrix([[0]]))
+    assert G.subs({a0: 1, a1: 2, b0: 3, b1: 4, b2: 5}) == expect
+    assert G.subs({a0: 1, a1: 2, b0: 3, b1: 4, b2: 5}).evalf() == expect_
+    assert expect.evalf() == expect_
+
+def test_conversion():
+    # StateSpace to TransferFunction for SISO
+    A1 = Matrix([[-5, -1], [3, -1]])
+    B1 = Matrix([2, 5])
+    C1 = Matrix([[1, 2]])
+    D1 = Matrix([0])
+    H1 = StateSpace(A1, B1, C1, D1)
+    tm1 = H1.rewrite(TransferFunction)
+    tm2 = (-H1).rewrite(TransferFunction)
+
+    tf1 = tm1[0][0]
+    tf2 = tm2[0][0]
+
+    assert tf1 == TransferFunction(12*s + 59, s**2 + 6*s + 8, s)
+    assert tf2.num == -tf1.num
+    assert tf2.den == tf1.den
+
+    # StateSpace to TransferFunction for MIMO
+    A2 = Matrix([[-1.5, -2, 3], [1, 0, 1], [2, 1, 1]])
+    B2 = Matrix([[0.5, 0, 1], [0, 1, 2], [2, 2, 3]])
+    C2 = Matrix([[0, 1, 0], [0, 2, 1], [1, 0, 2]])
+    D2 = Matrix([[2, 2, 0], [1, 1, 1], [3, 2, 1]])
+    H2 = StateSpace(A2, B2, C2, D2)
+    tm3 = H2.rewrite(TransferFunction)
+
+    # outputs for input i obtained at Index i-1. Consider input 1
+    assert tm3[0][0] == TransferFunction(2.0*s**3 + 1.0*s**2 - 10.5*s + 4.5, 1.0*s**3 + 0.5*s**2 - 6.5*s - 2.5, s)
+    assert tm3[0][1] == TransferFunction(2.0*s**3 + 2.0*s**2 - 10.5*s - 3.5, 1.0*s**3 + 0.5*s**2 - 6.5*s - 2.5, s)
+    assert tm3[0][2] == TransferFunction(2.0*s**2 + 5.0*s - 0.5, 1.0*s**3 + 0.5*s**2 - 6.5*s - 2.5, s)
+
+    # TransferFunction to StateSpace
+    SS = TF1.rewrite(StateSpace)
+    assert SS == \
+        StateSpace(Matrix([[     0,          1],
+                           [-wn**2, -2*wn*zeta]]),
+                   Matrix([[0],
+                           [1]]),
+                   Matrix([[1, 0]]),
+                   Matrix([[0]]))
+    assert SS.rewrite(TransferFunction)[0][0] == TF1
+
+    # Transfer function has to be proper
+    raises(ValueError, lambda: TransferFunction(b*s**2 + p**2 - a*p + s, b - p**2, s).rewrite(StateSpace))
+
+
+def test_StateSpace_functions():
+    # https://in.mathworks.com/help/control/ref/statespacemodel.obsv.html
+
+    A_mat = Matrix([[-1.5, -2], [1, 0]])
+    B_mat = Matrix([0.5, 0])
+    C_mat = Matrix([[0, 1]])
+    D_mat = Matrix([1])
+    SS1 = StateSpace(A_mat, B_mat, C_mat, D_mat)
+    SS2 = StateSpace(Matrix([[1, 1], [4, -2]]),Matrix([[0, 1], [0, 2]]),Matrix([[-1, 1], [1, -1]]))
+    SS3 = StateSpace(Matrix([[1, 1], [4, -2]]),Matrix([[1, -1], [1, -1]]))
+
+    # Observability
+    assert SS1.is_observable() == True
+    assert SS2.is_observable() == False
+    assert SS1.observability_matrix() == Matrix([[0, 1], [1, 0]])
+    assert SS2.observability_matrix() == Matrix([[-1,  1], [ 1, -1], [ 3, -3], [-3,  3]])
+    assert SS1.observable_subspace() == [Matrix([[0], [1]]), Matrix([[1], [0]])]
+    assert SS2.observable_subspace() == [Matrix([[-1], [ 1], [ 3], [-3]])]
+
+    # Controllability
+    assert SS1.is_controllable() == True
+    assert SS3.is_controllable() == False
+    assert SS1.controllability_matrix() ==  Matrix([[0.5, -0.75], [  0,   0.5]])
+    assert SS3.controllability_matrix() == Matrix([[1, -1, 2, -2], [1, -1, 2, -2]])
+    assert SS1.controllable_subspace() == [Matrix([[0.5], [  0]]), Matrix([[-0.75], [  0.5]])]
+    assert SS3.controllable_subspace() == [Matrix([[1], [1]])]
+
+    # Append
+    A1 = Matrix([[0, 1], [1, 0]])
+    B1 = Matrix([[0], [1]])
+    C1 = Matrix([[0, 1]])
+    D1 = Matrix([[0]])
+    ss1 = StateSpace(A1, B1, C1, D1)
+    ss2 = StateSpace(Matrix([[1, 0], [0, 1]]), Matrix([[1], [0]]), Matrix([[1, 0]]), Matrix([[1]]))
+    ss3 = ss1.append(ss2)
+
+    assert ss3.num_states == ss1.num_states + ss2.num_states
+    assert ss3.num_inputs == ss1.num_inputs + ss2.num_inputs
+    assert ss3.num_outputs == ss1.num_outputs + ss2.num_outputs
+    assert ss3.state_matrix == Matrix([[0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]])
+    assert ss3.input_matrix == Matrix([[0, 0], [1, 0], [0, 1], [0, 0]])
+    assert ss3.output_matrix == Matrix([[0, 1, 0, 0], [0, 0, 1, 0]])
+    assert ss3.feedforward_matrix == Matrix([[0, 0], [0, 1]])
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--- /dev/null
+++ b/parrot/lib/python3.10/site-packages/sympy/physics/tests/test_clebsch_gordan.py
@@ -0,0 +1,206 @@
+from sympy.core.numbers import (I, pi, Rational)
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.functions.special.spherical_harmonics import Ynm
+from sympy.matrices.dense import Matrix
+from sympy.physics.wigner import (clebsch_gordan, wigner_9j, wigner_6j, gaunt,
+        real_gaunt, racah, dot_rot_grad_Ynm, wigner_3j, wigner_d_small, wigner_d)
+from sympy.testing.pytest import raises, skip
+
+# for test cases, refer : https://en.wikipedia.org/wiki/Table_of_Clebsch%E2%80%93Gordan_coefficients
+
+def test_clebsch_gordan_docs():
+    assert clebsch_gordan(Rational(3, 2), S.Half, 2, Rational(3, 2), S.Half, 2) == 1
+    assert clebsch_gordan(Rational(3, 2), S.Half, 1, Rational(3, 2), Rational(-1, 2), 1) == sqrt(3)/2
+    assert clebsch_gordan(Rational(3, 2), S.Half, 1, Rational(-1, 2), S.Half, 0) == -sqrt(2)/2
+
+
+def test_clebsch_gordan():
+    # Argument order: (j_1, j_2, j, m_1, m_2, m)
+
+    h = S.One
+    k = S.Half
+    l = Rational(3, 2)
+    i = Rational(-1, 2)
+    n = Rational(7, 2)
+    p = Rational(5, 2)
+    assert clebsch_gordan(k, k, 1, k, k, 1) == 1
+    assert clebsch_gordan(k, k, 1, k, k, 0) == 0
+    assert clebsch_gordan(k, k, 1, i, i, -1) == 1
+    assert clebsch_gordan(k, k, 1, k, i, 0) == sqrt(2)/2
+    assert clebsch_gordan(k, k, 0, k, i, 0) == sqrt(2)/2
+    assert clebsch_gordan(k, k, 1, i, k, 0) == sqrt(2)/2
+    assert clebsch_gordan(k, k, 0, i, k, 0) == -sqrt(2)/2
+    assert clebsch_gordan(h, k, l, 1, k, l) == 1
+    assert clebsch_gordan(h, k, l, 1, i, k) == 1/sqrt(3)
+    assert clebsch_gordan(h, k, k, 1, i, k) == sqrt(2)/sqrt(3)
+    assert clebsch_gordan(h, k, k, 0, k, k) == -1/sqrt(3)
+    assert clebsch_gordan(h, k, l, 0, k, k) == sqrt(2)/sqrt(3)
+    assert clebsch_gordan(h, h, S(2), 1, 1, S(2)) == 1
+    assert clebsch_gordan(h, h, S(2), 1, 0, 1) == 1/sqrt(2)
+    assert clebsch_gordan(h, h, S(2), 0, 1, 1) == 1/sqrt(2)
+    assert clebsch_gordan(h, h, 1, 1, 0, 1) == 1/sqrt(2)
+    assert clebsch_gordan(h, h, 1, 0, 1, 1) == -1/sqrt(2)
+    assert clebsch_gordan(l, l, S(3), l, l, S(3)) == 1
+    assert clebsch_gordan(l, l, S(2), l, k, S(2)) == 1/sqrt(2)
+    assert clebsch_gordan(l, l, S(3), l, k, S(2)) == 1/sqrt(2)
+    assert clebsch_gordan(S(2), S(2), S(4), S(2), S(2), S(4)) == 1
+    assert clebsch_gordan(S(2), S(2), S(3), S(2), 1, S(3)) == 1/sqrt(2)
+    assert clebsch_gordan(S(2), S(2), S(3), 1, 1, S(2)) == 0
+    assert clebsch_gordan(p, h, n, p, 1, n) == 1
+    assert clebsch_gordan(p, h, p, p, 0, p) == sqrt(5)/sqrt(7)
+    assert clebsch_gordan(p, h, l, k, 1, l) == 1/sqrt(15)
+
+
+def test_clebsch_gordan_numpy():
+    try:
+        import numpy as np
+    except ImportError:
+        skip("numpy not installed")
+    assert clebsch_gordan(*np.zeros(6).astype(np.int64)) == 1
+
+
+def test_wigner():
+    def tn(a, b):
+        return (a - b).n(64) < S('1e-64')
+    assert tn(wigner_9j(1, 1, 1, 1, 1, 1, 1, 1, 0, prec=64), Rational(1, 18))
+    assert wigner_9j(3, 3, 2, 3, 3, 2, 3, 3, 2) == 3221*sqrt(
+        70)/(246960*sqrt(105)) - 365/(3528*sqrt(70)*sqrt(105))
+    assert wigner_6j(5, 5, 5, 5, 5, 5) == Rational(1, 52)
+    assert tn(wigner_6j(8, 8, 8, 8, 8, 8, prec=64), Rational(-12219, 965770))
+    # regression test for #8747
+    half = S.Half
+    assert wigner_9j(0, 0, 0, 0, half, half, 0, half, half) == half
+    assert (wigner_9j(3, 5, 4,
+                      7 * half, 5 * half, 4,
+                      9 * half, 9 * half, 0)
+            == -sqrt(Rational(361, 205821000)))
+    assert (wigner_9j(1, 4, 3,
+                      5 * half, 4, 5 * half,
+                      5 * half, 2, 7 * half)
+            == -sqrt(Rational(3971, 373403520)))
+    assert (wigner_9j(4, 9 * half, 5 * half,
+                      2, 4, 4,
+                      5, 7 * half, 7 * half)
+            == -sqrt(Rational(3481, 5042614500)))
+
+
+def test_gaunt():
+    def tn(a, b):
+        return (a - b).n(64) < S('1e-64')
+    assert gaunt(1, 0, 1, 1, 0, -1) == -1/(2*sqrt(pi))
+    assert isinstance(gaunt(1, 1, 0, -1, 1, 0).args[0], Rational)
+    assert isinstance(gaunt(0, 1, 1, 0, -1, 1).args[0], Rational)
+
+    assert tn(gaunt(
+        10, 10, 12, 9, 3, -12, prec=64), (Rational(-98, 62031)) * sqrt(6279)/sqrt(pi))
+    def gaunt_ref(l1, l2, l3, m1, m2, m3):
+        return (
+            sqrt((2 * l1 + 1) * (2 * l2 + 1) * (2 * l3 + 1) / (4 * pi)) *
+            wigner_3j(l1, l2, l3, 0, 0, 0) *
+            wigner_3j(l1, l2, l3, m1, m2, m3)
+        )
+    threshold = 1e-10
+    l_max = 3
+    l3_max = 24
+    for l1 in range(l_max + 1):
+        for l2 in range(l_max + 1):
+            for l3 in range(l3_max + 1):
+                for m1 in range(-l1, l1 + 1):
+                    for m2 in range(-l2, l2 + 1):
+                        for m3 in range(-l3, l3 + 1):
+                            args = l1, l2, l3, m1, m2, m3
+                            g  = gaunt(*args)
+                            g0 = gaunt_ref(*args)
+                            assert abs(g - g0) < threshold
+                            if m1 + m2 + m3 != 0:
+                                assert abs(g) < threshold
+                            if (l1 + l2 + l3) % 2:
+                                assert abs(g) < threshold
+    assert gaunt(1, 1, 0, 0, 2, -2) is S.Zero
+
+
+def test_realgaunt():
+    # All non-zero values corresponding to l values from 0 to 2
+    for l in range(3):
+        for m in range(-l, l+1):
+            assert real_gaunt(0, l, l, 0, m, m) == 1/(2*sqrt(pi))
+    assert real_gaunt(1, 1, 2, 0, 0, 0) == sqrt(5)/(5*sqrt(pi))
+    assert real_gaunt(1, 1, 2, 1, 1, 0) == -sqrt(5)/(10*sqrt(pi))
+    assert real_gaunt(2, 2, 2, 0, 0, 0) == sqrt(5)/(7*sqrt(pi))
+    assert real_gaunt(2, 2, 2, 0, 2, 2) == -sqrt(5)/(7*sqrt(pi))
+    assert real_gaunt(2, 2, 2, -2, -2, 0) == -sqrt(5)/(7*sqrt(pi))
+    assert real_gaunt(1, 1, 2, -1, 0, -1) == sqrt(15)/(10*sqrt(pi))
+    assert real_gaunt(1, 1, 2, 0, 1, 1) == sqrt(15)/(10*sqrt(pi))
+    assert real_gaunt(1, 1, 2, 1, 1, 2) == sqrt(15)/(10*sqrt(pi))
+    assert real_gaunt(1, 1, 2, -1, 1, -2) == -sqrt(15)/(10*sqrt(pi))
+    assert real_gaunt(1, 1, 2, -1, -1, 2) == -sqrt(15)/(10*sqrt(pi))
+    assert real_gaunt(2, 2, 2, 0, 1, 1) == sqrt(5)/(14*sqrt(pi))
+    assert real_gaunt(2, 2, 2, 1, 1, 2) == sqrt(15)/(14*sqrt(pi))
+    assert real_gaunt(2, 2, 2, -1, -1, 2) == -sqrt(15)/(14*sqrt(pi))
+
+    assert real_gaunt(-2, -2, -2, -2, -2, 0) is S.Zero  # m test
+    assert real_gaunt(-2, 1, 0, 1, 1, 1) is S.Zero  # l test
+    assert real_gaunt(-2, -1, -2, -1, -1, 0) is S.Zero  # m and l test
+    assert real_gaunt(-2, -2, -2, -2, -2, -2) is S.Zero  # m and k test
+    assert real_gaunt(-2, -1, -2, -1, -1, -1) is S.Zero  # m, l and k test
+
+    x = symbols('x', integer=True)
+    v = [0]*6
+    for i in range(len(v)):
+        v[i] = x  # non literal ints fail
+        raises(ValueError, lambda: real_gaunt(*v))
+        v[i] = 0
+
+
+def test_racah():
+    assert racah(3,3,3,3,3,3) == Rational(-1,14)
+    assert racah(2,2,2,2,2,2) == Rational(-3,70)
+    assert racah(7,8,7,1,7,7, prec=4).is_Float
+    assert racah(5.5,7.5,9.5,6.5,8,9) == -719*sqrt(598)/1158924
+    assert abs(racah(5.5,7.5,9.5,6.5,8,9, prec=4) - (-0.01517)) < S('1e-4')
+
+
+def test_dot_rota_grad_SH():
+    theta, phi = symbols("theta phi")
+    assert dot_rot_grad_Ynm(1, 1, 1, 1, 1, 0) !=  \
+        sqrt(30)*Ynm(2, 2, 1, 0)/(10*sqrt(pi))
+    assert dot_rot_grad_Ynm(1, 1, 1, 1, 1, 0).doit() ==  \
+        sqrt(30)*Ynm(2, 2, 1, 0)/(10*sqrt(pi))
+    assert dot_rot_grad_Ynm(1, 5, 1, 1, 1, 2) !=  \
+        0
+    assert dot_rot_grad_Ynm(1, 5, 1, 1, 1, 2).doit() ==  \
+        0
+    assert dot_rot_grad_Ynm(3, 3, 3, 3, theta, phi).doit() ==  \
+        15*sqrt(3003)*Ynm(6, 6, theta, phi)/(143*sqrt(pi))
+    assert dot_rot_grad_Ynm(3, 3, 1, 1, theta, phi).doit() ==  \
+        sqrt(3)*Ynm(4, 4, theta, phi)/sqrt(pi)
+    assert dot_rot_grad_Ynm(3, 2, 2, 0, theta, phi).doit() ==  \
+        3*sqrt(55)*Ynm(5, 2, theta, phi)/(11*sqrt(pi))
+    assert dot_rot_grad_Ynm(3, 2, 3, 2, theta, phi).doit().expand() ==  \
+        -sqrt(70)*Ynm(4, 4, theta, phi)/(11*sqrt(pi)) + \
+        45*sqrt(182)*Ynm(6, 4, theta, phi)/(143*sqrt(pi))
+
+
+def test_wigner_d():
+    half = S(1)/2
+    assert wigner_d_small(half, 0) == Matrix([[1, 0], [0, 1]])
+    assert wigner_d_small(half, pi/2) == Matrix([[1, 1], [-1, 1]])/sqrt(2)
+    assert wigner_d_small(half, pi) == Matrix([[0, 1], [-1, 0]])
+
+    alpha, beta, gamma = symbols("alpha, beta, gamma", real=True)
+    D = wigner_d(half, alpha, beta, gamma)
+    assert D[0, 0] == exp(I*alpha/2)*exp(I*gamma/2)*cos(beta/2)
+    assert D[0, 1] == exp(I*alpha/2)*exp(-I*gamma/2)*sin(beta/2)
+    assert D[1, 0] == -exp(-I*alpha/2)*exp(I*gamma/2)*sin(beta/2)
+    assert D[1, 1] == exp(-I*alpha/2)*exp(-I*gamma/2)*cos(beta/2)
+
+    # Test Y_{n mi}(g*x)=\sum_{mj}D^n_{mi mj}*Y_{n mj}(x)
+    theta, phi = symbols("theta phi", real=True)
+    v = Matrix([Ynm(1, mj, theta, phi) for mj in range(1, -2, -1)])
+    w = wigner_d(1, -pi/2, pi/2, -pi/2)@v.subs({theta: pi/4, phi: pi})
+    w_ = v.subs({theta: pi/2, phi: pi/4})
+    assert w.expand(func=True).as_real_imag() == w_.expand(func=True).as_real_imag()
diff --git a/parrot/lib/python3.10/site-packages/sympy/physics/tests/test_hydrogen.py b/parrot/lib/python3.10/site-packages/sympy/physics/tests/test_hydrogen.py
new file mode 100644
index 0000000000000000000000000000000000000000..eb11744dd8e731f24fcd6f6be2a92ada4fffc554
--- /dev/null
+++ b/parrot/lib/python3.10/site-packages/sympy/physics/tests/test_hydrogen.py
@@ -0,0 +1,126 @@
+from sympy.core.numbers import (I, Rational, oo, pi)
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.integrals.integrals import integrate
+from sympy.simplify.simplify import simplify
+from sympy.physics.hydrogen import R_nl, E_nl, E_nl_dirac, Psi_nlm
+from sympy.testing.pytest import raises
+
+n, r, Z = symbols('n r Z')
+
+
+def feq(a, b, max_relative_error=1e-12, max_absolute_error=1e-12):
+    a = float(a)
+    b = float(b)
+    # if the numbers are close enough (absolutely), then they are equal
+    if abs(a - b) < max_absolute_error:
+        return True
+    # if not, they can still be equal if their relative error is small
+    if abs(b) > abs(a):
+        relative_error = abs((a - b)/b)
+    else:
+        relative_error = abs((a - b)/a)
+    return relative_error <= max_relative_error
+
+
+def test_wavefunction():
+    a = 1/Z
+    R = {
+        (1, 0): 2*sqrt(1/a**3) * exp(-r/a),
+        (2, 0): sqrt(1/(2*a**3)) * exp(-r/(2*a)) * (1 - r/(2*a)),
+        (2, 1): S.Half * sqrt(1/(6*a**3)) * exp(-r/(2*a)) * r/a,
+        (3, 0): Rational(2, 3) * sqrt(1/(3*a**3)) * exp(-r/(3*a)) *
+        (1 - 2*r/(3*a) + Rational(2, 27) * (r/a)**2),
+        (3, 1): Rational(4, 27) * sqrt(2/(3*a**3)) * exp(-r/(3*a)) *
+        (1 - r/(6*a)) * r/a,
+        (3, 2): Rational(2, 81) * sqrt(2/(15*a**3)) * exp(-r/(3*a)) * (r/a)**2,
+        (4, 0): Rational(1, 4) * sqrt(1/a**3) * exp(-r/(4*a)) *
+        (1 - 3*r/(4*a) + Rational(1, 8) * (r/a)**2 - Rational(1, 192) * (r/a)**3),
+        (4, 1): Rational(1, 16) * sqrt(5/(3*a**3)) * exp(-r/(4*a)) *
+        (1 - r/(4*a) + Rational(1, 80) * (r/a)**2) * (r/a),
+        (4, 2): Rational(1, 64) * sqrt(1/(5*a**3)) * exp(-r/(4*a)) *
+        (1 - r/(12*a)) * (r/a)**2,
+        (4, 3): Rational(1, 768) * sqrt(1/(35*a**3)) * exp(-r/(4*a)) * (r/a)**3,
+    }
+    for n, l in R:
+        assert simplify(R_nl(n, l, r, Z) - R[(n, l)]) == 0
+
+
+def test_norm():
+    # Maximum "n" which is tested:
+    n_max = 2  # it works, but is slow, for n_max > 2
+    for n in range(n_max + 1):
+        for l in range(n):
+            assert integrate(R_nl(n, l, r)**2 * r**2, (r, 0, oo)) == 1
+
+def test_psi_nlm():
+    r=S('r')
+    phi=S('phi')
+    theta=S('theta')
+    assert (Psi_nlm(1, 0, 0, r, phi, theta) == exp(-r) / sqrt(pi))
+    assert (Psi_nlm(2, 1, -1, r, phi, theta)) == S.Half * exp(-r / (2)) * r \
+        * (sin(theta) * exp(-I * phi) / (4 * sqrt(pi)))
+    assert (Psi_nlm(3, 2, 1, r, phi, theta, 2) == -sqrt(2) * sin(theta) \
+         * exp(I * phi) * cos(theta) / (4 * sqrt(pi)) * S(2) / 81 \
+        * sqrt(2 * 2 ** 3) * exp(-2 * r / (3)) * (r * 2) ** 2)
+
+def test_hydrogen_energies():
+    assert E_nl(n, Z) == -Z**2/(2*n**2)
+    assert E_nl(n) == -1/(2*n**2)
+
+    assert E_nl(1, 47) == -S(47)**2/(2*1**2)
+    assert E_nl(2, 47) == -S(47)**2/(2*2**2)
+
+    assert E_nl(1) == -S.One/(2*1**2)
+    assert E_nl(2) == -S.One/(2*2**2)
+    assert E_nl(3) == -S.One/(2*3**2)
+    assert E_nl(4) == -S.One/(2*4**2)
+    assert E_nl(100) == -S.One/(2*100**2)
+
+    raises(ValueError, lambda: E_nl(0))
+
+
+def test_hydrogen_energies_relat():
+    # First test exact formulas for small "c" so that we get nice expressions:
+    assert E_nl_dirac(2, 0, Z=1, c=1) == 1/sqrt(2) - 1
+    assert simplify(E_nl_dirac(2, 0, Z=1, c=2) - ( (8*sqrt(3) + 16)
+                / sqrt(16*sqrt(3) + 32) - 4)) == 0
+    assert simplify(E_nl_dirac(2, 0, Z=1, c=3) - ( (54*sqrt(2) + 81)
+                / sqrt(108*sqrt(2) + 162) - 9)) == 0
+
+    # Now test for almost the correct speed of light, without floating point
+    # numbers:
+    assert simplify(E_nl_dirac(2, 0, Z=1, c=137) - ( (352275361 + 10285412 *
+        sqrt(1173)) / sqrt(704550722 + 20570824 * sqrt(1173)) - 18769)) == 0
+    assert simplify(E_nl_dirac(2, 0, Z=82, c=137) - ( (352275361 + 2571353 *
+        sqrt(12045)) / sqrt(704550722 + 5142706*sqrt(12045)) - 18769)) == 0
+
+    # Test using exact speed of light, and compare against the nonrelativistic
+    # energies:
+    for n in range(1, 5):
+        for l in range(n):
+            assert feq(E_nl_dirac(n, l), E_nl(n), 1e-5, 1e-5)
+            if l > 0:
+                assert feq(E_nl_dirac(n, l, False), E_nl(n), 1e-5, 1e-5)
+
+    Z = 2
+    for n in range(1, 5):
+        for l in range(n):
+            assert feq(E_nl_dirac(n, l, Z=Z), E_nl(n, Z), 1e-4, 1e-4)
+            if l > 0:
+                assert feq(E_nl_dirac(n, l, False, Z), E_nl(n, Z), 1e-4, 1e-4)
+
+    Z = 3
+    for n in range(1, 5):
+        for l in range(n):
+            assert feq(E_nl_dirac(n, l, Z=Z), E_nl(n, Z), 1e-3, 1e-3)
+            if l > 0:
+                assert feq(E_nl_dirac(n, l, False, Z), E_nl(n, Z), 1e-3, 1e-3)
+
+    # Test the exceptions:
+    raises(ValueError, lambda: E_nl_dirac(0, 0))
+    raises(ValueError, lambda: E_nl_dirac(1, -1))
+    raises(ValueError, lambda: E_nl_dirac(1, 0, False))
diff --git a/parrot/lib/python3.10/site-packages/sympy/physics/tests/test_paulialgebra.py b/parrot/lib/python3.10/site-packages/sympy/physics/tests/test_paulialgebra.py
new file mode 100644
index 0000000000000000000000000000000000000000..f773470a1802f2864b79f56d38be1de030ff86dc
--- /dev/null
+++ b/parrot/lib/python3.10/site-packages/sympy/physics/tests/test_paulialgebra.py
@@ -0,0 +1,57 @@
+from sympy.core.numbers import I
+from sympy.core.symbol import symbols
+from sympy.physics.paulialgebra import Pauli
+from sympy.testing.pytest import XFAIL
+from sympy.physics.quantum import TensorProduct
+
+sigma1 = Pauli(1)
+sigma2 = Pauli(2)
+sigma3 = Pauli(3)
+
+tau1 = symbols("tau1", commutative = False)
+
+
+def test_Pauli():
+
+    assert sigma1 == sigma1
+    assert sigma1 != sigma2
+
+    assert sigma1*sigma2 == I*sigma3
+    assert sigma3*sigma1 == I*sigma2
+    assert sigma2*sigma3 == I*sigma1
+
+    assert sigma1*sigma1 == 1
+    assert sigma2*sigma2 == 1
+    assert sigma3*sigma3 == 1
+
+    assert sigma1**0 == 1
+    assert sigma1**1 == sigma1
+    assert sigma1**2 == 1
+    assert sigma1**3 == sigma1
+    assert sigma1**4 == 1
+
+    assert sigma3**2 == 1
+
+    assert sigma1*2*sigma1 == 2
+
+
+def test_evaluate_pauli_product():
+    from sympy.physics.paulialgebra import evaluate_pauli_product
+
+    assert evaluate_pauli_product(I*sigma2*sigma3) == -sigma1
+
+    # Check issue 6471
+    assert evaluate_pauli_product(-I*4*sigma1*sigma2) == 4*sigma3
+
+    assert evaluate_pauli_product(
+        1 + I*sigma1*sigma2*sigma1*sigma2 + \
+        I*sigma1*sigma2*tau1*sigma1*sigma3 + \
+        ((tau1**2).subs(tau1, I*sigma1)) + \
+        sigma3*((tau1**2).subs(tau1, I*sigma1)) + \
+        TensorProduct(I*sigma1*sigma2*sigma1*sigma2, 1)
+    ) == 1 -I + I*sigma3*tau1*sigma2 - 1 - sigma3 - I*TensorProduct(1,1)
+
+
+@XFAIL
+def test_Pauli_should_work():
+    assert sigma1*sigma3*sigma1 == -sigma3
diff --git a/parrot/lib/python3.10/site-packages/sympy/physics/tests/test_pring.py b/parrot/lib/python3.10/site-packages/sympy/physics/tests/test_pring.py
new file mode 100644
index 0000000000000000000000000000000000000000..ed7398eac4a8bb1cd4af810825caf3fcefb5f18f
--- /dev/null
+++ b/parrot/lib/python3.10/site-packages/sympy/physics/tests/test_pring.py
@@ -0,0 +1,41 @@
+from sympy.physics.pring import wavefunction, energy
+from sympy.core.numbers import (I, pi)
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.integrals.integrals import integrate
+from sympy.simplify.simplify import simplify
+from sympy.abc import m, x, r
+from sympy.physics.quantum.constants import hbar
+
+
+def test_wavefunction():
+    Psi = {
+        0: (1/sqrt(2 * pi)),
+        1: (1/sqrt(2 * pi)) * exp(I * x),
+        2: (1/sqrt(2 * pi)) * exp(2 * I * x),
+        3: (1/sqrt(2 * pi)) * exp(3 * I * x)
+    }
+    for n in Psi:
+        assert simplify(wavefunction(n, x) - Psi[n]) == 0
+
+
+def test_norm(n=1):
+    # Maximum "n" which is tested:
+    for i in range(n + 1):
+        assert integrate(
+            wavefunction(i, x) * wavefunction(-i, x), (x, 0, 2 * pi)) == 1
+
+
+def test_orthogonality(n=1):
+    # Maximum "n" which is tested:
+    for i in range(n + 1):
+        for j in range(i+1, n+1):
+            assert integrate(
+                wavefunction(i, x) * wavefunction(j, x), (x, 0, 2 * pi)) == 0
+
+
+def test_energy(n=1):
+    # Maximum "n" which is tested:
+    for i in range(n+1):
+        assert simplify(
+            energy(i, m, r) - ((i**2 * hbar**2) / (2 * m * r**2))) == 0
diff --git a/parrot/lib/python3.10/site-packages/sympy/physics/tests/test_qho_1d.py b/parrot/lib/python3.10/site-packages/sympy/physics/tests/test_qho_1d.py
new file mode 100644
index 0000000000000000000000000000000000000000..34e52c9e3a721496fc61f7d2b31414db15caa7a8
--- /dev/null
+++ b/parrot/lib/python3.10/site-packages/sympy/physics/tests/test_qho_1d.py
@@ -0,0 +1,50 @@
+from sympy.core.numbers import (Rational, oo, pi)
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.integrals.integrals import integrate
+from sympy.simplify.simplify import simplify
+from sympy.abc import omega, m, x
+from sympy.physics.qho_1d import psi_n, E_n, coherent_state
+from sympy.physics.quantum.constants import hbar
+
+nu = m * omega / hbar
+
+
+def test_wavefunction():
+    Psi = {
+        0: (nu/pi)**Rational(1, 4) * exp(-nu * x**2 /2),
+        1: (nu/pi)**Rational(1, 4) * sqrt(2*nu) * x * exp(-nu * x**2 /2),
+        2: (nu/pi)**Rational(1, 4) * (2 * nu * x**2 - 1)/sqrt(2) * exp(-nu * x**2 /2),
+        3: (nu/pi)**Rational(1, 4) * sqrt(nu/3) * (2 * nu * x**3 - 3 * x) * exp(-nu * x**2 /2)
+    }
+    for n in Psi:
+        assert simplify(psi_n(n, x, m, omega) - Psi[n]) == 0
+
+
+def test_norm(n=1):
+    # Maximum "n" which is tested:
+    for i in range(n + 1):
+        assert integrate(psi_n(i, x, 1, 1)**2, (x, -oo, oo)) == 1
+
+
+def test_orthogonality(n=1):
+    # Maximum "n" which is tested:
+    for i in range(n + 1):
+        for j in range(i + 1, n + 1):
+            assert integrate(
+                psi_n(i, x, 1, 1)*psi_n(j, x, 1, 1), (x, -oo, oo)) == 0
+
+
+def test_energies(n=1):
+    # Maximum "n" which is tested:
+    for i in range(n + 1):
+        assert E_n(i, omega) == hbar * omega * (i + S.Half)
+
+def test_coherent_state(n=10):
+    # Maximum "n" which is tested:
+    # test whether coherent state is the eigenstate of annihilation operator
+    alpha = Symbol("alpha")
+    for i in range(n + 1):
+        assert simplify(sqrt(n + 1) * coherent_state(n + 1, alpha)) == simplify(alpha * coherent_state(n, alpha))
diff --git a/parrot/lib/python3.10/site-packages/sympy/physics/tests/test_sho.py b/parrot/lib/python3.10/site-packages/sympy/physics/tests/test_sho.py
new file mode 100644
index 0000000000000000000000000000000000000000..7248838b4bb9ad280fd4211bbe208063b65adcf5
--- /dev/null
+++ b/parrot/lib/python3.10/site-packages/sympy/physics/tests/test_sho.py
@@ -0,0 +1,21 @@
+from sympy.core import symbols, Rational, Function, diff
+from sympy.physics.sho import R_nl, E_nl
+from sympy.simplify.simplify import simplify
+
+
+def test_sho_R_nl():
+    omega, r = symbols('omega r')
+    l = symbols('l', integer=True)
+    u = Function('u')
+
+    # check that it obeys the Schrodinger equation
+    for n in range(5):
+        schreq = ( -diff(u(r), r, 2)/2 + ((l*(l + 1))/(2*r**2)
+                    + omega**2*r**2/2 - E_nl(n, l, omega))*u(r) )
+        result = schreq.subs(u(r), r*R_nl(n, l, omega/2, r))
+        assert simplify(result.doit()) == 0
+
+
+def test_energy():
+    n, l, hw = symbols('n l hw')
+    assert simplify(E_nl(n, l, hw) - (2*n + l + Rational(3, 2))*hw) == 0
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diff --git a/parrot/lib/python3.10/site-packages/sympy/physics/vector/tests/test_point.py b/parrot/lib/python3.10/site-packages/sympy/physics/vector/tests/test_point.py
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@@ -0,0 +1,382 @@
+from sympy.physics.vector import dynamicsymbols, Point, ReferenceFrame
+from sympy.testing.pytest import raises, ignore_warnings
+import warnings
+
+def test_point_v1pt_theorys():
+    q, q2 = dynamicsymbols('q q2')
+    qd, q2d = dynamicsymbols('q q2', 1)
+    qdd, q2dd = dynamicsymbols('q q2', 2)
+    N = ReferenceFrame('N')
+    B = ReferenceFrame('B')
+    B.set_ang_vel(N, qd * B.z)
+    O = Point('O')
+    P = O.locatenew('P', B.x)
+    P.set_vel(B, 0)
+    O.set_vel(N, 0)
+    assert P.v1pt_theory(O, N, B) == qd * B.y
+    O.set_vel(N, N.x)
+    assert P.v1pt_theory(O, N, B) == N.x + qd * B.y
+    P.set_vel(B, B.z)
+    assert P.v1pt_theory(O, N, B) == B.z + N.x + qd * B.y
+
+
+def test_point_a1pt_theorys():
+    q, q2 = dynamicsymbols('q q2')
+    qd, q2d = dynamicsymbols('q q2', 1)
+    qdd, q2dd = dynamicsymbols('q q2', 2)
+    N = ReferenceFrame('N')
+    B = ReferenceFrame('B')
+    B.set_ang_vel(N, qd * B.z)
+    O = Point('O')
+    P = O.locatenew('P', B.x)
+    P.set_vel(B, 0)
+    O.set_vel(N, 0)
+    assert P.a1pt_theory(O, N, B) == -(qd**2) * B.x + qdd * B.y
+    P.set_vel(B, q2d * B.z)
+    assert P.a1pt_theory(O, N, B) == -(qd**2) * B.x + qdd * B.y + q2dd * B.z
+    O.set_vel(N, q2d * B.x)
+    assert P.a1pt_theory(O, N, B) == ((q2dd - qd**2) * B.x + (q2d * qd + qdd) * B.y +
+                               q2dd * B.z)
+
+
+def test_point_v2pt_theorys():
+    q = dynamicsymbols('q')
+    qd = dynamicsymbols('q', 1)
+    N = ReferenceFrame('N')
+    B = N.orientnew('B', 'Axis', [q, N.z])
+    O = Point('O')
+    P = O.locatenew('P', 0)
+    O.set_vel(N, 0)
+    assert P.v2pt_theory(O, N, B) == 0
+    P = O.locatenew('P', B.x)
+    assert P.v2pt_theory(O, N, B) == (qd * B.z ^ B.x)
+    O.set_vel(N, N.x)
+    assert P.v2pt_theory(O, N, B) == N.x + qd * B.y
+
+
+def test_point_a2pt_theorys():
+    q = dynamicsymbols('q')
+    qd = dynamicsymbols('q', 1)
+    qdd = dynamicsymbols('q', 2)
+    N = ReferenceFrame('N')
+    B = N.orientnew('B', 'Axis', [q, N.z])
+    O = Point('O')
+    P = O.locatenew('P', 0)
+    O.set_vel(N, 0)
+    assert P.a2pt_theory(O, N, B) == 0
+    P.set_pos(O, B.x)
+    assert P.a2pt_theory(O, N, B) == (-qd**2) * B.x + (qdd) * B.y
+
+
+def test_point_funcs():
+    q, q2 = dynamicsymbols('q q2')
+    qd, q2d = dynamicsymbols('q q2', 1)
+    qdd, q2dd = dynamicsymbols('q q2', 2)
+    N = ReferenceFrame('N')
+    B = ReferenceFrame('B')
+    B.set_ang_vel(N, 5 * B.y)
+    O = Point('O')
+    P = O.locatenew('P', q * B.x + q2 * B.y)
+    assert P.pos_from(O) == q * B.x + q2 * B.y
+    P.set_vel(B, qd * B.x + q2d * B.y)
+    assert P.vel(B) == qd * B.x + q2d * B.y
+    O.set_vel(N, 0)
+    assert O.vel(N) == 0
+    assert P.a1pt_theory(O, N, B) == ((-25 * q + qdd) * B.x + (q2dd) * B.y +
+                               (-10 * qd) * B.z)
+
+    B = N.orientnew('B', 'Axis', [q, N.z])
+    O = Point('O')
+    P = O.locatenew('P', 10 * B.x)
+    O.set_vel(N, 5 * N.x)
+    assert O.vel(N) == 5 * N.x
+    assert P.a2pt_theory(O, N, B) == (-10 * qd**2) * B.x + (10 * qdd) * B.y
+
+    B.set_ang_vel(N, 5 * B.y)
+    O = Point('O')
+    P = O.locatenew('P', q * B.x + q2 * B.y)
+    P.set_vel(B, qd * B.x + q2d * B.y)
+    O.set_vel(N, 0)
+    assert P.v1pt_theory(O, N, B) == qd * B.x + q2d * B.y - 5 * q * B.z
+
+
+def test_point_pos():
+    q = dynamicsymbols('q')
+    N = ReferenceFrame('N')
+    B = N.orientnew('B', 'Axis', [q, N.z])
+    O = Point('O')
+    P = O.locatenew('P', 10 * N.x + 5 * B.x)
+    assert P.pos_from(O) == 10 * N.x + 5 * B.x
+    Q = P.locatenew('Q', 10 * N.y + 5 * B.y)
+    assert Q.pos_from(P) == 10 * N.y + 5 * B.y
+    assert Q.pos_from(O) == 10 * N.x + 10 * N.y + 5 * B.x + 5 * B.y
+    assert O.pos_from(Q) == -10 * N.x - 10 * N.y - 5 * B.x - 5 * B.y
+
+def test_point_partial_velocity():
+
+    N = ReferenceFrame('N')
+    A = ReferenceFrame('A')
+
+    p = Point('p')
+
+    u1, u2 = dynamicsymbols('u1, u2')
+
+    p.set_vel(N, u1 * A.x + u2 * N.y)
+
+    assert p.partial_velocity(N, u1) == A.x
+    assert p.partial_velocity(N, u1, u2) == (A.x, N.y)
+    raises(ValueError, lambda: p.partial_velocity(A, u1))
+
+def test_point_vel(): #Basic functionality
+    q1, q2 = dynamicsymbols('q1 q2')
+    N = ReferenceFrame('N')
+    B = ReferenceFrame('B')
+    Q = Point('Q')
+    O = Point('O')
+    Q.set_pos(O, q1 * N.x)
+    raises(ValueError , lambda: Q.vel(N)) # Velocity of O in N is not defined
+    O.set_vel(N, q2 * N.y)
+    assert O.vel(N) == q2 * N.y
+    raises(ValueError , lambda : O.vel(B)) #Velocity of O is not defined in B
+
+def test_auto_point_vel():
+    t = dynamicsymbols._t
+    q1, q2 = dynamicsymbols('q1 q2')
+    N = ReferenceFrame('N')
+    B = ReferenceFrame('B')
+    O = Point('O')
+    Q = Point('Q')
+    Q.set_pos(O, q1 * N.x)
+    O.set_vel(N, q2 * N.y)
+    assert Q.vel(N) == q1.diff(t) * N.x + q2 * N.y  # Velocity of Q using O
+    P1 = Point('P1')
+    P1.set_pos(O, q1 * B.x)
+    P2 = Point('P2')
+    P2.set_pos(P1, q2 * B.z)
+    raises(ValueError, lambda : P2.vel(B)) # O's velocity is defined in different frame, and no
+    #point in between has its velocity defined
+    raises(ValueError, lambda: P2.vel(N)) # Velocity of O not defined in N
+
+def test_auto_point_vel_multiple_point_path():
+    t = dynamicsymbols._t
+    q1, q2 = dynamicsymbols('q1 q2')
+    B = ReferenceFrame('B')
+    P = Point('P')
+    P.set_vel(B, q1 * B.x)
+    P1 = Point('P1')
+    P1.set_pos(P, q2 * B.y)
+    P1.set_vel(B, q1 * B.z)
+    P2 = Point('P2')
+    P2.set_pos(P1, q1 * B.z)
+    P3 = Point('P3')
+    P3.set_pos(P2, 10 * q1 * B.y)
+    assert P3.vel(B) == 10 * q1.diff(t) * B.y + (q1 + q1.diff(t)) * B.z
+
+def test_auto_vel_dont_overwrite():
+    t = dynamicsymbols._t
+    q1, q2, u1 = dynamicsymbols('q1, q2, u1')
+    N = ReferenceFrame('N')
+    P = Point('P1')
+    P.set_vel(N, u1 * N.x)
+    P1 = Point('P1')
+    P1.set_pos(P, q2 * N.y)
+    assert P1.vel(N) == q2.diff(t) * N.y + u1 * N.x
+    assert P.vel(N) == u1 * N.x
+    P1.set_vel(N, u1 * N.z)
+    assert P1.vel(N) == u1 * N.z
+
+def test_auto_point_vel_if_tree_has_vel_but_inappropriate_pos_vector():
+    q1, q2 = dynamicsymbols('q1 q2')
+    B = ReferenceFrame('B')
+    S = ReferenceFrame('S')
+    P = Point('P')
+    P.set_vel(B, q1 * B.x)
+    P1 = Point('P1')
+    P1.set_pos(P, S.y)
+    raises(ValueError, lambda : P1.vel(B)) # P1.pos_from(P) can't be expressed in B
+    raises(ValueError, lambda : P1.vel(S)) # P.vel(S) not defined
+
+def test_auto_point_vel_shortest_path():
+    t = dynamicsymbols._t
+    q1, q2, u1, u2 = dynamicsymbols('q1 q2 u1 u2')
+    B = ReferenceFrame('B')
+    P = Point('P')
+    P.set_vel(B, u1 * B.x)
+    P1 = Point('P1')
+    P1.set_pos(P, q2 * B.y)
+    P1.set_vel(B, q1 * B.z)
+    P2 = Point('P2')
+    P2.set_pos(P1, q1 * B.z)
+    P3 = Point('P3')
+    P3.set_pos(P2, 10 * q1 * B.y)
+    P4 = Point('P4')
+    P4.set_pos(P3, q1 * B.x)
+    O = Point('O')
+    O.set_vel(B, u2 * B.y)
+    O1 = Point('O1')
+    O1.set_pos(O, q2 * B.z)
+    P4.set_pos(O1, q1 * B.x + q2 * B.z)
+    with warnings.catch_warnings(): #There are two possible paths in this point tree, thus a warning is raised
+        warnings.simplefilter('error')
+        with ignore_warnings(UserWarning):
+            assert P4.vel(B) == q1.diff(t) * B.x + u2 * B.y + 2 * q2.diff(t) * B.z
+
+def test_auto_point_vel_connected_frames():
+    t = dynamicsymbols._t
+    q, q1, q2, u = dynamicsymbols('q q1 q2 u')
+    N = ReferenceFrame('N')
+    B = ReferenceFrame('B')
+    O = Point('O')
+    O.set_vel(N, u * N.x)
+    P = Point('P')
+    P.set_pos(O, q1 * N.x + q2 * B.y)
+    raises(ValueError, lambda: P.vel(N))
+    N.orient(B, 'Axis', (q, B.x))
+    assert P.vel(N) == (u + q1.diff(t)) * N.x + q2.diff(t) * B.y - q2 * q.diff(t) * B.z
+
+def test_auto_point_vel_multiple_paths_warning_arises():
+    q, u = dynamicsymbols('q u')
+    N = ReferenceFrame('N')
+    O = Point('O')
+    P = Point('P')
+    Q = Point('Q')
+    R = Point('R')
+    P.set_vel(N, u * N.x)
+    Q.set_vel(N, u *N.y)
+    R.set_vel(N, u * N.z)
+    O.set_pos(P, q * N.z)
+    O.set_pos(Q, q * N.y)
+    O.set_pos(R, q * N.x)
+    with warnings.catch_warnings(): #There are two possible paths in this point tree, thus a warning is raised
+        warnings.simplefilter("error")
+        raises(UserWarning ,lambda: O.vel(N))
+
+def test_auto_vel_cyclic_warning_arises():
+    P = Point('P')
+    P1 = Point('P1')
+    P2 = Point('P2')
+    P3 = Point('P3')
+    N = ReferenceFrame('N')
+    P.set_vel(N, N.x)
+    P1.set_pos(P, N.x)
+    P2.set_pos(P1, N.y)
+    P3.set_pos(P2, N.z)
+    P1.set_pos(P3, N.x + N.y)
+    with warnings.catch_warnings(): #The path is cyclic at P1, thus a warning is raised
+        warnings.simplefilter("error")
+        raises(UserWarning ,lambda: P2.vel(N))
+
+def test_auto_vel_cyclic_warning_msg():
+    P = Point('P')
+    P1 = Point('P1')
+    P2 = Point('P2')
+    P3 = Point('P3')
+    N = ReferenceFrame('N')
+    P.set_vel(N, N.x)
+    P1.set_pos(P, N.x)
+    P2.set_pos(P1, N.y)
+    P3.set_pos(P2, N.z)
+    P1.set_pos(P3, N.x + N.y)
+    with warnings.catch_warnings(record = True) as w: #The path is cyclic at P1, thus a warning is raised
+        warnings.simplefilter("always")
+        P2.vel(N)
+        msg = str(w[-1].message).replace("\n", " ")
+        assert issubclass(w[-1].category, UserWarning)
+        assert 'Kinematic loops are defined among the positions of points. This is likely not desired and may cause errors in your calculations.' in msg
+
+def test_auto_vel_multiple_path_warning_msg():
+    N = ReferenceFrame('N')
+    O = Point('O')
+    P = Point('P')
+    Q = Point('Q')
+    P.set_vel(N, N.x)
+    Q.set_vel(N, N.y)
+    O.set_pos(P, N.z)
+    O.set_pos(Q, N.y)
+    with warnings.catch_warnings(record = True) as w: #There are two possible paths in this point tree, thus a warning is raised
+        warnings.simplefilter("always")
+        O.vel(N)
+        msg = str(w[-1].message).replace("\n", " ")
+        assert issubclass(w[-1].category, UserWarning)
+        assert 'Velocity' in msg
+        assert 'automatically calculated based on point' in msg
+        assert 'Velocities from these points are not necessarily the same. This may cause errors in your calculations.' in msg
+
+def test_auto_vel_derivative():
+    q1, q2 = dynamicsymbols('q1:3')
+    u1, u2 = dynamicsymbols('u1:3', 1)
+    A = ReferenceFrame('A')
+    B = ReferenceFrame('B')
+    C = ReferenceFrame('C')
+    B.orient_axis(A, A.z, q1)
+    B.set_ang_vel(A, u1 * A.z)
+    C.orient_axis(B, B.z, q2)
+    C.set_ang_vel(B, u2 * B.z)
+
+    Am = Point('Am')
+    Am.set_vel(A, 0)
+    Bm = Point('Bm')
+    Bm.set_pos(Am, B.x)
+    Bm.set_vel(B, 0)
+    Bm.set_vel(C, 0)
+    Cm = Point('Cm')
+    Cm.set_pos(Bm, C.x)
+    Cm.set_vel(C, 0)
+    temp = Cm._vel_dict.copy()
+    assert Cm.vel(A) == (u1 * B.y + (u1 + u2) * C.y)
+    Cm._vel_dict = temp
+    Cm.v2pt_theory(Bm, B, C)
+    assert Cm.vel(A) == (u1 * B.y + (u1 + u2) * C.y)
+
+def test_auto_point_acc_zero_vel():
+    N = ReferenceFrame('N')
+    O = Point('O')
+    O.set_vel(N, 0)
+    assert O.acc(N) == 0 * N.x
+
+def test_auto_point_acc_compute_vel():
+    t = dynamicsymbols._t
+    q1 = dynamicsymbols('q1')
+    N = ReferenceFrame('N')
+    A = ReferenceFrame('A')
+    A.orient_axis(N, N.z, q1)
+
+    O = Point('O')
+    O.set_vel(N, 0)
+    P = Point('P')
+    P.set_pos(O, A.x)
+    assert P.acc(N) == -q1.diff(t) ** 2 * A.x + q1.diff(t, 2) * A.y
+
+def test_auto_acc_derivative():
+    # Tests whether the Point.acc method gives the correct acceleration of the
+    # end point of two linkages in series, while getting minimal information.
+    q1, q2 = dynamicsymbols('q1:3')
+    u1, u2 = dynamicsymbols('q1:3', 1)
+    v1, v2 = dynamicsymbols('q1:3', 2)
+    A = ReferenceFrame('A')
+    B = ReferenceFrame('B')
+    C = ReferenceFrame('C')
+    B.orient_axis(A, A.z, q1)
+    C.orient_axis(B, B.z, q2)
+
+    Am = Point('Am')
+    Am.set_vel(A, 0)
+    Bm = Point('Bm')
+    Bm.set_pos(Am, B.x)
+    Bm.set_vel(B, 0)
+    Bm.set_vel(C, 0)
+    Cm = Point('Cm')
+    Cm.set_pos(Bm, C.x)
+    Cm.set_vel(C, 0)
+
+    # Copy dictionaries to later check the calculation using the 2pt_theories
+    Bm_vel_dict, Cm_vel_dict = Bm._vel_dict.copy(), Cm._vel_dict.copy()
+    Bm_acc_dict, Cm_acc_dict = Bm._acc_dict.copy(), Cm._acc_dict.copy()
+    check = -u1 ** 2 * B.x + v1 * B.y - (u1 + u2) ** 2 * C.x + (v1 + v2) * C.y
+    assert Cm.acc(A) == check
+    Bm._vel_dict, Cm._vel_dict = Bm_vel_dict, Cm_vel_dict
+    Bm._acc_dict, Cm._acc_dict = Bm_acc_dict, Cm_acc_dict
+    Bm.v2pt_theory(Am, A, B)
+    Cm.v2pt_theory(Bm, A, C)
+    Bm.a2pt_theory(Am, A, B)
+    assert Cm.a2pt_theory(Bm, A, C) == check