hash stringlengths 64 64 | content stringlengths 0 1.51M |
|---|---|
be73f124654306fd71a55252b3439506856c2e4181a1c358a8f22c63a9a7d657 | """
AST nodes specific to Fortran.
The functions defined in this module allows the user to express functions such as ``dsign``
as a SymPy function for symbolic manipulation.
"""
from sympy.codegen.ast import (
Attribute, CodeBlock, FunctionCall, Node, none, String,
Token, _mk_Tuple, Variable
)
from sympy.core... |
8e5b43d385cb403e02b68e8c2edd2e9c360ca65245e8c2d11786b3d071dbc040 | from .abstract_nodes import List as AbstractList
class List(AbstractList):
pass
|
9d50e61276ffcb62704f537178184d948707741927049245b53e0a202fb8bd5e | """
Types used to represent a full function/module as an Abstract Syntax Tree.
Most types are small, and are merely used as tokens in the AST. A tree diagram
has been included below to illustrate the relationships between the AST types.
AST Type Tree
-------------
::
*Basic*
|
|
CodegenAST
... |
8377bc5c1eb494c939a6942196f05b2bd8699e9a285a22abc1e48c2b024b4daa | """
This file contains some classical ciphers and routines
implementing a linear-feedback shift register (LFSR)
and the Diffie-Hellman key exchange.
.. warning::
This module is intended for educational purposes only. Do not use the
functions in this module for real cryptographic applications. If you wish
to ... |
c0cd4838f60e5af47eba6081441a8c6d27de68fb6ea1338784f3af8b6a0d6c79 | """Module for querying SymPy objects about assumptions."""
from sympy.assumptions.assume import (global_assumptions, Predicate,
AppliedPredicate)
from sympy.assumptions.cnf import CNF, EncodedCNF, Literal
from sympy.core import sympify
from sympy.core.kind import BooleanKind
from sympy.core.relational import E... |
073ddb36f33047fbbb93ae8e06b08df1202a923361d140b7f305505ab6af5325 | from collections import defaultdict
from sympy.assumptions.ask import Q
from sympy.core import (Add, Mul, Pow, Number, NumberSymbol, Symbol)
from sympy.core.numbers import ImaginaryUnit
from sympy.functions.elementary.complexes import Abs
from sympy.logic.boolalg import (Equivalent, And, Or, Implies)
from sympy.matric... |
5ec84fc8fc0d4eed5dce9e5afd3d9e52628381b1ba2daff729fddbb758418ffb | from sympy.core.add import Add
from sympy.core.exprtools import factor_terms
from sympy.core.function import expand_log, _mexpand
from sympy.core.power import Pow
from sympy.core.singleton import S
from sympy.core.sorting import ordered
from sympy.core.symbol import Dummy
from sympy.functions.elementary.exponential imp... |
d8c1ca881fe1098642f7548a41298bf5b7aab781c14f3fda57a4e5596a2503c0 | from sympy.core import (Function, Pow, sympify, Expr)
from sympy.core.relational import Relational
from sympy.core.singleton import S
from sympy.polys import Poly, decompose
from sympy.utilities.misc import func_name
def decompogen(f, symbol):
"""
Computes General functional decomposition of ``f``.
Given ... |
2b4383b046f25d8a8d06a6d25b2481644ddf30cccd20fb2977167c2cf9ed5a53 | """
This module contains functions to:
- solve a single equation for a single variable, in any domain either real or complex.
- solve a single transcendental equation for a single variable in any domain either real or complex.
(currently supports solving in real domain only)
- solve a system of lin... |
ddc178c1910b0218fe690eb9a096b2e8c82c8c29c63340cc5c2d64992768d5cd | """Solvers of systems of polynomial equations. """
from sympy.core import S
from sympy.core.sorting import default_sort_key
from sympy.polys import Poly, groebner, roots
from sympy.polys.polytools import parallel_poly_from_expr
from sympy.polys.polyerrors import (ComputationFailed,
PolificationFailed, CoercionFail... |
5f47da838cada1a33337871c1ff1cbf89825ea28dc4ad0629a0e2ab3c422969f | """Tools for solving inequalities and systems of inequalities. """
from sympy.calculus.util import (continuous_domain, periodicity,
function_range)
from sympy.core import Symbol, Dummy, sympify
from sympy.core.exprtools import factor_terms
from sympy.core.relational import Relational, Eq, Ge, Lt
from sympy.sets.se... |
d03705e97a6f4419de411bd687c8882727c788d578e0384b9b9b7b4aa6edfd20 | """
This module contain solvers for all kinds of equations:
- algebraic or transcendental, use solve()
- recurrence, use rsolve()
- differential, use dsolve()
- nonlinear (numerically), use nsolve()
(you will need a good starting point)
"""
from sympy.core import (S, Add, Symbol, Dummy, Expr... |
da5e1a8793b6f171a15870f04ea767b3a074bc728d9f957eca79e26881ee4c4d | from sympy.core import Atom, Basic
class CartanType_generator(Basic):
"""
Constructor for actually creating things
"""
def __call__(self, *args):
c = args[0]
if isinstance(c, list):
letter, n = c[0], int(c[1])
elif isinstance(c, str):
letter, n = c[0], i... |
53341279dc836e25d173dfd424db7ab1f50afd6a0f14b278d9366f49e899621d | from .cartan_type import CartanType
from sympy.core.basic import Atom
class RootSystem(Atom):
"""Represent the root system of a simple Lie algebra
Every simple Lie algebra has a unique root system. To find the root
system, we first consider the Cartan subalgebra of g, which is the maximal
abelian sub... |
e58140f2a0b81960ccd162cd47fe95829b8d1590dfc8303b7c116305c65a2e00 | # -*- coding: utf-8 -*-
from .cartan_type import CartanType
from mpmath import fac
from sympy.core.backend import Matrix, eye, Rational, igcd
from sympy.core.basic import Atom
class WeylGroup(Atom):
"""
For each semisimple Lie group, we have a Weyl group. It is a subgroup of
the isometry group of the ro... |
8e58b900008a7af44e08720fae147d280d714acb2beb5cd8a6b35aae19997073 | """Calculus-related methods."""
from .euler import euler_equations
from .singularities import (singularities, is_increasing,
is_strictly_increasing, is_decreasing,
is_strictly_decreasing, is_monotonic)
from .finite_diff import finite_diff_weights, apply_finite_di... |
42d4d4612774cb7471dc02f2be8e57883b53de1daba36e48557ae14c21633313 | from sympy.core import Add, Mul, Pow, S
from sympy.core.basic import Basic
from sympy.core.expr import Expr
from sympy.core.numbers import _sympifyit, oo, zoo
from sympy.core.relational import is_le, is_lt, is_ge, is_gt
from sympy.core.sympify import _sympify
from sympy.functions.elementary.miscellaneous import Min, Ma... |
3466431e8831864ee263a0d413c45537eea099123b28eb0ef188d82601fbd668 | """
Singularities
=============
This module implements algorithms for finding singularities for a function
and identifying types of functions.
The differential calculus methods in this module include methods to identify
the following function types in the given ``Interval``:
- Increasing
- Strictly Increasing
- Decre... |
b57da958ab0b4ff2520648cc6ed2bb373c607039086308a26c773ef7cea87306 | from .accumulationbounds import AccumBounds, AccumulationBounds # noqa: F401
from .singularities import singularities
from sympy.core import Pow, S
from sympy.core.function import diff, expand_mul
from sympy.core.kind import NumberKind
from sympy.core.mod import Mod
from sympy.core.relational import Relational
from sym... |
a0b0129860a0fc070f09800451dcfb0719a042bddb834e275d6346a25b5493a9 | """
The objects in this module allow the usage of the MatchPy pattern matching
library on SymPy expressions.
"""
import re
from typing import List, Callable
from sympy.core.sympify import _sympify
from sympy.external import import_module
from sympy.functions import (log, sin, cos, tan, cot, csc, sec, erf, gamma, upper... |
0d4b5060e3642675a353616f01bbf1b913241a65e92cc79a88e707ed1f4eb3da | """Simple tools for timing functions' execution, when IPython is not available. """
import timeit
import math
_scales = [1e0, 1e3, 1e6, 1e9]
_units = ['s', 'ms', '\N{GREEK SMALL LETTER MU}s', 'ns']
def timed(func, setup="pass", limit=None):
"""Adaptively measure execution time of a function. """
timer = t... |
7122a741b5cf5b5a7dcf28048396ed4c4ea85b769cfeaea106c5aed3f4fde5b1 | from collections import defaultdict, OrderedDict
from itertools import (
combinations, combinations_with_replacement, permutations,
product
)
# For backwards compatibility
from itertools import product as cartes # noqa: F401
from operator import gt
# this is the logical location of these functions
# from sym... |
2506ff01987fce94a1e2eae2a4a7f13d5e95938de37b1beef7d730871e5afadb | from sympy.utilities.exceptions import SymPyDeprecationWarning
SymPyDeprecationWarning(
feature="Import sympy.utilities.randtest",
useinstead="Import from sympy.core.random",
issue=18095,
deprecated_since_version="1.6").warn()
from sympy.core.random import * # noqa:F401
|
dc0cd22d0ff1dfaa9112d67d655015107045ae56710c6d4140135a2fe4308d78 | """
Python code printers
This module contains Python code printers for plain Python as well as NumPy & SciPy enabled code.
"""
from collections import defaultdict
from itertools import chain
from sympy.core import S
from .precedence import precedence
from .codeprinter import CodePrinter
_kw_py2and3 = {
'and', 'as... |
47d4807070d9232ca74a6ec00adbe2c9a9f14c8330ed528289eabd2ff521dc22 | """
A Printer for generating readable representation of most SymPy classes.
"""
from typing import Any, Dict as tDict
from sympy.core import S, Rational, Pow, Basic, Mul, Number
from sympy.core.mul import _keep_coeff
from sympy.core.relational import Relational
from sympy.core.sorting import default_sort_key
from sym... |
c638d0b454cd39e593a3242d0916b800f627a13d626e2cc187da8c0fa4b4220f | """
A Printer which converts an expression into its LaTeX equivalent.
"""
from typing import Any, Dict as tDict
import itertools
from sympy.core import Add, Float, Mod, Mul, Number, S, Symbol
from sympy.core.alphabets import greeks
from sympy.core.containers import Tuple
from sympy.core.function import AppliedUndef,... |
94eaee867004d59d38cbaeec70a6cbb0526c568bfe255bd1b6bbb70c0ded9810 | from sympy.core.containers import Tuple
from sympy.core.singleton import S
from sympy.core.symbol import Symbol
from sympy.core.sympify import SympifyError
from types import FunctionType
class TableForm:
r"""
Create a nice table representation of data.
Examples
========
>>> from sympy import Ta... |
02a5fdbb7db36d5431c24a760aecdc642a1ff91171c8a10a30bc1a0af166b011 | from typing import Any, Dict as tDict, Set as tSet, Tuple as tTuple
from functools import wraps
from sympy.core import Add, Expr, Mul, Pow, S, sympify, Float
from sympy.core.basic import Basic
from sympy.core.expr import UnevaluatedExpr
from sympy.core.function import Lambda
from sympy.core.mul import _keep_coeff
fro... |
b0971458961a597e35119564854999aa92c0d884dc614eb941dd542995cc745a | import keyword as kw
import sympy
from .repr import ReprPrinter
from .str import StrPrinter
# A list of classes that should be printed using StrPrinter
STRPRINT = ("Add", "Infinity", "Integer", "Mul", "NegativeInfinity",
"Pow", "Zero")
class PythonPrinter(ReprPrinter, StrPrinter):
"""A printer which ... |
3245a1d7270d5f16788b7e88c5fd865a01b9cd2c444b7cd360e5c1a1dd989050 | """ Integral Transforms """
from functools import reduce, wraps
from itertools import repeat
from sympy.core import S, pi, I
from sympy.core.add import Add
from sympy.core.function import (AppliedUndef, count_ops, Derivative, expand,
expand_complex, expand_mul, Function, Lambda,
... |
904c3d998cff92eff633d372fb584c1bb82435cbf35c21cc55ac4e6af1b6b7e3 | from typing import Tuple as tTuple
from sympy.concrete.expr_with_limits import AddWithLimits
from sympy.core.add import Add
from sympy.core.basic import Basic
from sympy.core.containers import Tuple
from sympy.core.expr import Expr
from sympy.core.exprtools import factor_terms
from sympy.core.function import diff
from... |
ff589a2efd147351a7b043da1d74eabc71ab9d46699b509129276792e3696932 | from typing import Dict as tDict, List
from itertools import permutations
from functools import reduce
from sympy.core.add import Add
from sympy.core.basic import Basic
from sympy.core.mul import Mul
from sympy.core.symbol import Wild, Dummy, Symbol
from sympy.core.basic import sympify
from sympy.core.numbers import ... |
06b63167070381285e6f0ff928a6418c02efdbe5e86bf2779c5032176ae460b0 | """Base class for all the objects in SymPy"""
from collections import defaultdict
from collections.abc import Mapping
from itertools import chain, zip_longest
from typing import Set, Tuple
from .assumptions import ManagedProperties
from .cache import cacheit
from .core import BasicMeta
from .sympify import _sympify, s... |
67cef720dc569c7bbefa767fe872621054b1b995d6bdf56ce3219c6153fd069f | from typing import Callable, Tuple as tTuple
from math import log as _log, sqrt as _sqrt
from itertools import product
from .sympify import _sympify
from .cache import cacheit
from .singleton import S
from .expr import Expr
from .evalf import PrecisionExhausted
from .function import (expand_complex, expand_multinomial... |
c2e2713e0a67c5a17c17f308e21422230e39d6642ace8c02c22c2b9c7fab69eb | """
This module contains the machinery handling assumptions.
Do also consider the guide :ref:`assumptions`.
All symbolic objects have assumption attributes that can be accessed via
``.is_<assumption name>`` attribute.
Assumptions determine certain properties of symbolic objects and can
have 3 possible values: ``True`... |
4d658fdb757491ec2d0a87879ef0f5d05f51e485f08985c9bf89fe36f5027417 | """
There are three types of functions implemented in SymPy:
1) defined functions (in the sense that they can be evaluated) like
exp or sin; they have a name and a body:
f = exp
2) undefined function which have a name but no body. Undefined
functions can be defined using a Function cla... |
00026c6ed5a2819f400f1490fdb44109ba2ef3075bc3981a94599821203d5d74 | from .basic import Basic
from .sorting import ordered
from .sympify import sympify
from sympy.utilities.iterables import iterable
def iterargs(expr):
"""Yield the args of a Basic object in a breadth-first traversal.
Depth-traversal stops if `arg.args` is either empty or is not
an iterable.
Examples
... |
abb47eb45f3bb2dbc80d43507df2d603fa416dd8565ca60c365074b471518c99 | from typing import Tuple as tTuple
from collections import defaultdict
from functools import cmp_to_key, reduce
from operator import attrgetter
from .basic import Basic
from .parameters import global_parameters
from .logic import _fuzzy_group, fuzzy_or, fuzzy_not
from .singleton import S
from .operations import AssocOp... |
65c14aa62d0740e2e91baa5f27fc9dba7f601f95f8130a2b46101df0c005a833 | from typing import Tuple as tTuple
from collections.abc import Iterable
from functools import reduce
from .sympify import sympify, _sympify, SympifyError
from .basic import Basic, Atom
from .singleton import S
from .evalf import EvalfMixin, pure_complex, DEFAULT_MAXPREC
from .decorators import call_highest_priority, s... |
c2db61344f12f1e29a1dd2b2d960442528eaccbd9dfa8809ed73f3f251238042 | """When you need to use random, import it from here so there is only
one generator working for SymPy. Imports from here should behave the
same as if they were being imported from Python's random module. But
only the routines currently used in SymPy are included here. To use
others import `rng` and access the method dir... |
b6a11c532e3eddff061e2165378a0c8d3d8dfcb9bbca1d2b4a2d8d6f8acab4a3 | import numbers
import decimal
import fractions
import math
import re as regex
import sys
from functools import lru_cache
from typing import Set as tSet, Tuple as tTuple
from .containers import Tuple
from .sympify import (SympifyError, converter, sympify, _convert_numpy_types, _sympify,
_is_numpy_... |
25559d7402ba81bf0c7ef146edb3861331bbcba84df3487105c55f5f815e5801 | from operator import attrgetter
from typing import Tuple as tTuple, Type
from collections import defaultdict
from sympy.utilities.exceptions import SymPyDeprecationWarning
from .sympify import _sympify as _sympify_, sympify
from .basic import Basic
from .cache import cacheit
from .sorting import ordered
from .logic i... |
7e812884dd17f0f5dc976ff86469993826e6ea028072c9fcbe278dc6bfe34da2 | from .assumptions import StdFactKB, _assume_defined
from .basic import Basic, Atom
from .cache import cacheit
from .containers import Tuple
from .expr import Expr, AtomicExpr
from .function import AppliedUndef, FunctionClass
from .kind import NumberKind, UndefinedKind
from .logic import fuzzy_bool
from .singleton impor... |
cd286d7463a73588c5d4c23cacca53b71a2bdeb688d7fa8ed13b8213f464cc69 | """
Reimplementations of constructs introduced in later versions of Python than
we support. Also some functions that are needed SymPy-wide and are located
here for easy import.
"""
from .sorting import ordered as _ordered, _nodes as __nodes, default_sort_key as _default_sort_key
from sympy.utilities.decorator import ... |
ee163dd2644f9a8a7e9b08e5e7f9c5abfe9c7ec64ef252f90efe230dd571b1cf | """sympify -- convert objects SymPy internal format"""
import typing
if typing.TYPE_CHECKING:
from typing import Any, Callable, Dict as tDict, Type
from inspect import getmro
import string
from sympy.core.random import choice
from .parameters import global_parameters
from sympy.utilities.exceptions import SymPy... |
d20ba0ddd0bc7f8558ed9629bdd72134505767540c1f4fe89ca80970c724e796 | """
Adaptive numerical evaluation of SymPy expressions, using mpmath
for mathematical functions.
"""
from typing import Tuple as tTuple, Optional, Union as tUnion, Callable, List, Dict as tDict, Type, TYPE_CHECKING, \
Any, overload
import math
import mpmath.libmp as libmp
from mpmath import (
make_mpc, make_... |
e07d54f50005385ef21ddbff793372f9ea469b9ca97c65036b6948ee9b2e3308 | """Module for SymPy containers
(SymPy objects that store other SymPy objects)
The containers implemented in this module are subclassed to Basic.
They are supposed to work seamlessly within the SymPy framework.
"""
from collections import OrderedDict
from collections.abc import MutableSet
from typing impo... |
6c52cd7988c5716fd3a1d44162db4c8bfa73fe0e82e93eb6ff9ff91257efadc7 | from typing import Tuple as tTuple
from collections import defaultdict
from functools import cmp_to_key, reduce
from itertools import product
import operator
from .sympify import sympify
from .basic import Basic
from .singleton import S
from .operations import AssocOp, AssocOpDispatcher
from .cache import cacheit
from... |
14e637172d6005f965afd7f45975ce3aea6c5f99ab95b2419d47a6f30fca68ea | """OO layer for several polynomial representations. """
from sympy.core.numbers import oo
from sympy.core.sympify import CantSympify
from sympy.polys.polyerrors import CoercionFailed, NotReversible, NotInvertible
from sympy.polys.polyutils import PicklableWithSlots
class GenericPoly(PicklableWithSlots):
"""Base... |
ce501a59e0a314055c9c6753887b8a5d0c42d1999937b380fbd4a5d212448416 | """Implementation of RootOf class and related tools. """
from sympy.core.basic import Basic
from sympy.core import (S, Expr, Integer, Float, I, oo, Add, Lambda,
symbols, sympify, Rational, Dummy)
from sympy.core.cache import cacheit
from sympy.core.relational import is_le
from sympy.core.sorting import ordered
fr... |
262188678d32bc735f28fd617d7bc80f687e9904a0866c92eb017cffab5f0341 | """User-friendly public interface to polynomial functions. """
from functools import wraps, reduce
from operator import mul
from sympy.core import (
S, Expr, Add, Tuple
)
from sympy.core.basic import Basic
from sympy.core.decorators import _sympifyit
from sympy.core.exprtools import Factors, factor_nc, factor_te... |
c53071717b9997c3cce164ef35a00adb8100a2694ca2fb0b4321f7e11914af22 | """Polynomial manipulation algorithms and algebraic objects. """
__all__ = [
'Poly', 'PurePoly', 'poly_from_expr', 'parallel_poly_from_expr', 'degree',
'total_degree', 'degree_list', 'LC', 'LM', 'LT', 'pdiv', 'prem', 'pquo',
'pexquo', 'div', 'rem', 'quo', 'exquo', 'half_gcdex', 'gcdex', 'invert',
'subr... |
ac6b61893b691f93974c5a2fcb4609a6b57d0be474a7d0d22b25943e6aeab9df | """Dense univariate polynomials with coefficients in Galois fields. """
from sympy.core.random import uniform
from math import ceil as _ceil, sqrt as _sqrt
from sympy.core.mul import prod
from sympy.external.gmpy import SYMPY_INTS
from sympy.ntheory import factorint
from sympy.polys.polyconfig import query
from symp... |
04280a6569f74f11cdd131cebf57d119c649d14298914f27d85207b2294c8741 | """Sparse polynomial rings. """
from typing import Any, Dict as tDict
from operator import add, mul, lt, le, gt, ge
from functools import reduce
from types import GeneratorType
from sympy.core.expr import Expr
from sympy.core.numbers import igcd, oo
from sympy.core.symbol import Symbol, symbols as _symbols
from sym... |
e153f740d221c33680f4c311d2b20b11a9e22a733b7da1e8211ae8f6221043d4 | """Options manager for :class:`~.Poly` and public API functions. """
__all__ = ["Options"]
from typing import Dict as tDict, Type
from typing import List, Optional
from sympy.core import Basic, sympify
from sympy.polys.polyerrors import GeneratorsError, OptionError, FlagError
from sympy.utilities import numbered_sy... |
beaf0ca7ea59869bcc8d8fabada9cda7751433e102d048428ea55d79c27f8c57 | """Groebner bases algorithms. """
from sympy.core.symbol import Dummy
from sympy.polys.monomials import monomial_mul, monomial_lcm, monomial_divides, term_div
from sympy.polys.orderings import lex
from sympy.polys.polyerrors import DomainError
from sympy.polys.polyconfig import query
def groebner(seq, ring, method=N... |
eb56c0b80eaa7794ab1ffc268033c2108d2aaca308bfbd6942943a59b8390697 | """Real and complex root isolation and refinement algorithms. """
from sympy.polys.densearith import (
dup_neg, dup_rshift, dup_rem)
from sympy.polys.densebasic import (
dup_LC, dup_TC, dup_degree,
dup_strip, dup_reverse,
dup_convert,
dup_terms_gcd)
from sympy.polys.densetools import (
dup_cle... |
836f34a72db8061de6c608c096d37b4f08faa8851fd59fe81dfa1f487ead2b79 | """Useful utilities for higher level polynomial classes. """
from sympy.core import (S, Add, Mul, Pow, Eq, Expr,
expand_mul, expand_multinomial)
from sympy.core.exprtools import decompose_power, decompose_power_rat
from sympy.polys.polyerrors import PolynomialError, GeneratorsError
from sympy.polys.polyoptions im... |
029dd7e250a6050540a3caa87da676058eb17eb50902aee3563886f643ad18ca | """Polynomial factorization routines in characteristic zero. """
from sympy.polys.galoistools import (
gf_from_int_poly, gf_to_int_poly,
gf_lshift, gf_add_mul, gf_mul,
gf_div, gf_rem,
gf_gcdex,
gf_sqf_p,
gf_factor_sqf, gf_factor)
from sympy.polys.densebasic import (
dup_LC, dmp_LC, dmp_gr... |
3b4c6e67f8a115a5bdc943cd482388d73ec939442fc7dba1618c08dc49c6db00 | r"""
Sparse distributed elements of free modules over multivariate (generalized)
polynomial rings.
This code and its data structures are very much like the distributed
polynomials, except that the first "exponent" of the monomial is
a module generator index. That is, the multi-exponent ``(i, e_1, ..., e_n)``
represent... |
06a9e00fcaa03b0846bd610a171ba25f3c5460d6a69674d98e1729c79d10277c | from sympy.core.random import (
random_complex_number as A,
verify_numerically as B,
test_derivative_numerically as C,
_randrange as D,
_randint as E)
from sympy.utilities.decorator import deprecated
random_complex_number = deprecated(useinstead="sympy.core.random.random_complex_number",
deprec... |
10e4ad2880202c55a42aa071799cf03341deedbc61b61fd0e8dee3aafaf85b5c | from typing import Type
from sympy.core.add import Add
from sympy.core.assumptions import StdFactKB
from sympy.core.expr import AtomicExpr, Expr
from sympy.core.power import Pow
from sympy.core.singleton import S
from sympy.core.sorting import default_sort_key
from sympy.core.sympify import sympify
from sympy.function... |
63628424f5c2141111ff63748384342552456765376cd66814287cb44d0973ef | from typing import Type
from sympy.vector.basisdependent import (BasisDependent, BasisDependentAdd,
BasisDependentMul, BasisDependentZero)
from sympy.core import S, Pow
from sympy.core.expr import AtomicExpr
from sympy.matrices.immutable import ImmutableDenseMatrix as Matrix
im... |
63b87cfc8a77cff900df03382d2becebc22ad6390c67645e2eb5132622ef0cd1 | """Geometrical Planes.
Contains
========
Plane
"""
from sympy.core import Dummy, Rational, S, Symbol
from sympy.core.symbol import _symbol
from sympy.functions.elementary.trigonometric import cos, sin, acos, asin, sqrt
from .entity import GeometryEntity
from .line import (Line, Ray, Segment, Line3D, LinearEntity, Li... |
9ddaeb83944da291ccdb63a95df3d51926f6ad9036c79459cac9876bde1f51e1 | """Utility functions for geometrical entities.
Contains
========
intersection
convex_hull
closest_points
farthest_points
are_coplanar
are_similar
"""
from .point import Point, Point2D
from sympy.core.containers import OrderedSet
from sympy.core.function import Function
from sympy.core.sorting import ordered
from sym... |
8c365a2cc9d01bc5c8bd0f9e12943354cc692d224dbaa29de30ccdaed102d658 | """Line-like geometrical entities.
Contains
========
LinearEntity
Line
Ray
Segment
LinearEntity2D
Line2D
Ray2D
Segment2D
LinearEntity3D
Line3D
Ray3D
Segment3D
"""
from sympy.core.containers import Tuple
from sympy.core.evalf import N
from sympy.core.expr import Expr
from sympy.core.numbers import Rational, oo
from s... |
b19717e6836ad65b998c7e1c2665d4665b0e5e68ac358cd4c84947c85e82efd5 | """
This module implements Holonomic Functions and
various operations on them.
"""
from sympy.core import Add, Mul, Pow
from sympy.core.numbers import NaN, Infinity, NegativeInfinity, Float, I, pi
from sympy.core.singleton import S
from sympy.core.sorting import ordered
from sympy.core.symbol import Dummy, Symbol
from... |
491d8ef388d5d5b26f154f12c7b57e17ec2573c32640ef6a896b98ff3efd225b | """Transform a string with Python-like source code into SymPy expression. """
from tokenize import (generate_tokens, untokenize, TokenError,
NUMBER, STRING, NAME, OP, ENDMARKER, ERRORTOKEN, NEWLINE)
from keyword import iskeyword
import ast
import unicodedata
from io import StringIO
import builtins
import types
... |
17fcaf50c0ae06adc747edc08ba5b8a24b41b17460f0a76eb452f04fd1452656 | """
A module that helps solving problems in physics.
"""
from . import units
from .matrices import mgamma, msigma, minkowski_tensor, mdft
__all__ = [
'units',
'mgamma', 'msigma', 'minkowski_tensor', 'mdft',
]
|
d6bfea0c16d5ca5f37eaa2179550dda05f3d67dc1e746bd62241c06f041a2bee | """
This module implements Pauli algebra by subclassing Symbol. Only algebraic
properties of Pauli matrices are used (we do not use the Matrix class).
See the documentation to the class Pauli for examples.
References
==========
.. [1] https://en.wikipedia.org/wiki/Pauli_matrices
"""
from sympy.core.add import Add
f... |
a99b740bc9b82c9fb43f50fe7db00f0ec92ff32a153b87b8f145195a9ab2a3ae | from sympy.core.numbers import Float
from sympy.core.singleton import S
from sympy.functions.combinatorial.factorials import factorial
from sympy.functions.elementary.exponential import exp
from sympy.functions.elementary.miscellaneous import sqrt
from sympy.functions.special.polynomials import assoc_laguerre
from symp... |
af2f24d0dfde1ef86ffca2625d026296a6259c85bd7d7c670343f913b3a87835 | """Known matrices related to physics"""
from sympy.core.numbers import I
from sympy.matrices.dense import MutableDenseMatrix as Matrix
from sympy.utilities.decorator import deprecated
def msigma(i):
r"""Returns a Pauli matrix `\sigma_i` with ``i=1,2,3``.
References
==========
.. [1] https://en.wiki... |
8e34e5d1f82d684bb980fc422e63135f38d9ba6c826c13e1c0d49960f0f64f8d | """
Second quantization operators and states for bosons.
This follow the formulation of Fetter and Welecka, "Quantum Theory
of Many-Particle Systems."
"""
from collections import defaultdict
from sympy.core.add import Add
from sympy.core.basic import Basic
from sympy.core.cache import cacheit
from sympy.core.containe... |
3970d79f402785296af04bf2d85f3879952617f723e360cc77d1c2d90dd20003 | r"""Module that defines indexed objects
The classes ``IndexedBase``, ``Indexed``, and ``Idx`` represent a
matrix element ``M[i, j]`` as in the following diagram::
1) The Indexed class represents the entire indexed object.
|
___|___
' '
M[i, j]... |
f20a0cfc21205593cdcbfad8fc121f44c68b77696422aecaa60ea42208332bfc | """
Boolean algebra module for SymPy
"""
from collections import defaultdict
from itertools import chain, combinations, product, permutations
from sympy.core.add import Add
from sympy.core.basic import Basic
from sympy.core.cache import cacheit
from sympy.core.containers import Tuple
from sympy.core.decorators import ... |
5b51ea2bff32f9a096220c31d886e8cc8eb511fb021db609fd1715ec6a9b5893 | '''Functions returning normal forms of matrices'''
from sympy.polys.domains.integerring import ZZ
from sympy.polys.polytools import Poly
from sympy.polys.matrices import DomainMatrix
from sympy.polys.matrices.normalforms import (
smith_normal_form as _snf,
invariant_factors as _invf,
hermite_no... |
b653193e2ece49c5c8c14aba0c95ad65a69975a0d98616f096b31351fb2cda3d | from types import FunctionType
from sympy.simplify.simplify import (
simplify as _simplify, dotprodsimp as _dotprodsimp)
from .utilities import _get_intermediate_simp, _iszero
from .determinant import _find_reasonable_pivot
def _row_reduce_list(mat, rows, cols, one, iszerofunc, simpfunc,
normali... |
f9108beeb602a306fa670addbcac517203c41e9f601d3a33c7f825494226e479 | from sympy.core import S
from sympy.core.relational import Eq, Ne
from sympy.logic.boolalg import BooleanFunction
from sympy.utilities.misc import func_name
from .sets import Set
class Contains(BooleanFunction):
"""
Asserts that x is an element of the set S.
Examples
========
>>> from sympy impo... |
192c9a06aec11c90b7a6f828083a14299434204d955f21edc7afe0e4e4bae16e | from sympy.core import Basic, Integer
import operator
class OmegaPower(Basic):
"""
Represents ordinal exponential and multiplication terms one of the
building blocks of the :class:`Ordinal` class.
In ``OmegaPower(a, b)``, ``a`` represents exponent and ``b`` represents multiplicity.
"""
def __n... |
8cc3908a00ec70b4eb14f5ef1eaa353835511bd06a0b8ca7dfc123e26e963dad | from sympy.core import Expr
from sympy.core.decorators import call_highest_priority, _sympifyit
from .fancysets import ImageSet
from .sets import set_add, set_sub, set_mul, set_div, set_pow, set_function
class SetExpr(Expr):
"""An expression that can take on values of a set.
Examples
========
>>> fr... |
1d444c7dba97195b61c1bf7889b86291cb9937ca4a84c0a336b10d4aef8d44e8 | from sympy.core.decorators import _sympifyit
from sympy.core.parameters import global_parameters
from sympy.core.logic import fuzzy_bool
from sympy.core.singleton import S
from sympy.core.sympify import _sympify
from .sets import Set, FiniteSet
class PowerSet(Set):
r"""A symbolic object representing a power set.... |
0b646d22510a21c1024e369ff9b1351b472911954f0cfb723f7947da58383c8f | from functools import reduce
from itertools import product
from sympy.core.basic import Basic
from sympy.core.containers import Tuple
from sympy.core.expr import Expr
from sympy.core.function import Lambda
from sympy.core.logic import fuzzy_not, fuzzy_or, fuzzy_and
from sympy.core.mod import Mod
from sympy.core.number... |
712b94f7d2fbed4bff08b1f26dcf09fdce3e29a07774c7f0d80a083aab78fda3 | from typing import Any, Callable, Optional
from functools import reduce
from collections import defaultdict
import inspect
from sympy.core.basic import Basic
from sympy.core.containers import Tuple
from sympy.core.decorators import sympify_method_args, sympify_return
from sympy.core.evalf import EvalfMixin
from sympy.... |
6b6b31c8564a263c206e7f97447d583417d5dcb72f23ec0c7cbf955b09595b15 | from sympy.concrete.summations import Sum
from sympy.core.basic import Basic
from sympy.core.containers import Tuple
from sympy.core.function import Lambda
from sympy.core.numbers import (Rational, nan, oo, pi)
from sympy.core.relational import Eq
from sympy.core.singleton import S
from sympy.core.symbol import (Symbol... |
0bb421586735a7e4538db1ffcbe6b1b1a3a717dab00e96637c18ba3faeca570a | from sympy.concrete.products import Product
from sympy.concrete.summations import Sum
from sympy.core.numbers import (Rational, oo, pi)
from sympy.core.relational import Eq
from sympy.core.singleton import S
from sympy.core.symbol import symbols
from sympy.functions.combinatorial.factorials import (RisingFactorial, fac... |
939b6b49c322c12825f5dcc9b77d0157eb742ae61cc83facf47b53dbe855850d | from sympy.concrete.summations import Sum
from sympy.core.mul import Mul
from sympy.core.numbers import (oo, pi)
from sympy.core.relational import Eq
from sympy.core.symbol import (Dummy, symbols)
from sympy.functions.elementary.exponential import exp
from sympy.functions.elementary.miscellaneous import sqrt
from sympy... |
2f62ddc2593696adff09ec023f2b0f0d4d0516c64ff318d58c2b3523de6c9719 | from sympy.concrete.summations import Sum
from sympy.core.containers import Tuple
from sympy.core.function import Lambda
from sympy.core.numbers import (Float, Rational, oo, pi)
from sympy.core.relational import (Eq, Ge, Gt, Le, Lt, Ne)
from sympy.core.singleton import S
from sympy.core.symbol import (Symbol, symbols)
... |
302875d91aa3bbde01234dad28c8350a8e62eef01e8db2f99e5f227183c1e13b | from sympy.concrete.summations import Sum
from sympy.core.numbers import (I, Rational, oo, pi)
from sympy.core.singleton import S
from sympy.core.symbol import (Dummy, Symbol)
from sympy.functions.elementary.complexes import (im, re)
from sympy.functions.elementary.exponential import log
from sympy.functions.elementary... |
0a20f5855db93061f04df1c66a869e8460f7889e25a8d622f998b045e3ba0959 | from sympy.concrete.products import Product
from sympy.core.function import Lambda
from sympy.core.numbers import (I, Rational, pi)
from sympy.core.singleton import S
from sympy.core.symbol import Dummy
from sympy.functions.elementary.complexes import Abs
from sympy.functions.elementary.exponential import exp
from symp... |
cedc60dccb3f42fb60c73215cf669e5cd19604f1c940943debf77cdac7f1acc7 | from sympy.concrete.summations import Sum
from sympy.core.function import (Lambda, diff, expand_func)
from sympy.core.mul import Mul
from sympy.core import EulerGamma
from sympy.core.numbers import (E as e, I, Rational, pi)
from sympy.core.relational import (Eq, Ne)
from sympy.core.singleton import S
from sympy.core.sy... |
ae9fb027e50cea42bd1cd73d9a4e4feeed3cfbca11fc9d0ae09b7b26593d3c60 | from sympy.concrete.summations import summation
from sympy.core.containers import Dict
from sympy.core.mul import Mul
from sympy.core.power import Pow
from sympy.core.singleton import S
from sympy.core.symbol import Symbol
from sympy.functions.combinatorial.factorials import factorial as fac
from sympy.core.evalf impor... |
f915d792a3147d509878ef47a2795d38e2120ca0da5180827b909480ad7c2f7a | from sympy.core.random import randint
from sympy.ntheory.bbp_pi import pi_hex_digits
from sympy.testing.pytest import raises
# http://www.herongyang.com/Cryptography/Blowfish-First-8366-Hex-Digits-of-PI.html
# There are actually 8336 listed there; with the prepended 3 there are 8337
# below
dig=''.join('''
3243f6a88... |
b691dcc2d7aeb9001a85c3eabe0066e0cc2af9e7f37073a7f2695d8a3ca78e51 | from sympy.core.numbers import Rational
from sympy.ntheory.egyptian_fraction import egyptian_fraction
from sympy.core.add import Add
from sympy.testing.pytest import raises
from sympy.core.random import random_complex_number
def test_egyptian_fraction():
def test_equality(r, alg="Greedy"):
return r == Add... |
1d0a02a2d33f83e70577242e427cee7eac03e2e3e552523550aad62670e6172a | from sympy.core.containers import Tuple
from sympy.combinatorics.generators import rubik_cube_generators
from sympy.combinatorics.homomorphisms import is_isomorphic
from sympy.combinatorics.named_groups import SymmetricGroup, CyclicGroup,\
DihedralGroup, AlternatingGroup, AbelianGroup, RubikGroup
from sympy.combina... |
b8994ed3d5e00feb489825aed6a91a8e20b4eeb2b71a837dd6fdff3aa4f9faaa | from sympy.combinatorics.named_groups import SymmetricGroup, AlternatingGroup,\
CyclicGroup
from sympy.combinatorics.testutil import _verify_bsgs, _cmp_perm_lists,\
_naive_list_centralizer, _verify_centralizer,\
_verify_normal_closure
from sympy.combinatorics.permutations import Permutation
from sympy.combi... |
c2e4aab683270ac2e3db3bdc27bd7a3dc51c40cdfc2c4d4bd662fbce6ef3139c | from sympy.core import S, Rational
from sympy.combinatorics.schur_number import schur_partition, SchurNumber
from sympy.core.random import _randint
from sympy.testing.pytest import raises
from sympy.core.symbol import symbols
def _sum_free_test(subset):
"""
Checks if subset is sum-free(There are no x,y,z in t... |
704505d0e1fa48d84dfe4874ebdc0cb2aea1e1e495a9b0cb821ae0dabf47b78f | from sympy.combinatorics.fp_groups import FpGroup
from sympy.combinatorics.coset_table import (CosetTable,
coset_enumeration_r, coset_enumeration_c)
from sympy.combinatorics.coset_table import modified_coset_enumeration_r
from sympy.combinatorics.free_groups import free_group
from sympy.testing.pyt... |
56ea69a43020f4e0da1820d4f99d1d336b3286c5108e55c57c92e2eaa5296cb8 | from sympy.combinatorics import Permutation
from sympy.combinatorics.perm_groups import PermutationGroup
from sympy.combinatorics.homomorphisms import homomorphism, group_isomorphism, is_isomorphic
from sympy.combinatorics.free_groups import free_group
from sympy.combinatorics.fp_groups import FpGroup
from sympy.combin... |
91519ce21e5b9bf110683fce03632fba0456880853fc86e0b72dd31f7c74b3b9 | from sympy.concrete.products import (Product, product)
from sympy.concrete.summations import Sum
from sympy.core.function import (Derivative, Function, diff)
from sympy.core.numbers import (Rational, oo, pi)
from sympy.core.singleton import S
from sympy.core.symbol import (Dummy, Symbol, symbols)
from sympy.functions.c... |
4cf5ba1f2d753e8e952d91bf771f79c77b0c05897991c407f308c9e933adbbe9 | from sympy.concrete.guess import (
find_simple_recurrence_vector,
find_simple_recurrence,
rationalize,
guess_generating_function_rational,
guess_generating_function,
guess
)
from sympy.concrete.products import Product
from sympy.core.functi... |
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