hash stringlengths 64 64 | content stringlengths 0 1.51M |
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d621e885367152049f875649a71f6760a389ce43dc314afb1543292bcf43439b | """Tools for setting up interactive sessions. """
from sympy.external.gmpy import GROUND_TYPES
from sympy.external.importtools import version_tuple
from sympy.interactive.printing import init_printing
from sympy.utilities.misc import ARCH
preexec_source = """\
from sympy import *
x, y, z, t = symbols('x y z t')
k, ... |
8d4a2185c835ad365604212cfba45ec692276d8be0453891f2baa37af957a36c | """Power series evaluation and manipulation using sparse Polynomials
Implementing a new function
---------------------------
There are a few things to be kept in mind when adding a new function here::
- The implementation should work on all possible input domains/rings.
Special cases include the ``EX`` rin... |
46d32330018e06a1580317f1ad59cd09de41db2ecddff3118ffd1ea95e9e637d | """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... |
abbe500357b4ac7f53a556d3188c1181e8ac345b7eec789171d3d411d1d83761 | """Advanced tools for dense recursive polynomials in ``K[x]`` or ``K[X]``. """
from sympy.polys.densearith import (
dup_add_term, dmp_add_term,
dup_lshift,
dup_add, dmp_add,
dup_sub, dmp_sub,
dup_mul, dmp_mul,
dup_sqr,
dup_div,
dup_rem, dmp_rem,
dmp_expand,
dup_mul_ground, dmp_... |
b1481f00f10762aad40e9fa28d4d778571bcd6f8348bf4e6966d1c97da0e166c | """User-friendly public interface to polynomial functions. """
from functools import wraps, reduce
from operator import mul
from typing import Optional
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 F... |
12c039fe831e4a48d2c0bb476287ffcc73e330042b299b5fba066447bd3dc73b | """Functions for generating interesting polynomials, e.g. for benchmarking. """
from sympy.core import Add, Mul, Symbol, sympify, Dummy, symbols
from sympy.core.containers import Tuple
from sympy.core.singleton import S
from sympy.ntheory import nextprime
from sympy.polys.densearith import (
dmp_add_term, dmp_neg... |
bf04769fa0cd2af531f8abb4007afd9fad34fa31eb5a9bda51bf265a3dd470a0 | """Algorithms for computing symbolic roots of polynomials. """
import math
from functools import reduce
from sympy.core import S, I, pi
from sympy.core.exprtools import factor_terms
from sympy.core.function import _mexpand
from sympy.core.logic import fuzzy_not
from sympy.core.mul import expand_2arg, Mul
from sympy.... |
ea59181cda533e9daaabca8a04d88af55fb136a2e0d0c61ca22fe4b0a68d05c8 | """Arithmetics for dense recursive polynomials in ``K[x]`` or ``K[X]``. """
from sympy.polys.densebasic import (
dup_slice,
dup_LC, dmp_LC,
dup_degree, dmp_degree,
dup_strip, dmp_strip,
dmp_zero_p, dmp_zero,
dmp_one_p, dmp_one,
dmp_ground, dmp_zeros)
from sympy.polys.polyerrors import (Exa... |
b0828fc4d29501630d24c15ff1232502c870a0dc16786cd8a9480b670e54ca6b | """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.polys.polyconfig import query
from sympy.polys.polyerrors import ExactQuoti... |
3e735f67d570416564f4fbea635f243bae8a8bbdc9a15f8031273f330c8cbf59 | """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... |
c4d6e402f6191af3896ac333b93f2aef15569793711235b3cb96ab417290ee13 | """Sparse rational function fields. """
from typing import Any, Dict as tDict
from functools import reduce
from operator import add, mul, lt, le, gt, ge
from sympy.core.expr import Expr
from sympy.core.mod import Mod
from sympy.core.numbers import Exp1
from sympy.core.singleton import S
from sympy.core.symbol impor... |
4c2584fab9bfba43d6c579e6a91c0ffcdd9ce88321ed5ae41c95d6d7b101e733 | """Low-level linear systems solver. """
from sympy.utilities.exceptions import sympy_deprecation_warning
from sympy.utilities.iterables import connected_components
from sympy.core.sympify import sympify
from sympy.core.numbers import Integer, Rational
from sympy.matrices.dense import MutableDenseMatrix
from sympy.po... |
2ce5db25e96e51f3d1e37f6e91378a3bbebf57aa94e31f9f5d01b977f00049d4 | """Real and complex root isolation and refinement algorithms. """
from sympy.polys.densearith import (
dup_neg, dup_rshift, dup_rem,
dup_l2_norm_squared)
from sympy.polys.densebasic import (
dup_LC, dup_TC, dup_degree,
dup_strip, dup_reverse,
dup_convert,
dup_terms_gcd)
from sympy.polys.denset... |
3a4a59888ac3daeff5601edd1363499a1a6dd5466804da17d89058dead548b1a | """Compatibility interface between dense and sparse polys. """
from sympy.polys.densearith import dup_add_term
from sympy.polys.densearith import dmp_add_term
from sympy.polys.densearith import dup_sub_term
from sympy.polys.densearith import dmp_sub_term
from sympy.polys.densearith import dup_mul_term
from sympy.poly... |
d2c656a59e062c1aa3b7cabbaf3de9f1d89a7f202811cb6ddb8119d19a902414 | """
This module contains functions for two multivariate resultants. These
are:
- Dixon's resultant.
- Macaulay's resultant.
Multivariate resultants are used to identify whether a multivariate
system has common roots. That is when the resultant is equal to zero.
"""
from sympy.core.mul import (Mul, prod)
from sympy.m... |
9125b3143a82d7fc18cbb46346b5a04a1988269dc79b2a4bf93a81539e8bf4c3 | """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.core.numbers import _illegal
from sympy.polys.polyerrors import PolynomialError, Generat... |
87ca82d19b177fe64a3cb20c05a2d5d9a4821c3b972d005ccca65c53e27605a1 | """Euclidean algorithms, GCDs, LCMs and polynomial remainder sequences. """
from sympy.polys.densearith import (
dup_sub_mul,
dup_neg, dmp_neg,
dmp_add,
dmp_sub,
dup_mul, dmp_mul,
dmp_pow,
dup_div, dmp_div,
dup_rem,
dup_quo, dmp_quo,
dup_prem, dmp_prem,
dup_mul_ground, dmp_... |
44ab712b293240e3702260eaa1d395185159bad6dcfa8d0c1e54f7ceaae7538e | """Polynomial factorization routines in characteristic zero. """
from sympy.core.random import _randint
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.denseba... |
e4040e9ca8e519844011df7d83d166544ce3a3360f1ba4adaf1e8c40db465a4b | """py.test hacks to support XFAIL/XPASS"""
import sys
import re
import functools
import os
import contextlib
import warnings
import inspect
import pathlib
from typing import Any, Callable
from sympy.utilities.exceptions import SymPyDeprecationWarning
# Imported here for backwards compatibility. Note: do not import th... |
6499f4a824063b133f14a124f0bd1b3fa30780588d52ca47f1cd00e0909e575f | """
This is our testing framework.
Goals:
* it should be compatible with py.test and operate very similarly
(or identically)
* does not require any external dependencies
* preferably all the functionality should be in this file only
* no magic, just import the test file and execute the test functions, that's it
* p... |
20a0c5026f1bef66753a44fbbe9827663696e4bb1253fc1fea0df9b0292af48d | """
.. deprecated:: 1.10
``sympy.testing.randtest`` functions have been moved to
:mod:`sympy.core.random`.
"""
from sympy.utilities.exceptions import sympy_deprecation_warning
sympy_deprecation_warning("The sympy.testing.randtest submodule is deprecated. Use sympy.core.random instead.",
deprecated_since_ve... |
3b394007ab2cf7d7511c50c0dd0adaf1afa6175609e92b0dec0c263a386fa8df | from collections.abc import Callable
from sympy.core.basic import Basic
from sympy.core.cache import cacheit
from sympy.core import S, Dummy, Lambda
from sympy.core.symbol import Str
from sympy.core.symbol import symbols
from sympy.matrices.immutable import ImmutableDenseMatrix as Matrix
from sympy.matrices.matrices i... |
e0124d8e6237e361e455199e424a9abaabe26cab1fd873aece49d04df40c9298 | from sympy.core import Basic
from sympy.vector.operators import gradient, divergence, curl
class Del(Basic):
"""
Represents the vector differential operator, usually represented in
mathematical expressions as the 'nabla' symbol.
"""
def __new__(cls):
obj = super().__new__(cls)
obj... |
f1ae1c490d6c279ba2add3281e757b4965d4df324f2adff4a23a276bc0bea756 | from sympy.vector.coordsysrect import CoordSys3D
from sympy.vector.vector import (Vector, VectorAdd, VectorMul,
BaseVector, VectorZero, Cross, Dot, cross, dot)
from sympy.vector.dyadic import (Dyadic, DyadicAdd, DyadicMul,
BaseDyadic, DyadicZero)
from sy... |
19fa757e2a9e54e992e34c1505e33ea2b548fed179acba29d642a50308b55465 | 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... |
3ddb3fec9479c981326b089e674bd502c2214dcdeb5af68dd3c82cb110c00aef | import collections
from sympy.core.expr import Expr
from sympy.core import sympify, S, preorder_traversal
from sympy.vector.coordsysrect import CoordSys3D
from sympy.vector.vector import Vector, VectorMul, VectorAdd, Cross, Dot
from sympy.core.function import Derivative
from sympy.core.add import Add
from sympy.core.mu... |
6909943fe667ad649fa646ad2b22cecbae12dd5c04bb0abe70b18b993317182b | from sympy.vector.coordsysrect import CoordSys3D
from sympy.vector.deloperator import Del
from sympy.vector.scalar import BaseScalar
from sympy.vector.vector import Vector, BaseVector
from sympy.vector.operators import gradient, curl, divergence
from sympy.core.function import diff
from sympy.core.singleton import S
fr... |
8554f16856c512480babb4ad175093c8f6a73b6364c5fe84ff41115755f4cc30 | from sympy.core.singleton import S
from sympy.simplify.simplify import simplify
from sympy.core import Basic, diff
from sympy.core.sorting import default_sort_key
from sympy.matrices import Matrix
from sympy.vector import (CoordSys3D, Vector, ParametricRegion,
parametric_region_list, ImplicitReg... |
3ec4752328ba254cf386590b00b3e84dab52a0276b03bf39e5fbaf6c7653e2ed | """Parabolic geometrical entity.
Contains
* Parabola
"""
from sympy.core import S
from sympy.core.sorting import ordered
from sympy.core.symbol import _symbol, symbols
from sympy.geometry.entity import GeometryEntity, GeometrySet
from sympy.geometry.point import Point, Point2D
from sympy.geometry.line import Line, L... |
58ec8b7c9ff2efb303f37308e05c9d2cb86ccff0c7280056a52a9952708e20e1 | """Curves in 2-dimensional Euclidean space.
Contains
========
Curve
"""
from sympy.functions.elementary.miscellaneous import sqrt
from sympy.core import sympify, diff
from sympy.core.containers import Tuple
from sympy.core.symbol import _symbol
from sympy.geometry.entity import GeometryEntity, GeometrySet
from sympy... |
e0cd9e4eb0198cd5ffe91704ec19a1bfe1c989eb576e857a93f6e75e56f59921 | """Geometrical Points.
Contains
========
Point
Point2D
Point3D
When methods of Point require 1 or more points as arguments, they
can be passed as a sequence of coordinates or Points:
>>> from sympy import Point
>>> Point(1, 1).is_collinear((2, 2), (3, 4))
False
>>> Point(1, 1).is_collinear(Point(2, 2), Point(3, 4))
... |
4e05427bd085ef948af491dcf598d58143dfba0642b7705194117604e0482153 | """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... |
900f660569a46b1bffd44864cae9043e53b38b2839b58373084b4f0c40687805 | """Elliptical geometrical entities.
Contains
* Ellipse
* Circle
"""
from sympy.core.expr import Expr
from sympy.core.relational import Eq
from sympy.core import S, pi, sympify
from sympy.core.evalf import N
from sympy.core.parameters import global_parameters
from sympy.core.logic import fuzzy_bool
from sympy.core.nu... |
155604eeb3eb045c3f0aa4a5b7af30839da9d3e90b1c358b5d43c1e7577a958a | """The definition of the base geometrical entity with attributes common to
all derived geometrical entities.
Contains
========
GeometryEntity
GeometricSet
Notes
=====
A GeometryEntity is any object that has special geometric properties.
A GeometrySet is a superclass of any GeometryEntity that can also
be viewed as ... |
d82b08c46c9b983e2304e462a14e68f80fc0a9e54acfbb5e6b36c351db3a97cd | """Utility functions for geometrical entities.
Contains
========
intersection
convex_hull
closest_points
farthest_points
are_coplanar
are_similar
"""
from collections import deque
from math import sqrt as _sqrt
from .entity import GeometryEntity
from .exceptions import GeometryError
from .point import Point, Point... |
5c37e89ffce0c67990cbbe896b26316e4ba9fde9c544892434db90dc44e26771 | """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, Float... |
4de7fe470e9d839664cd30139ede95e2a3a582d774d3755fa72fc100354f40a0 | from sympy.core import Expr, S, oo, pi, sympify
from sympy.core.evalf import N
from sympy.core.sorting import default_sort_key, ordered
from sympy.core.symbol import _symbol, Dummy, symbols, Symbol
from sympy.functions.elementary.complexes import sign
from sympy.functions.elementary.piecewise import Piecewise
from symp... |
245812393de1bba77b321f6c76abd2c42dd1c655651ff73282c5e9b17f7b60c6 | """Recurrence Operators"""
from sympy.core.singleton import S
from sympy.core.symbol import (Symbol, symbols)
from sympy.printing import sstr
from sympy.core.sympify import sympify
def RecurrenceOperators(base, generator):
"""
Returns an Algebra of Recurrence Operators and the operator for
shifting i.e. ... |
bd9b2efb7160850499e34177045861b7b1c85f35ca03dce58d2e9cfe7ea14702 | """
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... |
6eddf5485e918f9c6325368b92fd4f8156eb08a757e24945f9ce19508b2a28b9 | import re
import typing
from itertools import product
from typing import Any, Dict as tDict, Tuple as tTuple, List, Optional, Union as tUnion, Callable
import sympy
from sympy import Mul, Add, Pow, log, exp, sqrt, cos, sin, tan, asin, acos, acot, asec, acsc, sinh, cosh, tanh, asinh, \
acosh, atanh, acoth, asech, a... |
d9c12d6a5024516d4865936d3aab9e51335e227ba53b6b50c98f502d4cfe1e4b | """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
f... |
3306bfffda516b03f82e24121b4e83fdc6d2da14a1737b1a31a728152aa042f8 | """
This module implements the functionality to take any Python expression as a
string and fix all numbers and other things before evaluating it,
thus
1/2
returns
Integer(1)/Integer(2)
We use the ast module for this. It is well documented at docs.python.org.
Some tips to understand how this works: use dump() to ge... |
795793f76c1ebd9d11ebd76f883f3abe8588cd03a38c9cab40311d7f90a0750d | 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... |
8c77db5a4ccbda6c85b7edfd928750a39c0fb9b0713592979658ee4b164be1b1 | """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.wikipe... |
aa664dca079391e56548f8f716dcf677d7cf6372ddbc17bca4430d710318def4 | from sympy import permutedims
from sympy.core.numbers import Number
from sympy.core.singleton import S
from sympy.core.symbol import Symbol
from sympy.core.sympify import sympify
from sympy.tensor.array.dense_ndim_array import MutableDenseNDimArray
from sympy.tensor.tensor import (Tensor, TensExpr, TensAdd, TensMul,
... |
4476468c895edcfd5f5bd25459b9e2f2106bbc2af147b06400b6aa306502efa8 | """
This module defines tensors with abstract index notation.
The abstract index notation has been first formalized by Penrose.
Tensor indices are formal objects, with a tensor type; there is no
notion of index range, it is only possible to assign the dimension,
used to trace the Kronecker delta; the dimension can be... |
d8f7a1e32dab16df646ca5828c6fedc3f32092fb05771d14dbdbe28fe79e4f2e | 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]... |
98d29dc87be3e62f646025bfe17a2a9642c69a1b4e0fdc9020edf080b6b82653 | """
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 ... |
98c9cdb034f118aaa21b42404ec3385bd6f98e096169ccbebe6470d9a6688e06 | from contextlib import contextmanager
from threading import local
from sympy.core.function import expand_mul
class DotProdSimpState(local):
def __init__(self):
self.state = None
_dotprodsimp_state = DotProdSimpState()
@contextmanager
def dotprodsimp(x):
old = _dotprodsimp_state.state
try:
... |
ed981479b1ef41a9c97630ef81e4a4c1702eda3dfa26d3637ddfaaf35610d984 | import copy
from sympy.core import S
from sympy.core.function import expand_mul
from sympy.functions.elementary.miscellaneous import Min, sqrt
from sympy.functions.elementary.complexes import sign
from .common import NonSquareMatrixError, NonPositiveDefiniteMatrixError
from .utilities import _get_intermediate_simp, _... |
bf06fa6dddab3dc01a0f9cd2cb00b2ee2bf4314dac4cadb372a50b57e5734873 | from types import FunctionType
from sympy.core.numbers import Float, Integer
from sympy.core.singleton import S
from sympy.core.symbol import uniquely_named_symbol
from sympy.core.mul import Mul
from sympy.polys import PurePoly, cancel
from sympy.core.sympify import sympify
from sympy.functions.combinatorial.numbers i... |
dba03829493a8e489f946f650a3d57da03ad4c4d53d2507084b32813bd7c348c | from types import FunctionType
from .utilities import _get_intermediate_simp, _iszero, _dotprodsimp, _simplify
from .determinant import _find_reasonable_pivot
def _row_reduce_list(mat, rows, cols, one, iszerofunc, simpfunc,
normalize_last=True, normalize=True, zero_above=True):
"""Row reduce a fl... |
dcd598f281e24c6756411e807d9a60d9f3ad8d1735287ef9cb19084cdcc270f8 | from mpmath.matrices.matrices import _matrix
from sympy.core import Basic, Dict, Tuple
from sympy.core.numbers import Integer
from sympy.core.cache import cacheit
from sympy.core.sympify import _sympy_converter as sympify_converter, _sympify
from sympy.matrices.dense import DenseMatrix
from sympy.matrices.expressions ... |
87006f67080a31827560d35083a5daa8e593dc5ee933b0f59fe725e9be697fe8 | """
Basic methods common to all matrices to be used
when creating more advanced matrices (e.g., matrices over rings,
etc.).
"""
from collections import defaultdict
from collections.abc import Iterable
from inspect import isfunction
from functools import reduce
from sympy.assumptions.refine import refine
from sympy.co... |
87952a4a3046267f4a8befe583817a7a6f22ee8ff7fa41409b4747b684837aa1 | import random
from sympy.core.basic import Basic
from sympy.core.singleton import S
from sympy.core.symbol import Symbol
from sympy.core.sympify import sympify
from sympy.functions.elementary.trigonometric import cos, sin
from sympy.utilities.decorator import doctest_depends_on
from sympy.utilities.exceptions import s... |
b37798f08a9ab7d36f9fc3d90ead29c3bcc86906ef8c9f933ff1b01882929ddb | from sympy.core.function import expand_mul
from sympy.core.symbol import Dummy, uniquely_named_symbol, symbols
from sympy.utilities.iterables import numbered_symbols
from .common import ShapeError, NonSquareMatrixError, NonInvertibleMatrixError
from .eigen import _fuzzy_positive_definite
from .utilities import _get_in... |
12ecbf049b118505cb7818d017b6c2e4ef24cce421224ef3ad95b172d7846d35 | from collections.abc import Callable
from sympy.core.containers import Dict
from sympy.utilities.exceptions import sympy_deprecation_warning
from sympy.utilities.iterables import is_sequence
from sympy.utilities.misc import as_int
from .matrices import MatrixBase
from .repmatrix import MutableRepMatrix, RepMatrix
fr... |
5d28390bf8e2e5cf83caea1f895f1660bb7c372f9e1db0c4e73ffd9d8f439f23 | import mpmath as mp
from collections.abc import Callable
from sympy.core.add import Add
from sympy.core.basic import Basic
from sympy.core.function import diff
from sympy.core.expr import Expr
from sympy.core.kind import _NumberKind, UndefinedKind
from sympy.core.mul import Mul
from sympy.core.power import Pow
from s... |
399723273f9828f2e38bbcecf553b215050ddb470a859e66f9da821dd3379988 | from types import FunctionType
from collections import Counter
from mpmath import mp, workprec
from mpmath.libmp.libmpf import prec_to_dps
from sympy.core.sorting import default_sort_key
from sympy.core.evalf import DEFAULT_MAXPREC, PrecisionExhausted
from sympy.core.logic import fuzzy_and, fuzzy_or
from sympy.core.n... |
6bfabbdad75c18d99a1a66a577a58d0ae44dcde84db9f7f215e989ed62d7d093 | from collections import defaultdict
from operator import index as index_
from sympy.core.expr import Expr
from sympy.core.kind import Kind, NumberKind, UndefinedKind
from sympy.core.numbers import Integer, Rational
from sympy.core.sympify import _sympify, SympifyError
from sympy.core.singleton import S
from sympy.pol... |
b8ba38aa73f4c6f15c168e6185fea0ee91d21e245b710d404c32b0181c56ec21 | from .utilities import _iszero
def _columnspace(M, simplify=False):
"""Returns a list of vectors (Matrix objects) that span columnspace of ``M``
Examples
========
>>> from sympy import Matrix
>>> M = Matrix(3, 3, [1, 3, 0, -2, -6, 0, 3, 9, 6])
>>> M
Matrix([
[ 1, 3, 0],
[-2, -6,... |
bc81a74982a78043c4b7a57ee9b78339700e63dba00cb27c7d73b1e47f4925c9 | 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, SetKind
class PowerSet(Set):
r"""A symbolic object representing a p... |
cac57720c6d513ed73837ce1b0cf3ef8fbcdd71439f4b0c0d481c78a7c8e3fba | 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... |
5757d6e71c54ddf8b07ffd5aadfcc5698be3c299eb06f1de13f63da41d84b8e0 | from typing import Any, Callable, Optional
from functools import reduce
from collections import defaultdict
import inspect
from sympy.core.kind import Kind, UndefinedKind, NumberKind
from sympy.core.basic import Basic
from sympy.core.containers import Tuple, TupleKind
from sympy.core.decorators import sympify_method_a... |
981c71547205b7d51f75d032bf07ddfae56c3397e2b0d512bc174d587e5037f0 | from sympy.core.singleton import S
from sympy.core.basic import Basic
from sympy.core.containers import Tuple
from sympy.core.function import Lambda, BadSignatureError
from sympy.core.logic import fuzzy_bool
from sympy.core.relational import Eq
from sympy.core.symbol import Dummy
from sympy.core.sympify import _sympify... |
02b33a4e1560a7802674622660d5af5644df974f8dadfdf5ca47cd3c87d8e48e | """Implicit plotting module for SymPy.
Explanation
===========
The module implements a data series called ImplicitSeries which is used by
``Plot`` class to plot implicit plots for different backends. The module,
by default, implements plotting using interval arithmetic. It switches to a
fall back algorithm if the exp... |
b6e9d41226f40b3c69f04e91f044d4cb7df33f70cf26411eacb6a3a5f53e4131 | """Plotting module for SymPy.
A plot is represented by the ``Plot`` class that contains a reference to the
backend and a list of the data series to be plotted. The data series are
instances of classes meant to simplify getting points and meshes from SymPy
expressions. ``plot_backends`` is a dictionary with all the bac... |
c08bc1d36bddac8fa71095f74ea227b1fd2ff3bd39248e6571580c26c25bb4ed | """ rewrite of lambdify - This stuff is not stable at all.
It is for internal use in the new plotting module.
It may (will! see the Q'n'A in the source) be rewritten.
It's completely self contained. Especially it does not use lambdarepr.
It does not aim to replace the current lambdify. Most importantly it will never... |
cec3bbd01ed13631a1b3c03aa6246950acfd0a789893aea02df61b07a8b75f9f | 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... |
c4a3a6ce5d46652fb0b21e2986306b78a30795aacc5d046429d5966a96eeb3d5 | 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... |
e42c2a2dee05320e6ca7634de6aeb47dc870944e55bb9001b230dff956d0cf4d | 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)
... |
4d33e702095333c717ba26529c5cfd1a523dfc8c0406ec77d244bf218fa894df | 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 Symbol
from sympy.functions.elementary.complexes import (im, re)
from sympy.functions.elementary.exponential import log
from sympy.functions.elementary.integers... |
8f74850b6fb86ba5f624e6cbdc953cce7424457386c73d9af573e518fa0192ed | 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... |
f696bed55e417529d0491c84225c4a856bb434ab7af16a4add5ed46a138de85e | """Tests for Gosper's algorithm for hypergeometric summation. """
from sympy.core.numbers import (Rational, pi)
from sympy.core.singleton import S
from sympy.core.symbol import Symbol
from sympy.functions.combinatorial.factorials import (binomial, factorial)
from sympy.functions.elementary.miscellaneous import sqrt
fr... |
257a956d2c5996532a9b38459260ac9ad7cf3be55734bfe9e88fc68a8fbe4beb | from sympy.concrete.products import (Product, product)
from sympy.concrete.summations import (Sum, summation)
from sympy.core.function import (Derivative, Function)
from sympy.core.mul import prod
from sympy.core import (Catalan, EulerGamma)
from sympy.core.numbers import (E, I, Rational, nan, oo, pi)
from sympy.core.r... |
4d0245d8140afa3ecc92bf77b00f8c77876df99fe7dfe6bc8d7fbcd66e856949 | from sympy.core.evalf import N
from sympy.core.function import (Derivative, Function, PoleError, Subs)
from sympy.core.numbers import (E, Rational, oo, pi, I)
from sympy.core.singleton import S
from sympy.core.symbol import (Symbol, symbols)
from sympy.functions.elementary.exponential import (LambertW, exp, log)
from s... |
3e12e6ba608df24e39cdf34a51efb75a59463a470f52dec4666691af2a205405 | from sympy.core.add import Add
from sympy.core.function import (Function, expand)
from sympy.core.numbers import (I, Rational, nan, oo, pi)
from sympy.core.singleton import S
from sympy.core.symbol import (Symbol, symbols)
from sympy.functions.elementary.complexes import (conjugate, transpose)
from sympy.functions.elem... |
91353299d6f6a067b57cf581c27400a0428d35d84d11dd5369a1e479a69abe22 | from itertools import product
from sympy.concrete.summations import Sum
from sympy.core.function import (Function, diff)
from sympy.core import EulerGamma
from sympy.core.numbers import (E, I, Rational, oo, pi, zoo)
from sympy.core.singleton import S
from sympy.core.symbol import (Symbol, symbols)
from sympy.functions... |
466ff1f7801f885d7ebd9b167196058aff88f88fd61741aece5e602781cc532b | from sympy.core.function import diff
from sympy.core.numbers import (E, I, Rational, pi)
from sympy.core.singleton import S
from sympy.core.symbol import (Symbol, symbols)
from sympy.functions.elementary.complexes import (Abs, conjugate, im, re, sign)
from sympy.functions.elementary.exponential import log
from sympy.fu... |
dc17a90abea779dfb80bfde67b8cd272ed3a1d71bd431fdd041c48a625c0bf2e | from sympy.core import Lambda, Symbol, symbols
from sympy.diffgeom.rn import R2, R2_p, R2_r, R3_r, R3_c, R3_s, R2_origin
from sympy.diffgeom import (Manifold, Patch, CoordSystem, Commutator, Differential, TensorProduct,
WedgeProduct, BaseCovarDerivativeOp, CovarDerivativeOp, LieDerivative,
covariant_ord... |
6bf18a7f716978d37ccdf31cf95f00692ad0b44235a222df24e728d952a248a2 | from sympy.core.symbol import symbols
from sympy.codegen.abstract_nodes import List
def test_List():
l = List(2, 3, 4)
assert l == List(2, 3, 4)
assert str(l) == "[2, 3, 4]"
x, y, z = symbols('x y z')
l = List(x**2,y**3,z**4)
# contrary to python's built-in list, we can call e.g. "replace" on ... |
b16fef8b0db174ef4a96a7f7d71dd89587069618118f9d875752459b0ae0b5be | """
This module defines base class for handlers and some core handlers:
``Q.commutative`` and ``Q.is_true``.
"""
from sympy.assumptions import Q, ask, AppliedPredicate
from sympy.core import Basic, Symbol
from sympy.core.logic import _fuzzy_group
from sympy.core.numbers import NaN, Number
from sympy.logic.boolalg impo... |
19d6ae936c64d6128f46be22e91a6f38c1ed0e7c950f7e31d4eca12fe3a1f077 | """
This module contains query handlers responsible for Matrices queries:
Square, Symmetric, Invertible etc.
"""
from sympy.logic.boolalg import conjuncts
from sympy.assumptions import Q, ask
from sympy.assumptions.handlers import test_closed_group
from sympy.matrices import MatrixBase
from sympy.matrices.expressions ... |
b5e1ec5d37cfc3fab8d7deed5dccf63affac715c431cff93fcba5c10b98e3272 | from sympy.abc import t, w, x, y, z, n, k, m, p, i
from sympy.assumptions import (ask, AssumptionsContext, Q, register_handler,
remove_handler)
from sympy.assumptions.assume import assuming, global_assumptions, Predicate
from sympy.assumptions.cnf import CNF, Literal
from sympy.assumptions.facts import (single_... |
3f56af6b8279672f77dced379bd4194d557b4854094ac95a25ed044176a76f75 | """
This module implements some special functions that commonly appear in
combinatorial contexts (e.g. in power series); in particular,
sequences of rational numbers such as Bernoulli and Fibonacci numbers.
Factorials, binomial coefficients and related functions are located in
the separate 'factorials' module.
"""
fr... |
9ed3716463347f61fc54397119e6056670a534ffb2d494b3a9705a7a199fba28 | from typing import List
from functools import reduce
from sympy.core import S, sympify, Dummy, Mod
from sympy.core.cache import cacheit
from sympy.core.function import Function, ArgumentIndexError, PoleError
from sympy.core.logic import fuzzy_and
from sympy.core.numbers import Integer, pi, I
from sympy.core.relational... |
9974af6ba7b89fe11eef98ee3e7d21902222e0bbd0812932bf35fce00e4e81d5 | from typing import Tuple as tTuple
from sympy.core.add import Add
from sympy.core.basic import sympify, cacheit
from sympy.core.expr import Expr
from sympy.core.function import Function, ArgumentIndexError, PoleError, expand_mul
from sympy.core.logic import fuzzy_not, fuzzy_or, FuzzyBool, fuzzy_and
from sympy.core.num... |
0ad0c64805521b57fb37c134ea56774f7a968a944e09564e999ff10457d2f56c | from sympy.core import S, Function, diff, Tuple, Dummy
from sympy.core.basic import Basic, as_Basic
from sympy.core.numbers import Rational, NumberSymbol, _illegal
from sympy.core.parameters import global_parameters
from sympy.core.relational import (Lt, Gt, Eq, Ne, Relational,
_canonical, _canonical_coeff)
from sy... |
eb9b04d1b95a9e81f78a68b5cfa6dd8e5937223ab9b48a4c1b5e96a63a76c1f3 | from typing import Tuple as tTuple
from sympy.core.basic import Basic
from sympy.core.expr import Expr
from sympy.core import Add, S
from sympy.core.evalf import get_integer_part, PrecisionExhausted
from sympy.core.function import Function
from sympy.core.logic import fuzzy_or
from sympy.core.numbers import Integer
f... |
76049c291c835fcbe43df3ac9345da5b194809cdafaa27f96e0ed1741325833e | from itertools import product
from typing import Tuple as tTuple
from sympy.core.expr import Expr
from sympy.core import sympify
from sympy.core.add import Add
from sympy.core.cache import cacheit
from sympy.core.function import (Function, ArgumentIndexError, expand_log,
expand_mul, FunctionClass, PoleError, expan... |
7380ba572e5562ef0a3199eaf681fcd863b666557241c2e734a306f86f3db22d | from sympy.core.logic import FuzzyBool
from sympy.core import S, sympify, cacheit, pi, I, Rational
from sympy.core.add import Add
from sympy.core.function import Function, ArgumentIndexError
from sympy.core.logic import fuzzy_or, fuzzy_and
from sympy.functions.combinatorial.factorials import (binomial, factorial,
... |
cf554de0fd3ac3cfa9fbdcd00ee88566e8ee3610d8bd26a0e7e1a62169295105 | from typing import Tuple as tTuple
from sympy.core import S, Add, Mul, sympify, Symbol, Dummy, Basic
from sympy.core.expr import Expr
from sympy.core.exprtools import factor_terms
from sympy.core.function import (Function, Derivative, ArgumentIndexError,
AppliedUndef, expand_mul)
from sympy.core.logic import fuzzy... |
6c1d3da38577202151cb396d07aa0acfe49e7397e638529952b816ae0f4684b5 | """Hypergeometric and Meijer G-functions"""
from functools import reduce
from sympy.core import S, I, pi, oo, zoo, ilcm, Mod
from sympy.core.add import Add
from sympy.core.expr import Expr
from sympy.core.function import Function, Derivative, ArgumentIndexError
from sympy.core.containers import Tuple
from sympy.core.... |
16532185521a37a6340c1e091f7af2fc544da45c99cf29205ea0ca0370aa7c76 | from sympy.core import S, sympify, diff
from sympy.core.function import Function, ArgumentIndexError
from sympy.core.logic import fuzzy_not
from sympy.core.relational import Eq, Ne
from sympy.functions.elementary.complexes import im, sign
from sympy.functions.elementary.piecewise import Piecewise
from sympy.polys.polye... |
2223194f38f59a95aeafb394008b0aeca1d8a6bc0b45fdbc5a3b45a80e770e26 | from sympy.core.expr import Expr
from sympy.core.function import Function, ArgumentIndexError
from sympy.core.numbers import I, pi
from sympy.core.singleton import S
from sympy.core.symbol import Dummy
from sympy.core.sympify import sympify
from sympy.functions import assoc_legendre
from sympy.functions.combinatorial.f... |
b7e6f4cab9a9d784062b6bc2de41e0351af6779b0092730e80bb3a4046851463 | from sympy.core import S, sympify
from sympy.core.symbol import (Dummy, symbols)
from sympy.functions import Piecewise, piecewise_fold
from sympy.logic.boolalg import And
from sympy.sets.sets import Interval
from functools import lru_cache
def _ivl(cond, x):
"""return the interval corresponding to the condition
... |
6d504d410662793b73083ebb22e8427e0aab28d1970a0048a840555b2db90ec7 | """ Riemann zeta and related function. """
from sympy.core.add import Add
from sympy.core import Function, S, sympify, pi, I
from sympy.core.function import ArgumentIndexError, expand_mul
from sympy.core.symbol import Dummy
from sympy.functions.combinatorial.numbers import bernoulli, factorial, harmonic
from sympy.fun... |
3b2190017084f8d15b9d5a9f18264dd88c7d2fe88672dc68a55e7d4f0691e238 | from functools import wraps
from sympy.core import S
from sympy.core.add import Add
from sympy.core.cache import cacheit
from sympy.core.expr import Expr
from sympy.core.function import Function, ArgumentIndexError, _mexpand
from sympy.core.logic import fuzzy_or, fuzzy_not
from sympy.core.numbers import Rational, pi, ... |
13861808f0078073413523702fc2e660bb97f1cbfdef125d4df9cb0c785351a6 | from sympy.core import S, Integer
from sympy.core.function import Function
from sympy.core.logic import fuzzy_not
from sympy.core.mul import prod
from sympy.core.relational import Ne
from sympy.core.sorting import default_sort_key
from sympy.external.gmpy import SYMPY_INTS
from sympy.functions.combinatorial.factorials ... |
9e5ed9b3b9a97ff3b73d5e024b584b259749e0f8cf7f0cbe098dc2ca78628973 | """ This module contains various functions that are special cases
of incomplete gamma functions. It should probably be renamed. """
from sympy.core import Add, S, sympify, cacheit, pi, I, Rational, EulerGamma
from sympy.core.function import Function, ArgumentIndexError, expand_mul
from sympy.core.relational import... |
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