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536 lines
28 KiB
536 lines
28 KiB
5 months ago
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"""
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SymPy is a Python library for symbolic mathematics. It aims to become a
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full-featured computer algebra system (CAS) while keeping the code as simple
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as possible in order to be comprehensible and easily extensible. SymPy is
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written entirely in Python. It depends on mpmath, and other external libraries
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may be optionally for things like plotting support.
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See the webpage for more information and documentation:
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https://sympy.org
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"""
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import sys
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if sys.version_info < (3, 8):
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raise ImportError("Python version 3.8 or above is required for SymPy.")
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del sys
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try:
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import mpmath
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except ImportError:
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raise ImportError("SymPy now depends on mpmath as an external library. "
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"See https://docs.sympy.org/latest/install.html#mpmath for more information.")
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del mpmath
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from sympy.release import __version__
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from sympy.core.cache import lazy_function
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if 'dev' in __version__:
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def enable_warnings():
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import warnings
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warnings.filterwarnings('default', '.*', DeprecationWarning, module='sympy.*')
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del warnings
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enable_warnings()
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del enable_warnings
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def __sympy_debug():
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# helper function so we don't import os globally
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import os
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debug_str = os.getenv('SYMPY_DEBUG', 'False')
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if debug_str in ('True', 'False'):
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return eval(debug_str)
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else:
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raise RuntimeError("unrecognized value for SYMPY_DEBUG: %s" %
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debug_str)
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SYMPY_DEBUG = __sympy_debug() # type: bool
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from .core import (sympify, SympifyError, cacheit, Basic, Atom,
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preorder_traversal, S, Expr, AtomicExpr, UnevaluatedExpr, Symbol,
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Wild, Dummy, symbols, var, Number, Float, Rational, Integer,
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NumberSymbol, RealNumber, igcd, ilcm, seterr, E, I, nan, oo, pi, zoo,
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AlgebraicNumber, comp, mod_inverse, Pow, integer_nthroot, integer_log,
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Mul, prod, Add, Mod, Rel, Eq, Ne, Lt, Le, Gt, Ge, Equality,
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GreaterThan, LessThan, Unequality, StrictGreaterThan, StrictLessThan,
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vectorize, Lambda, WildFunction, Derivative, diff, FunctionClass,
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Function, Subs, expand, PoleError, count_ops, expand_mul, expand_log,
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expand_func, expand_trig, expand_complex, expand_multinomial, nfloat,
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expand_power_base, expand_power_exp, arity, PrecisionExhausted, N,
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evalf, Tuple, Dict, gcd_terms, factor_terms, factor_nc, evaluate,
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Catalan, EulerGamma, GoldenRatio, TribonacciConstant, bottom_up, use,
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postorder_traversal, default_sort_key, ordered)
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from .logic import (to_cnf, to_dnf, to_nnf, And, Or, Not, Xor, Nand, Nor,
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Implies, Equivalent, ITE, POSform, SOPform, simplify_logic, bool_map,
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true, false, satisfiable)
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from .assumptions import (AppliedPredicate, Predicate, AssumptionsContext,
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assuming, Q, ask, register_handler, remove_handler, refine)
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from .polys import (Poly, PurePoly, poly_from_expr, parallel_poly_from_expr,
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degree, total_degree, degree_list, LC, LM, LT, pdiv, prem, pquo,
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pexquo, div, rem, quo, exquo, half_gcdex, gcdex, invert,
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subresultants, resultant, discriminant, cofactors, gcd_list, gcd,
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lcm_list, lcm, terms_gcd, trunc, monic, content, primitive, compose,
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decompose, sturm, gff_list, gff, sqf_norm, sqf_part, sqf_list, sqf,
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factor_list, factor, intervals, refine_root, count_roots, real_roots,
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nroots, ground_roots, nth_power_roots_poly, cancel, reduced, groebner,
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is_zero_dimensional, GroebnerBasis, poly, symmetrize, horner,
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interpolate, rational_interpolate, viete, together,
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BasePolynomialError, ExactQuotientFailed, PolynomialDivisionFailed,
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OperationNotSupported, HeuristicGCDFailed, HomomorphismFailed,
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IsomorphismFailed, ExtraneousFactors, EvaluationFailed,
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RefinementFailed, CoercionFailed, NotInvertible, NotReversible,
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NotAlgebraic, DomainError, PolynomialError, UnificationFailed,
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GeneratorsError, GeneratorsNeeded, ComputationFailed,
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UnivariatePolynomialError, MultivariatePolynomialError,
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PolificationFailed, OptionError, FlagError, minpoly,
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minimal_polynomial, primitive_element, field_isomorphism,
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to_number_field, isolate, round_two, prime_decomp, prime_valuation,
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galois_group, itermonomials, Monomial, lex, grlex,
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grevlex, ilex, igrlex, igrevlex, CRootOf, rootof, RootOf,
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ComplexRootOf, RootSum, roots, Domain, FiniteField, IntegerRing,
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RationalField, RealField, ComplexField, PythonFiniteField,
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GMPYFiniteField, PythonIntegerRing, GMPYIntegerRing, PythonRational,
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GMPYRationalField, AlgebraicField, PolynomialRing, FractionField,
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ExpressionDomain, FF_python, FF_gmpy, ZZ_python, ZZ_gmpy, QQ_python,
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QQ_gmpy, GF, FF, ZZ, QQ, ZZ_I, QQ_I, RR, CC, EX, EXRAW,
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construct_domain, swinnerton_dyer_poly, cyclotomic_poly,
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symmetric_poly, random_poly, interpolating_poly, jacobi_poly,
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chebyshevt_poly, chebyshevu_poly, hermite_poly, hermite_prob_poly,
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legendre_poly, laguerre_poly, apart, apart_list, assemble_partfrac_list,
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Options, ring, xring, vring, sring, field, xfield, vfield, sfield)
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from .series import (Order, O, limit, Limit, gruntz, series, approximants,
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residue, EmptySequence, SeqPer, SeqFormula, sequence, SeqAdd, SeqMul,
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fourier_series, fps, difference_delta, limit_seq)
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from .functions import (factorial, factorial2, rf, ff, binomial,
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RisingFactorial, FallingFactorial, subfactorial, carmichael,
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fibonacci, lucas, motzkin, tribonacci, harmonic, bernoulli, bell, euler,
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catalan, genocchi, andre, partition, sqrt, root, Min, Max, Id,
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real_root, Rem, cbrt, re, im, sign, Abs, conjugate, arg, polar_lift,
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periodic_argument, unbranched_argument, principal_branch, transpose,
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adjoint, polarify, unpolarify, sin, cos, tan, sec, csc, cot, sinc,
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asin, acos, atan, asec, acsc, acot, atan2, exp_polar, exp, ln, log,
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LambertW, sinh, cosh, tanh, coth, sech, csch, asinh, acosh, atanh,
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acoth, asech, acsch, floor, ceiling, frac, Piecewise, piecewise_fold,
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piecewise_exclusive, erf, erfc, erfi, erf2, erfinv, erfcinv, erf2inv,
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Ei, expint, E1, li, Li, Si, Ci, Shi, Chi, fresnels, fresnelc, gamma,
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lowergamma, uppergamma, polygamma, loggamma, digamma, trigamma,
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multigamma, dirichlet_eta, zeta, lerchphi, polylog, stieltjes, Eijk,
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LeviCivita, KroneckerDelta, SingularityFunction, DiracDelta, Heaviside,
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bspline_basis, bspline_basis_set, interpolating_spline, besselj,
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bessely, besseli, besselk, hankel1, hankel2, jn, yn, jn_zeros, hn1,
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hn2, airyai, airybi, airyaiprime, airybiprime, marcumq, hyper,
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meijerg, appellf1, legendre, assoc_legendre, hermite, hermite_prob,
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chebyshevt, chebyshevu, chebyshevu_root, chebyshevt_root, laguerre,
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assoc_laguerre, gegenbauer, jacobi, jacobi_normalized, Ynm, Ynm_c,
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Znm, elliptic_k, elliptic_f, elliptic_e, elliptic_pi, beta, mathieus,
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mathieuc, mathieusprime, mathieucprime, riemann_xi, betainc, betainc_regularized)
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from .ntheory import (nextprime, prevprime, prime, primepi, primerange,
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randprime, Sieve, sieve, primorial, cycle_length, composite,
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compositepi, isprime, divisors, proper_divisors, factorint,
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multiplicity, perfect_power, pollard_pm1, pollard_rho, primefactors,
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totient, trailing, divisor_count, proper_divisor_count, divisor_sigma,
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factorrat, reduced_totient, primenu, primeomega,
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mersenne_prime_exponent, is_perfect, is_mersenne_prime, is_abundant,
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is_deficient, is_amicable, abundance, npartitions, is_primitive_root,
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is_quad_residue, legendre_symbol, jacobi_symbol, n_order, sqrt_mod,
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quadratic_residues, primitive_root, nthroot_mod, is_nthpow_residue,
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sqrt_mod_iter, mobius, discrete_log, quadratic_congruence,
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binomial_coefficients, binomial_coefficients_list,
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multinomial_coefficients, continued_fraction_periodic,
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continued_fraction_iterator, continued_fraction_reduce,
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continued_fraction_convergents, continued_fraction, egyptian_fraction)
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from .concrete import product, Product, summation, Sum
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from .discrete import (fft, ifft, ntt, intt, fwht, ifwht, mobius_transform,
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inverse_mobius_transform, convolution, covering_product,
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intersecting_product)
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from .simplify import (simplify, hypersimp, hypersimilar, logcombine,
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separatevars, posify, besselsimp, kroneckersimp, signsimp,
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nsimplify, FU, fu, sqrtdenest, cse, epath, EPath, hyperexpand,
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collect, rcollect, radsimp, collect_const, fraction, numer, denom,
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trigsimp, exptrigsimp, powsimp, powdenest, combsimp, gammasimp,
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ratsimp, ratsimpmodprime)
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from .sets import (Set, Interval, Union, EmptySet, FiniteSet, ProductSet,
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Intersection, DisjointUnion, imageset, Complement, SymmetricDifference, ImageSet,
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Range, ComplexRegion, Complexes, Reals, Contains, ConditionSet, Ordinal,
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OmegaPower, ord0, PowerSet, Naturals, Naturals0, UniversalSet,
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Integers, Rationals)
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from .solvers import (solve, solve_linear_system, solve_linear_system_LU,
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solve_undetermined_coeffs, nsolve, solve_linear, checksol, det_quick,
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inv_quick, check_assumptions, failing_assumptions, diophantine,
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rsolve, rsolve_poly, rsolve_ratio, rsolve_hyper, checkodesol,
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classify_ode, dsolve, homogeneous_order, solve_poly_system,
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solve_triangulated, pde_separate, pde_separate_add, pde_separate_mul,
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pdsolve, classify_pde, checkpdesol, ode_order, reduce_inequalities,
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reduce_abs_inequality, reduce_abs_inequalities, solve_poly_inequality,
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solve_rational_inequalities, solve_univariate_inequality, decompogen,
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solveset, linsolve, linear_eq_to_matrix, nonlinsolve, substitution)
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from .matrices import (ShapeError, NonSquareMatrixError, GramSchmidt,
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casoratian, diag, eye, hessian, jordan_cell, list2numpy, matrix2numpy,
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matrix_multiply_elementwise, ones, randMatrix, rot_axis1, rot_axis2,
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rot_axis3, symarray, wronskian, zeros, MutableDenseMatrix,
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DeferredVector, MatrixBase, Matrix, MutableMatrix,
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MutableSparseMatrix, banded, ImmutableDenseMatrix,
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ImmutableSparseMatrix, ImmutableMatrix, SparseMatrix, MatrixSlice,
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BlockDiagMatrix, BlockMatrix, FunctionMatrix, Identity, Inverse,
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MatAdd, MatMul, MatPow, MatrixExpr, MatrixSymbol, Trace, Transpose,
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ZeroMatrix, OneMatrix, blockcut, block_collapse, matrix_symbols,
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Adjoint, hadamard_product, HadamardProduct, HadamardPower,
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Determinant, det, diagonalize_vector, DiagMatrix, DiagonalMatrix,
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DiagonalOf, trace, DotProduct, kronecker_product, KroneckerProduct,
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PermutationMatrix, MatrixPermute, Permanent, per, rot_ccw_axis1,
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rot_ccw_axis2, rot_ccw_axis3, rot_givens)
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from .geometry import (Point, Point2D, Point3D, Line, Ray, Segment, Line2D,
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Segment2D, Ray2D, Line3D, Segment3D, Ray3D, Plane, Ellipse, Circle,
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Polygon, RegularPolygon, Triangle, rad, deg, are_similar, centroid,
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convex_hull, idiff, intersection, closest_points, farthest_points,
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GeometryError, Curve, Parabola)
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from .utilities import (flatten, group, take, subsets, variations,
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numbered_symbols, cartes, capture, dict_merge, prefixes, postfixes,
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sift, topological_sort, unflatten, has_dups, has_variety, reshape,
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rotations, filldedent, lambdify,
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threaded, xthreaded, public, memoize_property, timed)
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from .integrals import (integrate, Integral, line_integrate, mellin_transform,
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inverse_mellin_transform, MellinTransform, InverseMellinTransform,
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laplace_transform, inverse_laplace_transform, LaplaceTransform,
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InverseLaplaceTransform, fourier_transform, inverse_fourier_transform,
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FourierTransform, InverseFourierTransform, sine_transform,
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inverse_sine_transform, SineTransform, InverseSineTransform,
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cosine_transform, inverse_cosine_transform, CosineTransform,
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InverseCosineTransform, hankel_transform, inverse_hankel_transform,
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HankelTransform, InverseHankelTransform, singularityintegrate)
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from .tensor import (IndexedBase, Idx, Indexed, get_contraction_structure,
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get_indices, shape, MutableDenseNDimArray, ImmutableDenseNDimArray,
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MutableSparseNDimArray, ImmutableSparseNDimArray, NDimArray,
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tensorproduct, tensorcontraction, tensordiagonal, derive_by_array,
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permutedims, Array, DenseNDimArray, SparseNDimArray)
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from .parsing import parse_expr
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from .calculus import (euler_equations, singularities, is_increasing,
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is_strictly_increasing, is_decreasing, is_strictly_decreasing,
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is_monotonic, finite_diff_weights, apply_finite_diff,
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differentiate_finite, periodicity, not_empty_in, AccumBounds,
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is_convex, stationary_points, minimum, maximum)
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from .algebras import Quaternion
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from .printing import (pager_print, pretty, pretty_print, pprint,
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pprint_use_unicode, pprint_try_use_unicode, latex, print_latex,
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multiline_latex, mathml, print_mathml, python, print_python, pycode,
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ccode, print_ccode, smtlib_code, glsl_code, print_glsl, cxxcode, fcode,
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print_fcode, rcode, print_rcode, jscode, print_jscode, julia_code,
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mathematica_code, octave_code, rust_code, print_gtk, preview, srepr,
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print_tree, StrPrinter, sstr, sstrrepr, TableForm, dotprint,
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maple_code, print_maple_code)
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test = lazy_function('sympy.testing.runtests', 'test')
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doctest = lazy_function('sympy.testing.runtests', 'doctest')
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# This module causes conflicts with other modules:
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# from .stats import *
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# Adds about .04-.05 seconds of import time
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# from combinatorics import *
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# This module is slow to import:
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#from physics import units
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from .plotting import plot, textplot, plot_backends, plot_implicit, plot_parametric
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from .interactive import init_session, init_printing, interactive_traversal
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evalf._create_evalf_table()
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__all__ = [
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'__version__',
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# sympy.core
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'sympify', 'SympifyError', 'cacheit', 'Basic', 'Atom',
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'preorder_traversal', 'S', 'Expr', 'AtomicExpr', 'UnevaluatedExpr',
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'Symbol', 'Wild', 'Dummy', 'symbols', 'var', 'Number', 'Float',
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'Rational', 'Integer', 'NumberSymbol', 'RealNumber', 'igcd', 'ilcm',
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'seterr', 'E', 'I', 'nan', 'oo', 'pi', 'zoo', 'AlgebraicNumber', 'comp',
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'mod_inverse', 'Pow', 'integer_nthroot', 'integer_log', 'Mul', 'prod',
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'Add', 'Mod', 'Rel', 'Eq', 'Ne', 'Lt', 'Le', 'Gt', 'Ge', 'Equality',
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'GreaterThan', 'LessThan', 'Unequality', 'StrictGreaterThan',
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'StrictLessThan', 'vectorize', 'Lambda', 'WildFunction', 'Derivative',
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'diff', 'FunctionClass', 'Function', 'Subs', 'expand', 'PoleError',
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'count_ops', 'expand_mul', 'expand_log', 'expand_func', 'expand_trig',
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'expand_complex', 'expand_multinomial', 'nfloat', 'expand_power_base',
|
||
|
|
'expand_power_exp', 'arity', 'PrecisionExhausted', 'N', 'evalf', 'Tuple',
|
||
|
|
'Dict', 'gcd_terms', 'factor_terms', 'factor_nc', 'evaluate', 'Catalan',
|
||
|
|
'EulerGamma', 'GoldenRatio', 'TribonacciConstant', 'bottom_up', 'use',
|
||
|
|
'postorder_traversal', 'default_sort_key', 'ordered',
|
||
|
|
|
||
|
|
# sympy.logic
|
||
|
|
'to_cnf', 'to_dnf', 'to_nnf', 'And', 'Or', 'Not', 'Xor', 'Nand', 'Nor',
|
||
|
|
'Implies', 'Equivalent', 'ITE', 'POSform', 'SOPform', 'simplify_logic',
|
||
|
|
'bool_map', 'true', 'false', 'satisfiable',
|
||
|
|
|
||
|
|
# sympy.assumptions
|
||
|
|
'AppliedPredicate', 'Predicate', 'AssumptionsContext', 'assuming', 'Q',
|
||
|
|
'ask', 'register_handler', 'remove_handler', 'refine',
|
||
|
|
|
||
|
|
# sympy.polys
|
||
|
|
'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',
|
||
|
|
'subresultants', 'resultant', 'discriminant', 'cofactors', 'gcd_list',
|
||
|
|
'gcd', 'lcm_list', 'lcm', 'terms_gcd', 'trunc', 'monic', 'content',
|
||
|
|
'primitive', 'compose', 'decompose', 'sturm', 'gff_list', 'gff',
|
||
|
|
'sqf_norm', 'sqf_part', 'sqf_list', 'sqf', 'factor_list', 'factor',
|
||
|
|
'intervals', 'refine_root', 'count_roots', 'real_roots', 'nroots',
|
||
|
|
'ground_roots', 'nth_power_roots_poly', 'cancel', 'reduced', 'groebner',
|
||
|
|
'is_zero_dimensional', 'GroebnerBasis', 'poly', 'symmetrize', 'horner',
|
||
|
|
'interpolate', 'rational_interpolate', 'viete', 'together',
|
||
|
|
'BasePolynomialError', 'ExactQuotientFailed', 'PolynomialDivisionFailed',
|
||
|
|
'OperationNotSupported', 'HeuristicGCDFailed', 'HomomorphismFailed',
|
||
|
|
'IsomorphismFailed', 'ExtraneousFactors', 'EvaluationFailed',
|
||
|
|
'RefinementFailed', 'CoercionFailed', 'NotInvertible', 'NotReversible',
|
||
|
|
'NotAlgebraic', 'DomainError', 'PolynomialError', 'UnificationFailed',
|
||
|
|
'GeneratorsError', 'GeneratorsNeeded', 'ComputationFailed',
|
||
|
|
'UnivariatePolynomialError', 'MultivariatePolynomialError',
|
||
|
|
'PolificationFailed', 'OptionError', 'FlagError', 'minpoly',
|
||
|
|
'minimal_polynomial', 'primitive_element', 'field_isomorphism',
|
||
|
|
'to_number_field', 'isolate', 'round_two', 'prime_decomp',
|
||
|
|
'prime_valuation', 'galois_group', 'itermonomials', 'Monomial', 'lex', 'grlex',
|
||
|
|
'grevlex', 'ilex', 'igrlex', 'igrevlex', 'CRootOf', 'rootof', 'RootOf',
|
||
|
|
'ComplexRootOf', 'RootSum', 'roots', 'Domain', 'FiniteField',
|
||
|
|
'IntegerRing', 'RationalField', 'RealField', 'ComplexField',
|
||
|
|
'PythonFiniteField', 'GMPYFiniteField', 'PythonIntegerRing',
|
||
|
|
'GMPYIntegerRing', 'PythonRational', 'GMPYRationalField',
|
||
|
|
'AlgebraicField', 'PolynomialRing', 'FractionField', 'ExpressionDomain',
|
||
|
|
'FF_python', 'FF_gmpy', 'ZZ_python', 'ZZ_gmpy', 'QQ_python', 'QQ_gmpy',
|
||
|
|
'GF', 'FF', 'ZZ', 'QQ', 'ZZ_I', 'QQ_I', 'RR', 'CC', 'EX', 'EXRAW',
|
||
|
|
'construct_domain', 'swinnerton_dyer_poly', 'cyclotomic_poly',
|
||
|
|
'symmetric_poly', 'random_poly', 'interpolating_poly', 'jacobi_poly',
|
||
|
|
'chebyshevt_poly', 'chebyshevu_poly', 'hermite_poly', 'hermite_prob_poly',
|
||
|
|
'legendre_poly', 'laguerre_poly', 'apart', 'apart_list', 'assemble_partfrac_list',
|
||
|
|
'Options', 'ring', 'xring', 'vring', 'sring', 'field', 'xfield', 'vfield',
|
||
|
|
'sfield',
|
||
|
|
|
||
|
|
# sympy.series
|
||
|
|
'Order', 'O', 'limit', 'Limit', 'gruntz', 'series', 'approximants',
|
||
|
|
'residue', 'EmptySequence', 'SeqPer', 'SeqFormula', 'sequence', 'SeqAdd',
|
||
|
|
'SeqMul', 'fourier_series', 'fps', 'difference_delta', 'limit_seq',
|
||
|
|
|
||
|
|
# sympy.functions
|
||
|
|
'factorial', 'factorial2', 'rf', 'ff', 'binomial', 'RisingFactorial',
|
||
|
|
'FallingFactorial', 'subfactorial', 'carmichael', 'fibonacci', 'lucas',
|
||
|
|
'motzkin', 'tribonacci', 'harmonic', 'bernoulli', 'bell', 'euler', 'catalan',
|
||
|
|
'genocchi', 'andre', 'partition', 'sqrt', 'root', 'Min', 'Max', 'Id', 'real_root',
|
||
|
|
'Rem', 'cbrt', 're', 'im', 'sign', 'Abs', 'conjugate', 'arg', 'polar_lift',
|
||
|
|
'periodic_argument', 'unbranched_argument', 'principal_branch',
|
||
|
|
'transpose', 'adjoint', 'polarify', 'unpolarify', 'sin', 'cos', 'tan',
|
||
|
|
'sec', 'csc', 'cot', 'sinc', 'asin', 'acos', 'atan', 'asec', 'acsc',
|
||
|
|
'acot', 'atan2', 'exp_polar', 'exp', 'ln', 'log', 'LambertW', 'sinh',
|
||
|
|
'cosh', 'tanh', 'coth', 'sech', 'csch', 'asinh', 'acosh', 'atanh',
|
||
|
|
'acoth', 'asech', 'acsch', 'floor', 'ceiling', 'frac', 'Piecewise',
|
||
|
|
'piecewise_fold', 'piecewise_exclusive', 'erf', 'erfc', 'erfi', 'erf2',
|
||
|
|
'erfinv', 'erfcinv', 'erf2inv', 'Ei', 'expint', 'E1', 'li', 'Li', 'Si',
|
||
|
|
'Ci', 'Shi', 'Chi', 'fresnels', 'fresnelc', 'gamma', 'lowergamma',
|
||
|
|
'uppergamma', 'polygamma', 'loggamma', 'digamma', 'trigamma', 'multigamma',
|
||
|
|
'dirichlet_eta', 'zeta', 'lerchphi', 'polylog', 'stieltjes', 'Eijk', 'LeviCivita',
|
||
|
|
'KroneckerDelta', 'SingularityFunction', 'DiracDelta', 'Heaviside',
|
||
|
|
'bspline_basis', 'bspline_basis_set', 'interpolating_spline', 'besselj',
|
||
|
|
'bessely', 'besseli', 'besselk', 'hankel1', 'hankel2', 'jn', 'yn',
|
||
|
|
'jn_zeros', 'hn1', 'hn2', 'airyai', 'airybi', 'airyaiprime',
|
||
|
|
'airybiprime', 'marcumq', 'hyper', 'meijerg', 'appellf1', 'legendre',
|
||
|
|
'assoc_legendre', 'hermite', 'hermite_prob', 'chebyshevt', 'chebyshevu',
|
||
|
|
'chebyshevu_root', 'chebyshevt_root', 'laguerre', 'assoc_laguerre',
|
||
|
|
'gegenbauer', 'jacobi', 'jacobi_normalized', 'Ynm', 'Ynm_c', 'Znm',
|
||
|
|
'elliptic_k', 'elliptic_f', 'elliptic_e', 'elliptic_pi', 'beta',
|
||
|
|
'mathieus', 'mathieuc', 'mathieusprime', 'mathieucprime', 'riemann_xi','betainc',
|
||
|
|
'betainc_regularized',
|
||
|
|
|
||
|
|
# sympy.ntheory
|
||
|
|
'nextprime', 'prevprime', 'prime', 'primepi', 'primerange', 'randprime',
|
||
|
|
'Sieve', 'sieve', 'primorial', 'cycle_length', 'composite', 'compositepi',
|
||
|
|
'isprime', 'divisors', 'proper_divisors', 'factorint', 'multiplicity',
|
||
|
|
'perfect_power', 'pollard_pm1', 'pollard_rho', 'primefactors', 'totient',
|
||
|
|
'trailing', 'divisor_count', 'proper_divisor_count', 'divisor_sigma',
|
||
|
|
'factorrat', 'reduced_totient', 'primenu', 'primeomega',
|
||
|
|
'mersenne_prime_exponent', 'is_perfect', 'is_mersenne_prime',
|
||
|
|
'is_abundant', 'is_deficient', 'is_amicable', 'abundance', 'npartitions',
|
||
|
|
'is_primitive_root', 'is_quad_residue', 'legendre_symbol',
|
||
|
|
'jacobi_symbol', 'n_order', 'sqrt_mod', 'quadratic_residues',
|
||
|
|
'primitive_root', 'nthroot_mod', 'is_nthpow_residue', 'sqrt_mod_iter',
|
||
|
|
'mobius', 'discrete_log', 'quadratic_congruence', 'binomial_coefficients',
|
||
|
|
'binomial_coefficients_list', 'multinomial_coefficients',
|
||
|
|
'continued_fraction_periodic', 'continued_fraction_iterator',
|
||
|
|
'continued_fraction_reduce', 'continued_fraction_convergents',
|
||
|
|
'continued_fraction', 'egyptian_fraction',
|
||
|
|
|
||
|
|
# sympy.concrete
|
||
|
|
'product', 'Product', 'summation', 'Sum',
|
||
|
|
|
||
|
|
# sympy.discrete
|
||
|
|
'fft', 'ifft', 'ntt', 'intt', 'fwht', 'ifwht', 'mobius_transform',
|
||
|
|
'inverse_mobius_transform', 'convolution', 'covering_product',
|
||
|
|
'intersecting_product',
|
||
|
|
|
||
|
|
# sympy.simplify
|
||
|
|
'simplify', 'hypersimp', 'hypersimilar', 'logcombine', 'separatevars',
|
||
|
|
'posify', 'besselsimp', 'kroneckersimp', 'signsimp',
|
||
|
|
'nsimplify', 'FU', 'fu', 'sqrtdenest', 'cse', 'epath', 'EPath',
|
||
|
|
'hyperexpand', 'collect', 'rcollect', 'radsimp', 'collect_const',
|
||
|
|
'fraction', 'numer', 'denom', 'trigsimp', 'exptrigsimp', 'powsimp',
|
||
|
|
'powdenest', 'combsimp', 'gammasimp', 'ratsimp', 'ratsimpmodprime',
|
||
|
|
|
||
|
|
# sympy.sets
|
||
|
|
'Set', 'Interval', 'Union', 'EmptySet', 'FiniteSet', 'ProductSet',
|
||
|
|
'Intersection', 'imageset', 'DisjointUnion', 'Complement', 'SymmetricDifference',
|
||
|
|
'ImageSet', 'Range', 'ComplexRegion', 'Reals', 'Contains', 'ConditionSet',
|
||
|
|
'Ordinal', 'OmegaPower', 'ord0', 'PowerSet', 'Naturals',
|
||
|
|
'Naturals0', 'UniversalSet', 'Integers', 'Rationals', 'Complexes',
|
||
|
|
|
||
|
|
# sympy.solvers
|
||
|
|
'solve', 'solve_linear_system', 'solve_linear_system_LU',
|
||
|
|
'solve_undetermined_coeffs', 'nsolve', 'solve_linear', 'checksol',
|
||
|
|
'det_quick', 'inv_quick', 'check_assumptions', 'failing_assumptions',
|
||
|
|
'diophantine', 'rsolve', 'rsolve_poly', 'rsolve_ratio', 'rsolve_hyper',
|
||
|
|
'checkodesol', 'classify_ode', 'dsolve', 'homogeneous_order',
|
||
|
|
'solve_poly_system', 'solve_triangulated', 'pde_separate',
|
||
|
|
'pde_separate_add', 'pde_separate_mul', 'pdsolve', 'classify_pde',
|
||
|
|
'checkpdesol', 'ode_order', 'reduce_inequalities',
|
||
|
|
'reduce_abs_inequality', 'reduce_abs_inequalities',
|
||
|
|
'solve_poly_inequality', 'solve_rational_inequalities',
|
||
|
|
'solve_univariate_inequality', 'decompogen', 'solveset', 'linsolve',
|
||
|
|
'linear_eq_to_matrix', 'nonlinsolve', 'substitution',
|
||
|
|
|
||
|
|
# sympy.matrices
|
||
|
|
'ShapeError', 'NonSquareMatrixError', 'GramSchmidt', 'casoratian', 'diag',
|
||
|
|
'eye', 'hessian', 'jordan_cell', 'list2numpy', 'matrix2numpy',
|
||
|
|
'matrix_multiply_elementwise', 'ones', 'randMatrix', 'rot_axis1',
|
||
|
|
'rot_axis2', 'rot_axis3', 'symarray', 'wronskian', 'zeros',
|
||
|
|
'MutableDenseMatrix', 'DeferredVector', 'MatrixBase', 'Matrix',
|
||
|
|
'MutableMatrix', 'MutableSparseMatrix', 'banded', 'ImmutableDenseMatrix',
|
||
|
|
'ImmutableSparseMatrix', 'ImmutableMatrix', 'SparseMatrix', 'MatrixSlice',
|
||
|
|
'BlockDiagMatrix', 'BlockMatrix', 'FunctionMatrix', 'Identity', 'Inverse',
|
||
|
|
'MatAdd', 'MatMul', 'MatPow', 'MatrixExpr', 'MatrixSymbol', 'Trace',
|
||
|
|
'Transpose', 'ZeroMatrix', 'OneMatrix', 'blockcut', 'block_collapse',
|
||
|
|
'matrix_symbols', 'Adjoint', 'hadamard_product', 'HadamardProduct',
|
||
|
|
'HadamardPower', 'Determinant', 'det', 'diagonalize_vector', 'DiagMatrix',
|
||
|
|
'DiagonalMatrix', 'DiagonalOf', 'trace', 'DotProduct',
|
||
|
|
'kronecker_product', 'KroneckerProduct', 'PermutationMatrix',
|
||
|
|
'MatrixPermute', 'Permanent', 'per', 'rot_ccw_axis1', 'rot_ccw_axis2',
|
||
|
|
'rot_ccw_axis3', 'rot_givens',
|
||
|
|
|
||
|
|
# sympy.geometry
|
||
|
|
'Point', 'Point2D', 'Point3D', 'Line', 'Ray', 'Segment', 'Line2D',
|
||
|
|
'Segment2D', 'Ray2D', 'Line3D', 'Segment3D', 'Ray3D', 'Plane', 'Ellipse',
|
||
|
|
'Circle', 'Polygon', 'RegularPolygon', 'Triangle', 'rad', 'deg',
|
||
|
|
'are_similar', 'centroid', 'convex_hull', 'idiff', 'intersection',
|
||
|
|
'closest_points', 'farthest_points', 'GeometryError', 'Curve', 'Parabola',
|
||
|
|
|
||
|
|
# sympy.utilities
|
||
|
|
'flatten', 'group', 'take', 'subsets', 'variations', 'numbered_symbols',
|
||
|
|
'cartes', 'capture', 'dict_merge', 'prefixes', 'postfixes', 'sift',
|
||
|
|
'topological_sort', 'unflatten', 'has_dups', 'has_variety', 'reshape',
|
||
|
|
'rotations', 'filldedent', 'lambdify', 'threaded', 'xthreaded',
|
||
|
|
'public', 'memoize_property', 'timed',
|
||
|
|
|
||
|
|
# sympy.integrals
|
||
|
|
'integrate', 'Integral', 'line_integrate', 'mellin_transform',
|
||
|
|
'inverse_mellin_transform', 'MellinTransform', 'InverseMellinTransform',
|
||
|
|
'laplace_transform', 'inverse_laplace_transform', 'LaplaceTransform',
|
||
|
|
'InverseLaplaceTransform', 'fourier_transform',
|
||
|
|
'inverse_fourier_transform', 'FourierTransform',
|
||
|
|
'InverseFourierTransform', 'sine_transform', 'inverse_sine_transform',
|
||
|
|
'SineTransform', 'InverseSineTransform', 'cosine_transform',
|
||
|
|
'inverse_cosine_transform', 'CosineTransform', 'InverseCosineTransform',
|
||
|
|
'hankel_transform', 'inverse_hankel_transform', 'HankelTransform',
|
||
|
|
'InverseHankelTransform', 'singularityintegrate',
|
||
|
|
|
||
|
|
# sympy.tensor
|
||
|
|
'IndexedBase', 'Idx', 'Indexed', 'get_contraction_structure',
|
||
|
|
'get_indices', 'shape', 'MutableDenseNDimArray', 'ImmutableDenseNDimArray',
|
||
|
|
'MutableSparseNDimArray', 'ImmutableSparseNDimArray', 'NDimArray',
|
||
|
|
'tensorproduct', 'tensorcontraction', 'tensordiagonal', 'derive_by_array',
|
||
|
|
'permutedims', 'Array', 'DenseNDimArray', 'SparseNDimArray',
|
||
|
|
|
||
|
|
# sympy.parsing
|
||
|
|
'parse_expr',
|
||
|
|
|
||
|
|
# sympy.calculus
|
||
|
|
'euler_equations', 'singularities', 'is_increasing',
|
||
|
|
'is_strictly_increasing', 'is_decreasing', 'is_strictly_decreasing',
|
||
|
|
'is_monotonic', 'finite_diff_weights', 'apply_finite_diff',
|
||
|
|
'differentiate_finite', 'periodicity', 'not_empty_in',
|
||
|
|
'AccumBounds', 'is_convex', 'stationary_points', 'minimum', 'maximum',
|
||
|
|
|
||
|
|
# sympy.algebras
|
||
|
|
'Quaternion',
|
||
|
|
|
||
|
|
# sympy.printing
|
||
|
|
'pager_print', 'pretty', 'pretty_print', 'pprint', 'pprint_use_unicode',
|
||
|
|
'pprint_try_use_unicode', 'latex', 'print_latex', 'multiline_latex',
|
||
|
|
'mathml', 'print_mathml', 'python', 'print_python', 'pycode', 'ccode',
|
||
|
|
'print_ccode', 'smtlib_code', 'glsl_code', 'print_glsl', 'cxxcode', 'fcode',
|
||
|
|
'print_fcode', 'rcode', 'print_rcode', 'jscode', 'print_jscode',
|
||
|
|
'julia_code', 'mathematica_code', 'octave_code', 'rust_code', 'print_gtk',
|
||
|
|
'preview', 'srepr', 'print_tree', 'StrPrinter', 'sstr', 'sstrrepr',
|
||
|
|
'TableForm', 'dotprint', 'maple_code', 'print_maple_code',
|
||
|
|
|
||
|
|
# sympy.plotting
|
||
|
|
'plot', 'textplot', 'plot_backends', 'plot_implicit', 'plot_parametric',
|
||
|
|
|
||
|
|
# sympy.interactive
|
||
|
|
'init_session', 'init_printing', 'interactive_traversal',
|
||
|
|
|
||
|
|
# sympy.testing
|
||
|
|
'test', 'doctest',
|
||
|
|
]
|
||
|
|
|
||
|
|
|
||
|
|
#===========================================================================#
|
||
|
|
# #
|
||
|
|
# XXX: The names below were importable before SymPy 1.6 using #
|
||
|
|
# #
|
||
|
|
# from sympy import * #
|
||
|
|
# #
|
||
|
|
# This happened implicitly because there was no __all__ defined in this #
|
||
|
|
# __init__.py file. Not every package is imported. The list matches what #
|
||
|
|
# would have been imported before. It is possible that these packages will #
|
||
|
|
# not be imported by a star-import from sympy in future. #
|
||
|
|
# #
|
||
|
|
#===========================================================================#
|
||
|
|
|
||
|
|
|
||
|
|
__all__.extend((
|
||
|
|
'algebras',
|
||
|
|
'assumptions',
|
||
|
|
'calculus',
|
||
|
|
'concrete',
|
||
|
|
'discrete',
|
||
|
|
'external',
|
||
|
|
'functions',
|
||
|
|
'geometry',
|
||
|
|
'interactive',
|
||
|
|
'multipledispatch',
|
||
|
|
'ntheory',
|
||
|
|
'parsing',
|
||
|
|
'plotting',
|
||
|
|
'polys',
|
||
|
|
'printing',
|
||
|
|
'release',
|
||
|
|
'strategies',
|
||
|
|
'tensor',
|
||
|
|
'utilities',
|
||
|
|
))
|