112 lines
5.1 KiB
Python
112 lines
5.1 KiB
Python
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"""A functions module, includes all the standard functions.
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Combinatorial - factorial, fibonacci, harmonic, bernoulli...
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Elementary - hyperbolic, trigonometric, exponential, floor and ceiling, sqrt...
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Special - gamma, zeta,spherical harmonics...
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"""
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from sympy.functions.combinatorial.factorials import (factorial, factorial2,
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rf, ff, binomial, RisingFactorial, FallingFactorial, subfactorial)
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from sympy.functions.combinatorial.numbers import (carmichael, fibonacci, lucas, tribonacci,
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harmonic, bernoulli, bell, euler, catalan, genocchi, andre, partition, motzkin)
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from sympy.functions.elementary.miscellaneous import (sqrt, root, Min, Max,
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Id, real_root, cbrt, Rem)
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from sympy.functions.elementary.complexes import (re, im, sign, Abs,
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conjugate, arg, polar_lift, periodic_argument, unbranched_argument,
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principal_branch, transpose, adjoint, polarify, unpolarify)
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from sympy.functions.elementary.trigonometric import (sin, cos, tan,
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sec, csc, cot, sinc, asin, acos, atan, asec, acsc, acot, atan2)
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from sympy.functions.elementary.exponential import (exp_polar, exp, log,
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LambertW)
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from sympy.functions.elementary.hyperbolic import (sinh, cosh, tanh, coth,
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sech, csch, asinh, acosh, atanh, acoth, asech, acsch)
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from sympy.functions.elementary.integers import floor, ceiling, frac
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from sympy.functions.elementary.piecewise import (Piecewise, piecewise_fold,
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piecewise_exclusive)
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from sympy.functions.special.error_functions import (erf, erfc, erfi, erf2,
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erfinv, erfcinv, erf2inv, Ei, expint, E1, li, Li, Si, Ci, Shi, Chi,
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fresnels, fresnelc)
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from sympy.functions.special.gamma_functions import (gamma, lowergamma,
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uppergamma, polygamma, loggamma, digamma, trigamma, multigamma)
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from sympy.functions.special.zeta_functions import (dirichlet_eta, zeta,
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lerchphi, polylog, stieltjes, riemann_xi)
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from sympy.functions.special.tensor_functions import (Eijk, LeviCivita,
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KroneckerDelta)
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from sympy.functions.special.singularity_functions import SingularityFunction
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from sympy.functions.special.delta_functions import DiracDelta, Heaviside
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from sympy.functions.special.bsplines import bspline_basis, bspline_basis_set, interpolating_spline
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from sympy.functions.special.bessel import (besselj, bessely, besseli, besselk,
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hankel1, hankel2, jn, yn, jn_zeros, hn1, hn2, airyai, airybi, airyaiprime, airybiprime, marcumq)
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from sympy.functions.special.hyper import hyper, meijerg, appellf1
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from sympy.functions.special.polynomials import (legendre, assoc_legendre,
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hermite, hermite_prob, chebyshevt, chebyshevu, chebyshevu_root,
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chebyshevt_root, laguerre, assoc_laguerre, gegenbauer, jacobi, jacobi_normalized)
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from sympy.functions.special.spherical_harmonics import Ynm, Ynm_c, Znm
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from sympy.functions.special.elliptic_integrals import (elliptic_k,
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elliptic_f, elliptic_e, elliptic_pi)
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from sympy.functions.special.beta_functions import beta, betainc, betainc_regularized
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from sympy.functions.special.mathieu_functions import (mathieus, mathieuc,
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mathieusprime, mathieucprime)
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ln = log
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__all__ = [
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'factorial', 'factorial2', 'rf', 'ff', 'binomial', 'RisingFactorial',
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'FallingFactorial', 'subfactorial',
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'carmichael', 'fibonacci', 'lucas', 'motzkin', 'tribonacci', 'harmonic',
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'bernoulli', 'bell', 'euler', 'catalan', 'genocchi', 'andre', 'partition',
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'sqrt', 'root', 'Min', 'Max', 'Id', 'real_root', 'cbrt', 'Rem',
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're', 'im', 'sign', 'Abs', 'conjugate', 'arg', 'polar_lift',
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'periodic_argument', 'unbranched_argument', 'principal_branch',
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'transpose', 'adjoint', 'polarify', 'unpolarify',
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'sin', 'cos', 'tan', 'sec', 'csc', 'cot', 'sinc', 'asin', 'acos', 'atan',
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'asec', 'acsc', 'acot', 'atan2',
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'exp_polar', 'exp', 'ln', 'log', 'LambertW',
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'sinh', 'cosh', 'tanh', 'coth', 'sech', 'csch', 'asinh', 'acosh', 'atanh',
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'acoth', 'asech', 'acsch',
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'floor', 'ceiling', 'frac',
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'Piecewise', 'piecewise_fold', 'piecewise_exclusive',
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'erf', 'erfc', 'erfi', 'erf2', 'erfinv', 'erfcinv', 'erf2inv', 'Ei',
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'expint', 'E1', 'li', 'Li', 'Si', 'Ci', 'Shi', 'Chi', 'fresnels',
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'fresnelc',
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'gamma', 'lowergamma', 'uppergamma', 'polygamma', 'loggamma', 'digamma',
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'trigamma', 'multigamma',
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'dirichlet_eta', 'zeta', 'lerchphi', 'polylog', 'stieltjes', 'riemann_xi',
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'Eijk', 'LeviCivita', 'KroneckerDelta',
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'SingularityFunction',
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'DiracDelta', 'Heaviside',
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'bspline_basis', 'bspline_basis_set', 'interpolating_spline',
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'besselj', 'bessely', 'besseli', 'besselk', 'hankel1', 'hankel2', 'jn',
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'yn', 'jn_zeros', 'hn1', 'hn2', 'airyai', 'airybi', 'airyaiprime',
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'airybiprime', 'marcumq',
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'hyper', 'meijerg', 'appellf1',
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'legendre', 'assoc_legendre', 'hermite', 'hermite_prob', 'chebyshevt',
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'chebyshevu', 'chebyshevu_root', 'chebyshevt_root', 'laguerre',
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'assoc_laguerre', 'gegenbauer', 'jacobi', 'jacobi_normalized',
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'Ynm', 'Ynm_c', 'Znm',
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'elliptic_k', 'elliptic_f', 'elliptic_e', 'elliptic_pi',
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'beta', 'betainc', 'betainc_regularized',
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'mathieus', 'mathieuc', 'mathieusprime', 'mathieucprime',
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]
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