Vehicle-cpp/hkpc/software/sympy/functions/__init__.py

"""A functions module, includes all the standard functions.

Combinatorial - factorial, fibonacci, harmonic, bernoulli...
Elementary - hyperbolic, trigonometric, exponential, floor and ceiling, sqrt...
Special - gamma, zeta,spherical harmonics...
"""

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

__all__ = [
    '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', 'cbrt', 'Rem',

    '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', 'riemann_xi',

    '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', 'betainc', 'betainc_regularized',

    'mathieus', 'mathieuc', 'mathieusprime', 'mathieucprime',
]