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""" |
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Mathematica code printer |
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""" |
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from __future__ import annotations |
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from typing import Any |
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from sympy.core import Basic, Expr, Float |
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from sympy.core.sorting import default_sort_key |
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from sympy.printing.codeprinter import CodePrinter |
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from sympy.printing.precedence import precedence |
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known_functions = { |
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"exp": [(lambda x: True, "Exp")], |
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"log": [(lambda x: True, "Log")], |
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"sin": [(lambda x: True, "Sin")], |
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"cos": [(lambda x: True, "Cos")], |
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"tan": [(lambda x: True, "Tan")], |
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"cot": [(lambda x: True, "Cot")], |
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"sec": [(lambda x: True, "Sec")], |
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"csc": [(lambda x: True, "Csc")], |
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"asin": [(lambda x: True, "ArcSin")], |
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"acos": [(lambda x: True, "ArcCos")], |
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"atan": [(lambda x: True, "ArcTan")], |
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"acot": [(lambda x: True, "ArcCot")], |
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"asec": [(lambda x: True, "ArcSec")], |
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"acsc": [(lambda x: True, "ArcCsc")], |
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"sinh": [(lambda x: True, "Sinh")], |
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"cosh": [(lambda x: True, "Cosh")], |
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"tanh": [(lambda x: True, "Tanh")], |
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"coth": [(lambda x: True, "Coth")], |
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"sech": [(lambda x: True, "Sech")], |
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"csch": [(lambda x: True, "Csch")], |
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"asinh": [(lambda x: True, "ArcSinh")], |
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"acosh": [(lambda x: True, "ArcCosh")], |
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"atanh": [(lambda x: True, "ArcTanh")], |
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"acoth": [(lambda x: True, "ArcCoth")], |
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"asech": [(lambda x: True, "ArcSech")], |
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"acsch": [(lambda x: True, "ArcCsch")], |
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"sinc": [(lambda x: True, "Sinc")], |
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"conjugate": [(lambda x: True, "Conjugate")], |
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"Max": [(lambda *x: True, "Max")], |
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"Min": [(lambda *x: True, "Min")], |
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"erf": [(lambda x: True, "Erf")], |
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"erf2": [(lambda *x: True, "Erf")], |
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"erfc": [(lambda x: True, "Erfc")], |
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"erfi": [(lambda x: True, "Erfi")], |
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"erfinv": [(lambda x: True, "InverseErf")], |
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"erfcinv": [(lambda x: True, "InverseErfc")], |
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"erf2inv": [(lambda *x: True, "InverseErf")], |
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"expint": [(lambda *x: True, "ExpIntegralE")], |
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"Ei": [(lambda x: True, "ExpIntegralEi")], |
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"fresnelc": [(lambda x: True, "FresnelC")], |
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"fresnels": [(lambda x: True, "FresnelS")], |
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"gamma": [(lambda x: True, "Gamma")], |
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"uppergamma": [(lambda *x: True, "Gamma")], |
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"polygamma": [(lambda *x: True, "PolyGamma")], |
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"loggamma": [(lambda x: True, "LogGamma")], |
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"beta": [(lambda *x: True, "Beta")], |
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"Ci": [(lambda x: True, "CosIntegral")], |
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"Si": [(lambda x: True, "SinIntegral")], |
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"Chi": [(lambda x: True, "CoshIntegral")], |
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"Shi": [(lambda x: True, "SinhIntegral")], |
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"li": [(lambda x: True, "LogIntegral")], |
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"factorial": [(lambda x: True, "Factorial")], |
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"factorial2": [(lambda x: True, "Factorial2")], |
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"subfactorial": [(lambda x: True, "Subfactorial")], |
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"catalan": [(lambda x: True, "CatalanNumber")], |
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"harmonic": [(lambda *x: True, "HarmonicNumber")], |
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"lucas": [(lambda x: True, "LucasL")], |
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"RisingFactorial": [(lambda *x: True, "Pochhammer")], |
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"FallingFactorial": [(lambda *x: True, "FactorialPower")], |
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"laguerre": [(lambda *x: True, "LaguerreL")], |
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"assoc_laguerre": [(lambda *x: True, "LaguerreL")], |
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"hermite": [(lambda *x: True, "HermiteH")], |
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"jacobi": [(lambda *x: True, "JacobiP")], |
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"gegenbauer": [(lambda *x: True, "GegenbauerC")], |
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"chebyshevt": [(lambda *x: True, "ChebyshevT")], |
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"chebyshevu": [(lambda *x: True, "ChebyshevU")], |
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"legendre": [(lambda *x: True, "LegendreP")], |
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"assoc_legendre": [(lambda *x: True, "LegendreP")], |
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"mathieuc": [(lambda *x: True, "MathieuC")], |
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"mathieus": [(lambda *x: True, "MathieuS")], |
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"mathieucprime": [(lambda *x: True, "MathieuCPrime")], |
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"mathieusprime": [(lambda *x: True, "MathieuSPrime")], |
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"stieltjes": [(lambda x: True, "StieltjesGamma")], |
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"elliptic_e": [(lambda *x: True, "EllipticE")], |
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"elliptic_f": [(lambda *x: True, "EllipticE")], |
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"elliptic_k": [(lambda x: True, "EllipticK")], |
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"elliptic_pi": [(lambda *x: True, "EllipticPi")], |
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"zeta": [(lambda *x: True, "Zeta")], |
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"dirichlet_eta": [(lambda x: True, "DirichletEta")], |
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"riemann_xi": [(lambda x: True, "RiemannXi")], |
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"besseli": [(lambda *x: True, "BesselI")], |
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"besselj": [(lambda *x: True, "BesselJ")], |
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"besselk": [(lambda *x: True, "BesselK")], |
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"bessely": [(lambda *x: True, "BesselY")], |
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"hankel1": [(lambda *x: True, "HankelH1")], |
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"hankel2": [(lambda *x: True, "HankelH2")], |
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"airyai": [(lambda x: True, "AiryAi")], |
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"airybi": [(lambda x: True, "AiryBi")], |
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"airyaiprime": [(lambda x: True, "AiryAiPrime")], |
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"airybiprime": [(lambda x: True, "AiryBiPrime")], |
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"polylog": [(lambda *x: True, "PolyLog")], |
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"lerchphi": [(lambda *x: True, "LerchPhi")], |
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"gcd": [(lambda *x: True, "GCD")], |
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"lcm": [(lambda *x: True, "LCM")], |
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"jn": [(lambda *x: True, "SphericalBesselJ")], |
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"yn": [(lambda *x: True, "SphericalBesselY")], |
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"hyper": [(lambda *x: True, "HypergeometricPFQ")], |
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"meijerg": [(lambda *x: True, "MeijerG")], |
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"appellf1": [(lambda *x: True, "AppellF1")], |
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"DiracDelta": [(lambda x: True, "DiracDelta")], |
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"Heaviside": [(lambda x: True, "HeavisideTheta")], |
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"KroneckerDelta": [(lambda *x: True, "KroneckerDelta")], |
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"sqrt": [(lambda x: True, "Sqrt")], |
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} |
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class MCodePrinter(CodePrinter): |
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"""A printer to convert Python expressions to |
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strings of the Wolfram's Mathematica code |
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""" |
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printmethod = "_mcode" |
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language = "Wolfram Language" |
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_default_settings: dict[str, Any] = dict(CodePrinter._default_settings, **{ |
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'precision': 15, |
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'user_functions': {}, |
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}) |
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_number_symbols: set[tuple[Expr, Float]] = set() |
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_not_supported: set[Basic] = set() |
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def __init__(self, settings={}): |
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"""Register function mappings supplied by user""" |
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CodePrinter.__init__(self, settings) |
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self.known_functions = dict(known_functions) |
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userfuncs = settings.get('user_functions', {}).copy() |
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for k, v in userfuncs.items(): |
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if not isinstance(v, list): |
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userfuncs[k] = [(lambda *x: True, v)] |
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self.known_functions.update(userfuncs) |
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def _format_code(self, lines): |
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return lines |
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def _print_Pow(self, expr): |
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PREC = precedence(expr) |
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return '%s^%s' % (self.parenthesize(expr.base, PREC), |
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self.parenthesize(expr.exp, PREC)) |
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def _print_Mul(self, expr): |
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PREC = precedence(expr) |
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c, nc = expr.args_cnc() |
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res = super()._print_Mul(expr.func(*c)) |
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if nc: |
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res += '*' |
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res += '**'.join(self.parenthesize(a, PREC) for a in nc) |
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return res |
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def _print_Relational(self, expr): |
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lhs_code = self._print(expr.lhs) |
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rhs_code = self._print(expr.rhs) |
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op = expr.rel_op |
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return "{} {} {}".format(lhs_code, op, rhs_code) |
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def _print_Zero(self, expr): |
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return '0' |
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def _print_One(self, expr): |
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return '1' |
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def _print_NegativeOne(self, expr): |
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return '-1' |
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def _print_Half(self, expr): |
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return '1/2' |
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def _print_ImaginaryUnit(self, expr): |
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return 'I' |
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def _print_Infinity(self, expr): |
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return 'Infinity' |
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def _print_NegativeInfinity(self, expr): |
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return '-Infinity' |
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def _print_ComplexInfinity(self, expr): |
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return 'ComplexInfinity' |
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def _print_NaN(self, expr): |
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return 'Indeterminate' |
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def _print_Exp1(self, expr): |
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return 'E' |
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def _print_Pi(self, expr): |
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return 'Pi' |
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def _print_GoldenRatio(self, expr): |
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return 'GoldenRatio' |
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def _print_TribonacciConstant(self, expr): |
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expanded = expr.expand(func=True) |
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PREC = precedence(expr) |
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return self.parenthesize(expanded, PREC) |
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def _print_EulerGamma(self, expr): |
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return 'EulerGamma' |
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def _print_Catalan(self, expr): |
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return 'Catalan' |
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def _print_list(self, expr): |
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return '{' + ', '.join(self.doprint(a) for a in expr) + '}' |
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_print_tuple = _print_list |
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_print_Tuple = _print_list |
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def _print_ImmutableDenseMatrix(self, expr): |
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return self.doprint(expr.tolist()) |
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def _print_ImmutableSparseMatrix(self, expr): |
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def print_rule(pos, val): |
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return '{} -> {}'.format( |
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self.doprint((pos[0]+1, pos[1]+1)), self.doprint(val)) |
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def print_data(): |
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items = sorted(expr.todok().items(), key=default_sort_key) |
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return '{' + \ |
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', '.join(print_rule(k, v) for k, v in items) + \ |
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'}' |
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def print_dims(): |
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return self.doprint(expr.shape) |
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return 'SparseArray[{}, {}]'.format(print_data(), print_dims()) |
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def _print_ImmutableDenseNDimArray(self, expr): |
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return self.doprint(expr.tolist()) |
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def _print_ImmutableSparseNDimArray(self, expr): |
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def print_string_list(string_list): |
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return '{' + ', '.join(a for a in string_list) + '}' |
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def to_mathematica_index(*args): |
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"""Helper function to change Python style indexing to |
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Pathematica indexing. |
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Python indexing (0, 1 ... n-1) |
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-> Mathematica indexing (1, 2 ... n) |
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""" |
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return tuple(i + 1 for i in args) |
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def print_rule(pos, val): |
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"""Helper function to print a rule of Mathematica""" |
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return '{} -> {}'.format(self.doprint(pos), self.doprint(val)) |
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def print_data(): |
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"""Helper function to print data part of Mathematica |
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sparse array. |
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It uses the fourth notation ``SparseArray[data,{d1,d2,...}]`` |
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from |
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https://reference.wolfram.com/language/ref/SparseArray.html |
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``data`` must be formatted with rule. |
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""" |
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return print_string_list( |
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[print_rule( |
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to_mathematica_index(*(expr._get_tuple_index(key))), |
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value) |
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for key, value in sorted(expr._sparse_array.items())] |
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) |
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def print_dims(): |
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"""Helper function to print dimensions part of Mathematica |
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sparse array. |
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It uses the fourth notation ``SparseArray[data,{d1,d2,...}]`` |
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from |
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https://reference.wolfram.com/language/ref/SparseArray.html |
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""" |
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return self.doprint(expr.shape) |
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return 'SparseArray[{}, {}]'.format(print_data(), print_dims()) |
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def _print_Function(self, expr): |
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if expr.func.__name__ in self.known_functions: |
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cond_mfunc = self.known_functions[expr.func.__name__] |
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for cond, mfunc in cond_mfunc: |
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if cond(*expr.args): |
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return "%s[%s]" % (mfunc, self.stringify(expr.args, ", ")) |
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elif expr.func.__name__ in self._rewriteable_functions: |
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target_f, required_fs = self._rewriteable_functions[expr.func.__name__] |
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if self._can_print(target_f) and all(self._can_print(f) for f in required_fs): |
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return self._print(expr.rewrite(target_f)) |
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return expr.func.__name__ + "[%s]" % self.stringify(expr.args, ", ") |
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_print_MinMaxBase = _print_Function |
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def _print_LambertW(self, expr): |
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if len(expr.args) == 1: |
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return "ProductLog[{}]".format(self._print(expr.args[0])) |
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return "ProductLog[{}, {}]".format( |
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self._print(expr.args[1]), self._print(expr.args[0])) |
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def _print_atan2(self, expr): |
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return "ArcTan[{}, {}]".format( |
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self._print(expr.args[1]), self._print(expr.args[0])) |
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def _print_Integral(self, expr): |
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if len(expr.variables) == 1 and not expr.limits[0][1:]: |
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args = [expr.args[0], expr.variables[0]] |
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else: |
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args = expr.args |
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return "Hold[Integrate[" + ', '.join(self.doprint(a) for a in args) + "]]" |
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def _print_Sum(self, expr): |
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return "Hold[Sum[" + ', '.join(self.doprint(a) for a in expr.args) + "]]" |
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def _print_Derivative(self, expr): |
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dexpr = expr.expr |
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dvars = [i[0] if i[1] == 1 else i for i in expr.variable_count] |
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return "Hold[D[" + ', '.join(self.doprint(a) for a in [dexpr] + dvars) + "]]" |
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def _get_comment(self, text): |
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return "(* {} *)".format(text) |
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def mathematica_code(expr, **settings): |
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r"""Converts an expr to a string of the Wolfram Mathematica code |
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Examples |
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======== |
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>>> from sympy import mathematica_code as mcode, symbols, sin |
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>>> x = symbols('x') |
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>>> mcode(sin(x).series(x).removeO()) |
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'(1/120)*x^5 - 1/6*x^3 + x' |
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""" |
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return MCodePrinter(settings).doprint(expr) |
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