355 lines
12 KiB
Python
355 lines
12 KiB
Python
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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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# Used in MCodePrinter._print_Function(self)
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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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"atan2": [(lambda *x: True, "ArcTan")],
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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")], # For automatic rewrites
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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] = {
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'order': None,
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'full_prec': 'auto',
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'precision': 15,
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'user_functions': {},
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'human': True,
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'allow_unknown_functions': False,
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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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# Primitive numbers
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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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# Infinity and invalid numbers
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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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# Mathematical constants
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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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# Simple rewrite to supported function possible
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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_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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