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312 lines
10 KiB
312 lines
10 KiB
"""
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Maple code printer
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The MapleCodePrinter converts single SymPy expressions into single
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Maple expressions, using the functions defined in the Maple objects where possible.
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FIXME: This module is still under actively developed. Some functions may be not completed.
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"""
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from sympy.core import S
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from sympy.core.numbers import Integer, IntegerConstant, equal_valued
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from sympy.printing.codeprinter import CodePrinter
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from sympy.printing.precedence import precedence, PRECEDENCE
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import sympy
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_known_func_same_name = (
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'sin', 'cos', 'tan', 'sec', 'csc', 'cot', 'sinh', 'cosh', 'tanh', 'sech',
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'csch', 'coth', 'exp', 'floor', 'factorial', 'bernoulli', 'euler',
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'fibonacci', 'gcd', 'lcm', 'conjugate', 'Ci', 'Chi', 'Ei', 'Li', 'Si', 'Shi',
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'erf', 'erfc', 'harmonic', 'LambertW',
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'sqrt', # For automatic rewrites
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)
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known_functions = {
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# SymPy -> Maple
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'Abs': 'abs',
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'log': 'ln',
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'asin': 'arcsin',
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'acos': 'arccos',
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'atan': 'arctan',
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'asec': 'arcsec',
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'acsc': 'arccsc',
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'acot': 'arccot',
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'asinh': 'arcsinh',
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'acosh': 'arccosh',
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'atanh': 'arctanh',
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'asech': 'arcsech',
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'acsch': 'arccsch',
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'acoth': 'arccoth',
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'ceiling': 'ceil',
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'Max' : 'max',
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'Min' : 'min',
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'factorial2': 'doublefactorial',
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'RisingFactorial': 'pochhammer',
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'besseli': 'BesselI',
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'besselj': 'BesselJ',
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'besselk': 'BesselK',
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'bessely': 'BesselY',
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'hankelh1': 'HankelH1',
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'hankelh2': 'HankelH2',
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'airyai': 'AiryAi',
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'airybi': 'AiryBi',
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'appellf1': 'AppellF1',
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'fresnelc': 'FresnelC',
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'fresnels': 'FresnelS',
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'lerchphi' : 'LerchPhi',
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}
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for _func in _known_func_same_name:
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known_functions[_func] = _func
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number_symbols = {
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# SymPy -> Maple
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S.Pi: 'Pi',
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S.Exp1: 'exp(1)',
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S.Catalan: 'Catalan',
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S.EulerGamma: 'gamma',
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S.GoldenRatio: '(1/2 + (1/2)*sqrt(5))'
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}
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spec_relational_ops = {
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# SymPy -> Maple
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'==': '=',
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'!=': '<>'
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}
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not_supported_symbol = [
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S.ComplexInfinity
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]
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class MapleCodePrinter(CodePrinter):
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"""
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Printer which converts a SymPy expression into a maple code.
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"""
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printmethod = "_maple"
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language = "maple"
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_default_settings = {
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'order': None,
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'full_prec': 'auto',
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'human': True,
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'inline': True,
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'allow_unknown_functions': True,
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}
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def __init__(self, settings=None):
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if settings is None:
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settings = {}
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super().__init__(settings)
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self.known_functions = dict(known_functions)
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userfuncs = settings.get('user_functions', {})
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self.known_functions.update(userfuncs)
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def _get_statement(self, codestring):
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return "%s;" % codestring
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def _get_comment(self, text):
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return "# {}".format(text)
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def _declare_number_const(self, name, value):
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return "{} := {};".format(name,
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value.evalf(self._settings['precision']))
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def _format_code(self, lines):
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return lines
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def _print_tuple(self, expr):
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return self._print(list(expr))
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def _print_Tuple(self, expr):
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return self._print(list(expr))
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def _print_Assignment(self, expr):
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lhs = self._print(expr.lhs)
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rhs = self._print(expr.rhs)
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return "{lhs} := {rhs}".format(lhs=lhs, rhs=rhs)
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def _print_Pow(self, expr, **kwargs):
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PREC = precedence(expr)
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if equal_valued(expr.exp, -1):
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return '1/%s' % (self.parenthesize(expr.base, PREC))
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elif equal_valued(expr.exp, 0.5):
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return 'sqrt(%s)' % self._print(expr.base)
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elif equal_valued(expr.exp, -0.5):
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return '1/sqrt(%s)' % self._print(expr.base)
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else:
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return '{base}^{exp}'.format(
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base=self.parenthesize(expr.base, PREC),
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exp=self.parenthesize(expr.exp, PREC))
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def _print_Piecewise(self, expr):
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if (expr.args[-1].cond is not True) and (expr.args[-1].cond != S.BooleanTrue):
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# We need the last conditional to be a True, otherwise the resulting
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# function may not return a result.
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raise ValueError("All Piecewise expressions must contain an "
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"(expr, True) statement to be used as a default "
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"condition. Without one, the generated "
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"expression may not evaluate to anything under "
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"some condition.")
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_coup_list = [
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("{c}, {e}".format(c=self._print(c),
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e=self._print(e)) if c is not True and c is not S.BooleanTrue else "{e}".format(
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e=self._print(e)))
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for e, c in expr.args]
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_inbrace = ', '.join(_coup_list)
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return 'piecewise({_inbrace})'.format(_inbrace=_inbrace)
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def _print_Rational(self, expr):
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p, q = int(expr.p), int(expr.q)
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return "{p}/{q}".format(p=str(p), q=str(q))
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def _print_Relational(self, expr):
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PREC=precedence(expr)
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lhs_code = self.parenthesize(expr.lhs, PREC)
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rhs_code = self.parenthesize(expr.rhs, PREC)
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op = expr.rel_op
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if op in spec_relational_ops:
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op = spec_relational_ops[op]
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return "{lhs} {rel_op} {rhs}".format(lhs=lhs_code, rel_op=op, rhs=rhs_code)
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def _print_NumberSymbol(self, expr):
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return number_symbols[expr]
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def _print_NegativeInfinity(self, expr):
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return '-infinity'
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def _print_Infinity(self, expr):
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return 'infinity'
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def _print_Idx(self, expr):
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return self._print(expr.label)
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def _print_BooleanTrue(self, expr):
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return "true"
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def _print_BooleanFalse(self, expr):
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return "false"
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def _print_bool(self, expr):
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return 'true' if expr else 'false'
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def _print_NaN(self, expr):
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return 'undefined'
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def _get_matrix(self, expr, sparse=False):
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if S.Zero in expr.shape:
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_strM = 'Matrix([], storage = {storage})'.format(
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storage='sparse' if sparse else 'rectangular')
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else:
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_strM = 'Matrix({list}, storage = {storage})'.format(
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list=self._print(expr.tolist()),
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storage='sparse' if sparse else 'rectangular')
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return _strM
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def _print_MatrixElement(self, expr):
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return "{parent}[{i_maple}, {j_maple}]".format(
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parent=self.parenthesize(expr.parent, PRECEDENCE["Atom"], strict=True),
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i_maple=self._print(expr.i + 1),
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j_maple=self._print(expr.j + 1))
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def _print_MatrixBase(self, expr):
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return self._get_matrix(expr, sparse=False)
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def _print_SparseRepMatrix(self, expr):
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return self._get_matrix(expr, sparse=True)
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def _print_Identity(self, expr):
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if isinstance(expr.rows, (Integer, IntegerConstant)):
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return self._print(sympy.SparseMatrix(expr))
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else:
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return "Matrix({var_size}, shape = identity)".format(var_size=self._print(expr.rows))
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def _print_MatMul(self, expr):
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PREC=precedence(expr)
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_fact_list = list(expr.args)
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_const = None
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if not isinstance(_fact_list[0], (sympy.MatrixBase, sympy.MatrixExpr,
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sympy.MatrixSlice, sympy.MatrixSymbol)):
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_const, _fact_list = _fact_list[0], _fact_list[1:]
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if _const is None or _const == 1:
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return '.'.join(self.parenthesize(_m, PREC) for _m in _fact_list)
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else:
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return '{c}*{m}'.format(c=_const, m='.'.join(self.parenthesize(_m, PREC) for _m in _fact_list))
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def _print_MatPow(self, expr):
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# This function requires LinearAlgebra Function in Maple
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return 'MatrixPower({A}, {n})'.format(A=self._print(expr.base), n=self._print(expr.exp))
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def _print_HadamardProduct(self, expr):
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PREC = precedence(expr)
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_fact_list = list(expr.args)
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return '*'.join(self.parenthesize(_m, PREC) for _m in _fact_list)
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def _print_Derivative(self, expr):
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_f, (_var, _order) = expr.args
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if _order != 1:
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_second_arg = '{var}${order}'.format(var=self._print(_var),
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order=self._print(_order))
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else:
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_second_arg = '{var}'.format(var=self._print(_var))
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return 'diff({func_expr}, {sec_arg})'.format(func_expr=self._print(_f), sec_arg=_second_arg)
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def maple_code(expr, assign_to=None, **settings):
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r"""Converts ``expr`` to a string of Maple code.
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Parameters
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==========
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expr : Expr
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A SymPy expression to be converted.
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assign_to : optional
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When given, the argument is used as the name of the variable to which
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the expression is assigned. Can be a string, ``Symbol``,
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``MatrixSymbol``, or ``Indexed`` type. This can be helpful for
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expressions that generate multi-line statements.
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precision : integer, optional
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The precision for numbers such as pi [default=16].
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user_functions : dict, optional
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A dictionary where keys are ``FunctionClass`` instances and values are
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their string representations. Alternatively, the dictionary value can
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be a list of tuples i.e. [(argument_test, cfunction_string)]. See
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below for examples.
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human : bool, optional
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If True, the result is a single string that may contain some constant
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declarations for the number symbols. If False, the same information is
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returned in a tuple of (symbols_to_declare, not_supported_functions,
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code_text). [default=True].
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contract: bool, optional
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If True, ``Indexed`` instances are assumed to obey tensor contraction
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rules and the corresponding nested loops over indices are generated.
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Setting contract=False will not generate loops, instead the user is
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responsible to provide values for the indices in the code.
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[default=True].
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inline: bool, optional
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If True, we try to create single-statement code instead of multiple
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statements. [default=True].
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"""
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return MapleCodePrinter(settings).doprint(expr, assign_to)
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def print_maple_code(expr, **settings):
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"""Prints the Maple representation of the given expression.
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See :func:`maple_code` for the meaning of the optional arguments.
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Examples
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========
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>>> from sympy import print_maple_code, symbols
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>>> x, y = symbols('x y')
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>>> print_maple_code(x, assign_to=y)
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y := x
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"""
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print(maple_code(expr, **settings))
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