def _eval_evalf(self, prec): try: _roots = self.poly.nroots(n=prec_to_dps(prec)) except (DomainError, PolynomialError): return self else: return Add(*[self.fun(r) for r in _roots])
def doit(self, **hints): if not hints.get('roots', True): return self _roots = roots(self.poly, multiple=True) if len(_roots) < self.poly.degree(): return self else: return Add(*[self.fun(r) for r in _roots])
def _print_Add(self, expr): # purpose: print complex numbers nicely in Fortran. # collect the purely real and purely imaginary parts: pure_real = [] pure_imaginary = [] mixed = [] for arg in expr.args: if arg.is_number and arg.is_extended_real: pure_real.append(arg) elif arg.is_number and arg.is_imaginary: pure_imaginary.append(arg) else: mixed.append(arg) if len(pure_imaginary) > 0: if len(mixed) > 0: PREC = precedence(expr) term = Add(*mixed) t = self._print(term) if t.startswith('-'): sign = "-" t = t[1:] else: sign = "+" if precedence(term) < PREC: t = "(%s)" % t return "cmplx(%s,%s) %s %s" % ( self._print(Add(*pure_real)), self._print(-S.ImaginaryUnit * Add(*pure_imaginary)), sign, t, ) else: return "cmplx(%s,%s)" % ( self._print(Add(*pure_real)), self._print(-S.ImaginaryUnit * Add(*pure_imaginary)), ) else: return CodePrinter._print_Add(self, expr)
def ratsimp(expr): """ Put an expression over a common denominator, cancel and reduce. Examples ======== >>> from diofant import ratsimp >>> from diofant.abc import x, y >>> ratsimp(1/x + 1/y) (x + y)/(x*y) """ f, g = cancel(expr).as_numer_denom() try: Q, r = reduced(f, [g], field=True, expand=False) except ComputationFailed: return f / g return Add(*Q) + cancel(r / g)