Status: Accepted
Owner: ----
Labels: Type-Defect Priority-Medium Integration

New issue 1426 by Vinzent.Steinberg: failing integral
http://code.google.com/p/sympy/issues/detail?id=1426

>>> e=(x**m * (1 - x)**n * (a + b*x + c*x**2))/(1 + x**2)
>>> e
x**m*(1 - x)**n*(a + b*x + c*x**2)/(1 + x**2)
>>> integrate(e, (x,0,1))
Traceback (most recent call last):
   File "/base/data/home/apps/sympy-live/1.332569642222447358/shell.py",
line 296, in get
     exec compiled in statement_module.__dict__
   File "<string>", line 1, in <module>
   File
"/base/data/home/apps/sympy-live/1.332569642222447358/sympy/utilities/decorator.py",
line 55, in threaded_decorator
     return func(expr, *args, **kwargs)
   File
"/base/data/home/apps/sympy-live/1.332569642222447358/sympy/integrals/integrals.py",
line 395, in integrate
     return integral.doit()
   File
"/base/data/home/apps/sympy-live/1.332569642222447358/sympy/integrals/integrals.py",
line 134, in doit
     antideriv = self._eval_integral(function, x)
   File "/base/data/home/apps/sympy-live/1.332569642222447358/sympy
/integrals/integrals.py", line 307, in _eval_integral
     h = heurisch(g, x, hints=[])
   File
"/base/data/home/apps/sympy-live/1.332569642222447358/sympy/integrals/risch.py",
line 216, in heurisch
     denom = reduce(lambda p, q: lcm(p, q, V), denoms)
   File
"/base/data/home/apps/sympy-live/1.332569642222447358/sympy/integrals/risch.py",
line 216, in <lambda>
     denom = reduce(lambda p, q: lcm(p, q, V), denoms)
   File "<string>", line 3, in lcm
   File
"/base/data/home/apps/sympy-live/1.332569642222447358/sympy/polys/wrappers.py",
line 23, in _map_basic
     result = f(*_conv_args(n, args), **kwargs)
   File
"/base/data/home/apps/sympy-live/1.332569642222447358/sympy/polys/algorithms.py",
line 366, in poly_lcm
     f = Poly(f, *symbols)
   File
"/base/data/home/apps/sympy-live/1.332569642222447358/sympy/polys/polynomial.py",
line 402, in __new__
     terms = Poly._decompose(poly, *symbols)
   File
"/base/data/home/apps/sympy-live/1.332569642222447358/sympy/polys/polynomial.py",
line 545, in _decompose
     raise PolynomialError("Can't decompose %s" % factor)
PolynomialError: Can't decompose _x4**(4 - 2*m)

If we can't do it, Integral() should be returned instead.

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