Updates:
Status: Accepted
Cc: mattpap
Comment #4 on issue 1576 by asmeurer: Integral of strictly positive
function is zero
http://code.google.com/p/sympy/issues/detail?id=1576
This was working in Sympy 0.6.7, but something in the new polys broke it:
In [1]: f = Symbol('f')
In [2]: fn=Symbol('fn', positive=True)
In [3]: integrate(4*pi**2*f**2*fn**4*(fn**2+9*f**2)/(fn**2+f**2)**3, f)
---------------------------------------------------------------------------
NotInvertible Traceback (most recent call last)
/Users/aaronmeurer/Documents/python/sympy/sympy-scratch/<ipython console>
in <module>()
/Users/aaronmeurer/Documents/python/sympy/sympy-scratch/sympy/utilities/decorator.pyc
in
threaded_decorator(expr, *args, **kwargs)
54 return Add(*[ func(f, *args, **kwargs) for f in
expr.args ])
55 else:
---> 56 return func(expr, *args, **kwargs)
57
58 threaded_decorator.__doc__ = func.__doc__
/Users/aaronmeurer/Documents/python/sympy/sympy-scratch/sympy/integrals/integrals.pyc
in
integrate(*args, **kwargs)
539
540 if isinstance(integral, Integral):
--> 541 return integral.doit(deep = False)
542 else:
543 return integral
/Users/aaronmeurer/Documents/python/sympy/sympy-scratch/sympy/integrals/integrals.pyc
in
doit(self,
**hints)
152
153 for x,ab in self.limits:
--> 154 antideriv = self._eval_integral(function, x)
155
156 if antideriv is None:
/Users/aaronmeurer/Documents/python/sympy/sympy-scratch/sympy/integrals/integrals.pyc
in
_eval_integral(self, f, x)
329 # poly(x)
330 if g.is_rational_function(x):
--> 331 parts.append(coeff * ratint(g, x))
332 continue
333
/Users/aaronmeurer/Documents/python/sympy/sympy-scratch/sympy/integrals/rationaltools.py
in
ratint(f,
x, **flags)
62 t = symbol
63
---> 64 L = ratint_logpart(r, Q, x, t)
65
66 real = flags.get('real')
/Users/aaronmeurer/Documents/python/sympy/sympy-scratch/sympy/integrals/rationaltools.py
in
ratint_logpart(f, g, x, t)
184 h = h.exquo(Poly(a.gcd(q)**j, x))
185
--> 186 inv, coeffs = h_lc.invert(q), [S(1)]
187
188 for coeff in h.coeffs()[1:]:
/Users/aaronmeurer/Documents/python/sympy/sympy-scratch/sympy/polys/polytools.py
in
invert(f, g,
**args)
969
970 try:
--> 971 result = F.invert(G)
972 except AttributeError:
973 raise OperationNotSupported(f, 'invert')
/Users/aaronmeurer/Documents/python/sympy/sympy-scratch/sympy/polys/polyclasses.py
in
invert(f, g)
1328
1329 if not lev:
-> 1330 return per(dup_invert(F, G, dom))
1331 else:
1332 raise ValueError('univariate polynomial expected')
/Users/aaronmeurer/Documents/python/sympy/sympy-scratch/sympy/polys/densetools.py
in
dup_invert(f,
g, K)
303 return dup_rem(s, g, K)
304 else:
--> 305 raise NotInvertible("zero divisor")
306
307 def dup_inner_subresultants(f, g, K):
NotInvertible: zero divisor
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