Comment #6 on issue 2630 by [email protected]: DeltaIntegrate provides
wrong answer on Multivariable integrals
http://code.google.com/p/sympy/issues/detail?id=2630
Just ran into this problem again. deltaintegrate gives me nonsense results
without letting me know. Previous discussion on this issue has been about
finding when the bug was put into SymPy. This isn't the result of an
inserted bug. Deltaintegrate has always been incorrect. I've looked at this
and don't know what the solution should be. Does anyone know the standard
algorithm to handle integration of delta functions? Ours appears to be
ad-hoc. Wolfram alpha does this computation correctly.
SymPy:
In [1]: integrate(exp(-(x**2+y**2))/pi, (x,-oo, oo), (y,-oo, oo))
Out[1]: 1
In [2]: integrate(exp(-(x**2+y**2))/pi * DiracDelta(x-10*y), (x,-oo, oo),
(y,-oo, oo))
Out[2]:
_____
\/ 101
----------
____
101*\/ pi
In [3]: integrate(exp(-(x**2+y**2))/pi * DiracDelta(10*x-y), (x,-oo, oo),
(y,-oo, oo))
Out[3]:
_____
10*\/ 101
----------
____
101*\/ pi
Out[2] and Out[3] should be the same
WolframAlpha:
http://www.wolframalpha.com/input/?i=integrate+exp(-(x^2%2By^2))/(pi)+,+x+from+-infinity+to+%2Binfinity,+y+from+-infinity+to+%2Binfinity
http://www.wolframalpha.com/input/?i=integrate+exp(-(x^2%2By^2))/(pi)+*+delta(10*x-y),+x+from+-infinity+to+%2Binfinity,+y+from+-infinity+to+%2Binfinity
http://www.wolframalpha.com/input/?i=integrate+exp(-(x^2%2By^2))/(pi)+*+delta(x-10*y),+x+from+-infinity+to+%2Binfinity,+y+from+-infinity+to+%2Binfinity
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