Status: Accepted
Owner: [email protected]
Labels: Type-Defect Priority-Medium WrongResult

New issue 2549 by [email protected]: as_independent gives incorrect output for some functions of non commutative symbols
http://code.google.com/p/sympy/issues/detail?id=2549

Best illustrated with examples

x,y = symbols('x,y')
n = symbols('n', commutative = False)
f = (x-n)*(x-y)
f.as_independent(x)
(x - n, x - y)
g = DiracDelta(x-n)*DiracDelta(x-y)
g.as_independent(x)
(DiracDelta(x - n), DiracDelta(x - y))

It seems that if the variable we wish to separate out is in an expression with a non-commutative symbol, then that term is treated as independent even though it clearly depends on the variable.

Because as_independent is used by integration, this means that functions which should be integrated over are treated as coefficients just because they contain non-commutative symbols. This should definitely be fixed.

Curiously, simpler cases where the non-commutative symbol is in a mul on its own work fine.

f = x*y*n
f.as_independent(x)
(y * n, x)

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