Apparently running

assume(x<1/8)

first gives a more correct answer (or at least the Sympy answer). If that helps narrow it down.

Last edit: Anonymous 2016-01-12

Maxima 5.27.0 http://maxima.sourceforge.net

using Lisp SBCL 1.0.24

Distributed under the GNU Public License. See the file COPYING.

Dedicated to the memory of William Schelter.

The function bug_report() provides bug reporting information.

(%i1) residue(( x/((4*x - 1)*(t^2 - t + x)) ),t,(1-sqrt(1-4*x))/2);

(%o1) 0

But apparently this should give a result in x?

sage: from sympy import Symbol, residue

sage: x = Symbol("x")

sage: t = Symbol("t")

sage: residue(x/((4*x - 1)*(t^2 - t + x)),t,(1-sqrt(1-4*x))/2)

-x/((-4*x + 1)**(1/2)*(4*x - 1))

This was first reported at http://ask.sagemath.org/question/1588/calculating-residue-with-maxima_methods

I make no claim for the mathematical correctness - just reporting quickly - but since the function has t in the denominator, that it would be nonzero seems reasonable.