GSoC Week 4

This week, as planned, was focused on addressing the review comments from the PR.

SingularityFunction._eval_nseries function was added, as the default series expansion would check n (the parameter of nseries) times differentiability of the function, and SingularityFunction are infinite with n=-1 and n=-2 (n here refers to the power of singularity function), so they would raise a PoleError. Since the default function did not work, a custom _eval_nseries was needed.

mrv_leadterm now handles logx substitution. Gamma and factorial leading term methods now raise PoleError if arg is unbounded. They previously returned the original function itself.

It was also observed that the Limit.doit code for handling leading terms should invert cdir. Consider the limit as x->oo. In this case, the cdir parameter is set to -1, as we can only approach oo from -, + does not make sense. For finding the limit, the variable is inverted, so x->1/x and hence oo->0. So the limit becomes Limit(a(1/x), x, 0). Note that now the direction should be changed to +, to agree with oo. 0- would correspond to a negative answer, which is the case of -oo. Hence, cdir needs to be inverted.

The PR was merged just at the end of this week. Next, I will try to look at more improvements to Limit.doit, and the corresponding leading term and nseries bugs found would be fixed.