#4760 crazy question: Is "1" zero or nonzero? from one-arg limit

[Barton Willis]

This should either ask for the parity of n, or return something like (-1)^n * minf. It should not ask if `1' is zero or nonzero.

(%i1)   declare(n,integer)$

(%i2)   assume(n < 0)$

(%i3)   limit((-1)^n/zerob);
"Is "1" zero or nonzero?"nz;
(%o3)   minf

[Stavros Macrakis]

Agreed this is a bug.

Single-argument limit isn't supposed to return things like (-1)^n*minf, but to resolve them. In this case, I think the only correct result is infinity, which is what it returns for limit((-1)^x/zerob) and limit((-1)^(-x^2-1)/zerob) with no declarations on x.

[Barton Willis]

FYI: For the bit of code I was working with, I worked around this bug by using ask-integer to determine the parity of the integer. Not ideal, but it works.

[Barton Willis]

A simpler example

(%i1) assume(n < 0);
(%o1)                               [n < 0]

(%i2) asksign(-(-1)^n);
Is 1 zero or nonzero?

nz;
(%o2)                                 neg