Fix product(-x, x, 1, SR.var('n')) to return (-1)^n*factorial(n)

[slel]

From #30520.

Observed:

sage: product(-x, x, 1, SR.var('n'))
#0: simplify_product(product='product(-_SAGE_VAR_x,_SAGE_VAR_x,1,_SAGE_VAR_n))
...
Traceback (most recent call last)
...
RuntimeError: ECL says: Error executing code in Maxima:
factorial: factorial of negative integer -1 not defined.

or equivalently:

sage: from sage.calculus.calculus import symbolic_product
sage: x, n = SR.var('x, n')
sage: symbolic_product(-x, x, 1, n)
#0: simplify_product(product='product(-_SAGE_VAR_x,_SAGE_VAR_x,1,_SAGE_VAR_n))
...
Traceback (most recent call last)
...
RuntimeError: ECL says: Error executing code in Maxima:
factorial: factorial of negative integer -1 not defined.

Expected:

sage: from sage.calculus.calculus import symbolic_product
sage: x, n = SR.var('x, n')
sage: symbolic_product(-x, x, 1, n)
(-1)^n*factorial(n)

Upstream: Reported upstream. Developers acknowledge bug.

CC: @robert-dodier @slel

Component: symbolics

Keywords: symbolic_product, maxima

Issue created by migration from https://trac.sagemath.org/ticket/31557

[slel]

comment:1

Robert Dodier's analysis at #30520, comment 16 points to:

https://github.com/andrejv/maxima/blob/5.36.0.1/share/solve_rec/solve_rec.mac#L1095-L1112

[robert-dodier]

comment:2

I've pushed commit c584c24 on maxima-code/master to fix this bug.

[slel]

Upstream: Fixed upstream, but not in a stable release.

[slel]

comment:3

Thanks for fixing this and for the heads-up.

This should be applied as a patch in Sage until
a Maxima release has this and we upgrade to it.

[slel]

comment:4

Adding link to commit to ticket description.

• https://sourceforge.net/p/maxima/code/ci/c584c24ac0542a4ada435aad41f1e5adf892bbc2/

[robert-dodier]

comment:5

Oops, spoke too soon. Commit c584c24 causes a stack overflow in some other code (namely simplify_sum). Commit c584c24 has been reverted, and I'm working on an update. Sorry to say the problem isn't actually fixed yet.

[mkoeppe]

comment:6

Moving to 9.4, as 9.3 has been released.

[DaveWitteMorris]

Changed upstream from Fixed upstream, but not in a stable release. to Reported upstream. Developers acknowledge bug.