SR.wild and maxima don't mix

[nbruin]

This came up in ask-sage:

sage: tanh(SR.wild(0)) #for references; this works
tanh($0)
sage: coth(SR.wild(0))
ValueError: The name "" is not a valid Python identifier.

The traceback shows that this error happens when trying to parse back a maxima result with bare _SAGE_VAR_ in it (i.e., a sage variable with an empty name)

It seems #20134 is implicated.

Another problem arises when a wildcard expression gets sent to maxima:

sage: sin(SR.wild(0)).simplify_full()
TypeError: ECL says: THROW: The catch MACSYMA-QUIT is undefined.

It may be that we can resolve both errors by ensuring that wildcards roundtrip properly to maxima (e.g., convert them to _SAGE_WILDCARD_0 rather than the syntactically illegal _SAGE_VAR_$0 and parse them back properly too).

It may also be that by giving coth and friends a slightly different treatment we can get them in line with tanh etc.

CC: @rwst

Component: symbolics

Reviewer: Michael Orlitzky

Issue created by migration from https://trac.sagemath.org/ticket/21444

[rwst]

comment:3

This works in 7.4beta3, i.e., the coth(SR.wild(0)) part, not the simplify of course.

[kcrisman]

comment:4

This works in 7.4beta3, i.e., the coth(SR.wild(0)) part, not the simplify of course.

I was figuring that a Pynac upgrade might do it, because I remembered you adding those functions recently. Should we have one ticket just to doctest that works, and then leave this ticket for the round-trip issue?

[rwst]

comment:5

Yes please.

[kcrisman]

comment:6

See #21455

[rwst]

comment:7

Probably a duplicate of #16335.

[orlitzky]

Reviewer: Michael Orlitzky