Better product error messages when can't multiply

[kcrisman]

See #10683, where the following less-than-helpful message was discovered.

sage: k.<b> = FiniteField(9); k
Finite Field in b of size 3^2
sage: vector([1,i]).dot_product(vector(k,[1,b]))
---------------------------------------------------------
ArithmeticError: 

Of course you can't multiply elements of the symbolic ring and this finite field. But if this happened buried deep in some other code, it could take a long time to track down.

This actually happens when you just multiply as well, unsurprisingly, so that's where it would have to be caught.

sage: k.<b> = FiniteField(9)
sage: i*b
<boom>

CC: @rbeezer @orlitzky

Component: basic arithmetic

Keywords: multiply, arithmetic, incompatible

Reviewer: Michael Orlitzky

Issue created by migration from https://trac.sagemath.org/ticket/10960

[orlitzky]

comment:1

This is fixed by Burcin's patch in #13739. I just accidentally rebased it without noticing that it had a dependency, but I think the dependency is just for the line or two of context in the patch.

Anyway, I added the test case from this ticket, so when #13739 gets applied we can close this, too.

[orlitzky]

comment:2

The fix and doctest are both in, so this can be closed.

[orlitzky]

Reviewer: Michael Orlitzky