fix wrong results & huge slowdown due to broken caching in .multiplication_by_m() #33156
Description
On 9.5.rc0:
sage: E = EllipticCurve(GF(65537), [5,5])
sage: %prun _ = E.multiplication_by_m(127)
5078 function calls (4879 primitive calls) in 0.406 seconds
[...]
sage: %prun _ = E.multiplication_by_m(127, x_only=True)
327932 function calls (327450 primitive calls) in 21.238 seconds
Ordered by: internal time
ncalls tottime percall cumtime percall filename:lineno(function)
32263 19.549 0.001 19.584 0.001 polynomial_ring.py:309(_element_constructor_)
[...]
The main reason seems to be the same as that underlying #33164: The variables x of PolynomialRing(R,'x') and PolynomialRing(R,'x,y') compare equal, hence we obtain a multivariate polynomial when querying the cache with the univariate variable, and then we run into the multivariate incarnation of #33165.
This can also lead to incorrect results when using the ._multiple_x_{numerator,denominator}() methods directly:
sage: E = EllipticCurve(GF(65537), [5,5])
sage: R.<x> = E.base_field()[]
sage: E._multiple_x_numerator(5, x=R.quotient(x^2).gen())
10220*xbar + 42539
sage: E._multiple_x_numerator(5)
10220*xbar + 42539
Component: elliptic curves
Author: Lorenz Panny
Branch/Commit: 1f2fd60
Reviewer: Travis Scrimshaw
Issue created by migration from https://trac.sagemath.org/ticket/33156