random doctest failure in rings/polynomial/polynomial_element_generic.py

[yyyyx4]

Part of #32544:

sage -t --long --random-seed=43805222569518434108329399959452339425 src/sage/rings/polynomial/polynomial_element_generic.py
**********************************************************************
File "src/sage/rings/polynomial/polynomial_element_generic.py", line 783, in sage.rings.polynomial.polynomial_element_generic.Polynomial_generic_sparse.quo_rem
Failed example:
    f.quo_rem(g)
Expected:
    Traceback (most recent call last):
    ...
    ArithmeticError: Division non exact (consider coercing to polynomials over the fraction field)
Got:
    (-y^5 + 2*y^2, y^3 - 2*x^2*y^2 - y)
**********************************************************************

(From a patchbot run in #32380.)

CC: @tscrim

Component: algebra

Author: Jonathan Kliem

Branch/Commit: 0f7cca7

Reviewer: Markus Wageringel

Issue created by migration from https://trac.sagemath.org/ticket/32816

[kliem]

comment:1

Took a while to understand what the doctest is about.

Thing is, Euclidean algorithm may still work, if the leading coefficient is not a unit, e.g.
25*x^2 + 5*x is divisible by 5*x. Its a bit like claiming, that integers cannot be divided...

---

New commits:

0f7cca7

euclidean division may still work, if the leading coefficient is not a unit

[kliem]

Author: Jonathan Kliem

[kliem]

Branch: public/32816

[kliem]

Commit: 0f7cca7

[mwageringel]

comment:2

LGTM.

[mwageringel]

Reviewer: Markus Wageringel

[kliem]

comment:3

Thank you.

[vbraun]

Changed branch from public/32816 to 0f7cca7