MPolynomial_libsingular.is_squarefree fails with linear factors

[culler]

sage: x, y = QQ['x','y'].gens()
sage: f = x*y
sage: f.is_squarefree()
False
sage: f = (x+y)*(x+3)
sage: f.is_squarefree()
False

This may be related to an inconsistency in the Singular sqrfree function, which sometimes includes a unit in the square free factorization, but other times does not.

CC: @sagetrac-jakobkroeker

Component: algebra

Keywords: square free

Stopgaps: todo

Author: Paul Zimmermann, John Cremona

Branch/Commit: u/cremona/12129 @ 17fdcc1

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/12129

[zimmermann6]

comment:1

see also #12198 and #12404. Maybe some of those tickets can be removed as duplicate.

Paul

[sagetrac-jakobkroeker]

Stopgaps: todo