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

[JohnCremona]

comment:8

This can surely be closed as the examples posted are now computed correctly. Same as at #12198.

[tscrim]

Reviewer: Travis Scrimshaw

[zimmermann6]

comment:11

shouldn't we include a non-regression test?

[tscrim]

comment:12

I am not opposed. Feel free to use this ticket for that.

[zimmermann6]

comment:13

here is a corresponding patch:

--- a/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx
+++ b/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx
@@ -4734,6 +4734,18 @@ cdef class MPolynomial_libsingular(MPolynomial):
             sage: h = f^2
             sage: h.is_squarefree()
             False
+
+        TESTS::
+
+Check if :trac:`12129` is fixed::
+
+            sage: x, y = QQ['x','y'].gens()
+            sage: f = x*y
+            sage: f.is_squarefree()
+            True
+            sage: f = (x+y)*(x+3)
+            sage: f.is_squarefree()
+            True
         """
         # TODO:  Use Singular (4.x) intrinsics.  (Temporary solution from #17254.)
         return all([ e == 1 for (f, e) in self.factor() ])

[JohnCremona]

comment:14

I agree that tests should be added, both here and at #12198, but was a little too lazy to do it myself.

[JohnCremona]

comment:15

Travis could you re-review this? I thought that this doctest would do for both tickets. Thanks.

---

New commits:

17fdcc1

#12129: add doctest to show issue has been fixed

[JohnCremona]

Author: Paul Zimmermann, John Cremona

[JohnCremona]

Branch: u/cremona/12129

[JohnCremona]

Commit: 17fdcc1

[tscrim]

comment:16

I was also a little too lazy to do it as well. ^^;; Thanks Paul and John.