fix is_free method for new version Singular

[cxzhong]

Since the Singular 4.4.1p4 treat the zero element as the lastest element of free resolution. So we need to check the lastest term is zero or not. And someone may use the system's singular. Like the Ubuntu package is 4.4.1p3. It also has the problem.

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[dimpase]

@jhpalmieri - this should be also fixing some of the doctests errors you report with Homebrew Singular, could you have a look?

[jhpalmieri]

I unfortunately still get doctest failures with this (and I think the same doctest failures — no change in behavior).

[cxzhong]

I unfortunately still get doctest failures with this (and I think the same doctest failures — no change in behavior).

It is just fix the is_free method. there are many function changes break the doctests. First, check the version of Singular you used is 4.4.1p4 or other version larger than 4.4.1 p1
Can you run

sage: a = hyperplane_arrangements.IshB(2)
sage: a.cone().is_free()

If it returns True. Then this patch fixed the issue

[jhpalmieri]

Expanding on my earlier comment: compared to the issue reported at #40873, this fixes two doctest failures: in geometry/hyperplane_arrangement/arrangement.py and in geometry/hyperplane_arrangement/library.py. Other failures remain.

[dimpase]

I don't think this way is to fix these discrepancies is sustainable.

We should not try to test tests just outputting particular strings, when different strings are just different notation for the same thing.

[cxzhong]

We should not try to test tests just outputting particular strings, when different strings are just different notation for the same thing.

but this problem is not simple string issue. It directly cause if you use newer singular It will output False instead of True. It is a wrong output. It is must be fixed. @dimpase