add minimal interface for using ZZ[x]-matrices from flint

[fchapoton]

So that one may use this later to compute determinants in this case, for example.

CC: @videlec

Component: interfaces

Author: Frédéric Chapoton

Branch/Commit: 1f52255

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/29894

[fchapoton]

Branch: u/chapoton/29894

[fchapoton]

Commit: 1f52255

[fchapoton]

New commits:

1f52255

introduce minimal interface for using ZZ[x] matrices in Flint

[tscrim]

comment:2

Could we add at least one little direct use for this interface, say in computing the determinants as mentioned in the ticket description?

[fchapoton]

comment:3

ok, I will try to think about it. I had some use case, but it turned out to be slower than the existing method.

[tscrim]

comment:4

That is interesting and surprising to me. Bill probably would like to know about that. The flint version might also be asymptotically faster. Plus, I am generally a fan of having multiple implementations available and giving the choice to the user (if for nothing else other than testing).

[fchapoton]

comment:5

My test case was (for M upper triangular square matrix with 1 on the diagonal)

det(x M^t + M)

versus

charpoly(-M (M^t)^(-1))

and the inversion + product + charpoly over ZZ was much faster than the det over ZZ[x]

[fchapoton]

comment:6

maybe useful for Alexander polynomial from Seifert matrix, see #29952

[tscrim]

comment:7

Perhaps that is just a special case of the fact it is a upper unitriangular matrix? Anyways, I am not going to fret over not having a definitive use case at this time. It doesn't hurt anything to have the interface all setup.

[tscrim]

Reviewer: Travis Scrimshaw