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

[Frédéric Chapoton]

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

[Frédéric Chapoton]

New commits:

​1f52255

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

[Travis Scrimshaw]

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

[Frédéric Chapoton]

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

[Travis Scrimshaw]

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).

[Frédéric Chapoton]

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]

[Frédéric Chapoton]

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

[Travis Scrimshaw]

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.