FEATURE REQUEST: hnf_modular_eldiv over QQ[x] or ZZ[x]

[JohnAAbbott]

It would be useful to have an extension of hnf_modular_eldiv for matrices over QQ[x] (or maybe ZZ[x]).
@thofma Could such an extension be made easily? (and in the not-to-distant future?)

[thofma]

There is a generic howell_form/strong_echelon_form in AbstractAlgebra. This is all one needs (see https://github.com/flintlib/flint/blob/main/src/fmpz_mat/hnf_modular_eldiv.c#L35-L46). Just call strong_echelon_form and then lift and adjust the missing diagonal.

This will work for $\bf{Q}[X]$.

For $\bf{Z}[X]$ there is no Hermite form in the first place, so hnf_modular_eldiv cannot exist.

[JohnAAbbott]

Maybe I am making a silly mistake...

QQx,x = polynomial_ring(QQ, "x");
M = matrix(QQx, 2,2, [x,0,1,1]);
AbstractAlgebra.howell_form(M);

produces ERROR: MethodError: no method matching gcdxx(::QQPolyRingElem, ::QQPolyRingElem)
What should I have done?

[thofma]

You compute the Howell form of a matrix over a quotient ring:

julia> Q, = quo(QQx, x);

julia> AbstractAlgebra.howell_form(Q.(M))
[1   1]
[0   0]