wrapper for determinant, minpoly, etc. from linbox for sparse matrices

[sagetrac-Bouillaguet]

Superseeded by #23214.

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Currently, computing the determinant, minimum polynomial, characteristic polynomial, etc of sparse matrices over the integers and finite fields switch them to a dense representation, then runs the dense algorithm.

This works, but is quite suboptimal. Linbox packs a few algorithms tailored for sparse matrices, e.g. iterative methods for the determinant, minpoly, etc. These methods have the advantage that they only read the matrix, and are memory efficient.

The aim of this ticket is to make these algorithms available in Sage.

CC: @ClementPernet

Component: linear algebra

Keywords: linbox, sd75

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/13915

[sagetrac-Bouillaguet]

comment:1

Examples of things that are presently bad (where a sparse matrix is converted to a dense representation) :

• kernel, determinant of sparse integers matrices
• rank of integers matrices relies on echelonization, which very likely switch it to dense. Linbox has other ways of dealing with this.
• elementary divisors and smith form of sparse integer matrices (idem).

[sagetrac-Bouillaguet]

Changed keywords from linbox to linbox, sd75

[tscrim]

comment:8

See #25257 for an initial attempt for rank.

[videlec]

comment:10

superseeded by #23214. I propose to close this as duplicate

[tscrim]

comment:11

Concur.

[tscrim]

Reviewer: Travis Scrimshaw

[videlec]

comment:13

closing positively reviewed duplicates