Enhanced linbox interface

[videlec]

In sage/libs/linbox/linbox.pxd we currently have two classes that gives an interface for dense integer matrix (Linbox_integer_dense) and sparse matrix over Z/nZ (Linbox_modn_sparse). These interfaces are then used in different matrix implementations in sage/matrix/.

This task ticket stands for improvement of the LinBox interface

• moving the implementation directly in sage/matrix without the intermediate Cython classes. In particular, avoid calling the linbox-sage interface (on LinBox side) but directly invoque LinBox C++ code (as Cython now allows it) (done in cleaning of linbox for dense integer matrices #22924 and cleaning linbox declarations + reimplement modn interface #24544)
• more documentation and testing
• support for other matrix types (e.g. sparse integer matrix (done in enhance sparse integer matrix with linbox (+ cleaning) #23214), interface with m4ri that Sage uses for matrix over GF(2))
• expose more algorithms
  • solving A X = B with B a matrix without repeated call
    to LinBox column by column
  • parallel features from LinBox
  • more options for computing determinant (LinBox knows how to do this in more than one way)
  • open-mp is explicitely disabled in spkg-install with a reference to #17635 comment 67
  • fplll is explicitely disabled in spkg-install with a reference to update fplll to version 5.x #21221

Concrete ticket list

• cleaning of linbox for dense integer matrices #22924: implement a direct flint/LinBox interface and use it in matrix_integer_dense.pyx
• Silence off cython's warning compiling element_givaro.pyx #22966: warning while compiling element_givaro.pyx
• use flint fmpq_mat for rational dense matrices #22970: use fmpq_mat_t for rational dense matrices
• more linbox for rational dense matrices #22971: more linbox in rational dense matrices
• LinBox patch for integer sparse linear solver #23158: LinBox patch for integer sparse linear solving
• cleaning linbox declarations + reimplement modn interface #24544: clean declarations + matrix modn
• enhance sparse integer matrix with linbox (+ cleaning) #23214: solve/det/rank/charpoly/minpoly for sparse integral matrices (see also wrapper for determinant, minpoly, etc. from linbox for sparse matrices #13915, Implement rank for sparse integer matrix using LinBox #25257)
• fix linbox solve for sparse matrices #26178: unsigned int and int64_t behave very differently!

CC: @ClementPernet @JohnCremona @sagetrac-dlucas

Component: interfaces

Keywords: linbox

Issue created by migration from https://trac.sagemath.org/ticket/22872

[videlec]

comment:3

I just noticed that there was a previous attempt to clean the interface in #21327 by C. Bouillaguet.

[fchapoton]

Changed keywords from none to linbox

[videlec]

comment:21

update milestone 8.3 -> 8.4