Enhanced linbox interface

[vdelecroix]

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 #22924 and #24544)
• more documentation and testing
• support for other matrix types (e.g. sparse integer matrix (done in #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 #21221

Concrete ticket list

• #22924: implement a direct flint/LinBox interface and use it in matrix_integer_dense.pyx
• #22966: warning while compiling element_givaro.pyx
• #22970: use fmpq_mat_t for rational dense matrices
• #22971: more linbox in rational dense matrices
• #23158: LinBox patch for integer sparse linear solving
• #24544: clean declarations + matrix modn
• #23214: solve/det/rank/charpoly/minpoly for sparse integral matrices (see also #13915, #25257)
• #26178: unsigned int and int64_t behave very differently!

[vdelecroix]

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

[vdelecroix]

update milestone 8.3 -> 8.4