Unifying modn matrices

[sagetrac-kartikv]

This is a consolidation of several matrix related tickets, e.g. #2705, #10734, #11161, #12177, #12679, #13177, #13915, #15104, ... basically, the world of matrices over finite fields. The fundamental issues are the following

• there is inconsistency over the size of fields that are allowed to use the "fast" matrix methods. Specifically, some places use mod_int and either a int_fast64_t or a long, while other places use int or int32_t specifically. Moreover, the size of the maximum modulus differs even when the sizes of the representations are the same.

• because of this, there are many cases when fast methods could be used but aren't: the code generally just reverts to generic matrices and slow internal operations

• the code totally ignores linbox's support for GMP-based matrix operations, which are not quite as fast as word-size ones but are still better than Sage internal operations

I intend to build a consolidated class framework for modular vectors and matrices, with system-optimized choice of crossover between small and large moduli and uniform use of linbox throughout. As part of this, I also intent to consolidate the existing code and update it to modern standards, e.g. move pxi files to pxd, add kwargs to all overloadable functions, etc.

CC: @kedlaya

Component: linear algebra

Keywords: matrix, sparse, modn, int

Author: Kartik Venkatram

Reviewer: rbeezer, jason

Issue created by migration from https://trac.sagemath.org/ticket/19076

[sagetrac-kartikv]

Reviewer: rbeezer, jason

[kedlaya]

comment:3

Another relevant ticket: #9888.