Kernels for dense matrices mod p

[malb]

This seems too slow:

sage: A = random_matrix(GF(127),4000,5000)
sage: %time _ = A.echelon_form() # okay
CPU times: user 8.07 s, sys: 0.13 s, total: 8.20 s
Wall time: 8.24 s
sage: %time A.right_kernel() # slow!
CPU times: user 56.33 s, sys: 0.23 s, total: 56.56 s
Wall time: 56.83 s

CC: @burcin

Component: linear algebra

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/13500

[mezzarobba]

comment:4

The timings look much better now:

$ sage
┌────────────────────────────────────────────────────────────────────┐
│ Sage Version 6.2.beta3, Release Date: 2014-03-03                   │
│ Type "notebook()" for the browser-based notebook interface.        │
│ Type "help()" for help.                                            │
└────────────────────────────────────────────────────────────────────┘
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ Warning: this is a prerelease version, and it may be unstable.     ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛
sage: A = random_matrix(GF(127),4000,5000)
sage: %time _ = A.echelon_form() # okay
CPU times: user 4.96 s, sys: 96 ms, total: 5.05 s
Wall time: 5.05 s
sage: %time A.right_kernel() # slow!
CPU times: user 6.78 s, sys: 84 ms, total: 6.87 s
Wall time: 6.85 s
Vector space of degree 5000 and dimension 1000 over Finite Field of size 127

[tscrim]

Reviewer: Travis Scrimshaw