Differences between revisions 1 and 3 (spanning 2 versions)

William Stein: Optimized exact sparse and dense linear algebra (especially for computing modular forms)

Issues to address

Robert Bradshaw implemented multimodular matrix multiply over ZZ.
1. This seems to work fine on 32-bit machines, but is totally broken on 64-bit machines, so is currently disabled (in sage-2.1.2).
2. It is interesting to fine tune the algorithm, and decide when to switch over to a multimodular method.
3. Why is this so much slower than linbox?
4. Why is it slower than MAGMA? (How much slower?)
Linbox: Charpoly and minpoly over ZZ.
1. They hang on 32-bit Debian Linux and on sage.math, so are disabled in the sage-2.1.2.

The SmithForm (or invariant factors) algorithm, which gives the invariant factors, is literally a hundred times slower than MAGMA.

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+== Issues to address ==

 * Robert Bradshaw implemented multimodular matrix multiply over ZZ.  
    1. This seems to work fine on 32-bit machines, but is totally broken on 64-bit machines, so is currently disabled (in sage-2.1.2).
    2. It is interesting to fine tune the algorithm, and decide when to switch over to a multimodular method.
    3. Why is this so much '''slower''' than linbox? 
    4. Why is it slower than MAGMA? (How much slower?)

 * Linbox: Charpoly and minpoly over ZZ.
    1. They hang on 32-bit Debian Linux and on sage.math, so are disabled in the sage-2.1.2.

== Benchmarks to help direct our work ==

=== New code written from scratch in C/SageX/Python ===

=== IML -- Integer Matrix Library ===

=== Linbox ===

The SmithForm (or invariant factors) algorithm, which gives the invariant factors, is literally a hundred times slower than MAGMA.