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| == Issues to address == | |
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| * Robert Bradshaw implemented multimodular matrix multiply over ZZ. | == Matrix multiplication over ZZ == Robert Bradshaw implemented multimodular matrix multiply over ZZ. |
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| * 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. |
== Charpoly and minpoly over ZZ == |
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| == Benchmarks to help direct our work == | The linbox versions hang on 32-bit Debian Linux and on sage.math, so are disabled in the sage-2.1.2. |
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| === New code written from scratch in C/SageX/Python === | === Smith Normal Form === The SmithForm (or invariant factors) algorithm, which gives the invariant factors, is literally a hundred times slower than MAGMA. It's even slower than PARI for small n. |
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| === Linbox === | This has optimized dense echelon form over finite fields and a very fast implementation of the p-adic nullspace algorithm (which is very useful for echelon forms over QQ!). Problems: |
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| The SmithForm (or invariant factors) algorithm, which gives the invariant factors, is literally a hundred times slower than MAGMA. | 1. the p-adic nullspace algorithm is only implemented for matrices whose entries are C long's. But looking at the source code very strongly suggests it could easily be extended to the general case. 2. IML currently depends on atlas, so we have to rewrite it so it doesn't. This is probably not too hard. |
William Stein: Optimized exact sparse and dense linear algebra (especially for computing modular forms)
Matrix multiplication over ZZ
Robert Bradshaw implemented multimodular matrix multiply over ZZ.
- 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).
- It is interesting to fine tune the algorithm, and decide when to switch over to a multimodular method.
Why is this so much slower than linbox?
- Why is it slower than MAGMA? (How much slower?)
Charpoly and minpoly over ZZ
The linbox versions hang on 32-bit Debian Linux and on sage.math, so are disabled in the sage-2.1.2.
Smith Normal Form
The SmithForm (or invariant factors) algorithm, which gives the invariant factors, is literally a hundred times slower than MAGMA. It's even slower than PARI for small n.
IML -- Integer Matrix Library
This has optimized dense echelon form over finite fields and a very fast implementation of the p-adic nullspace algorithm (which is very useful for echelon forms over QQ!). Problems:
- the p-adic nullspace algorithm is only implemented for matrices whose entries are C long's. But looking at the source code very strongly suggests it could easily be extended to the general case.
- IML currently depends on atlas, so we have to rewrite it so it doesn't. This is probably not too hard.