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basis strategy and order for toric varieties #3577

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mahrud opened this issue Nov 11, 2024 · 0 comments
Open

basis strategy and order for toric varieties #3577

mahrud opened this issue Nov 11, 2024 · 0 comments

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@mahrud
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mahrud commented Nov 11, 2024

When I added rawHilbertBasis from Normaliz I also changed latticePoints Polyhedron to use it instead, which is in turn used by monomials ToricDivisor. This improved the speed greatly because Normaliz parallelizes this computation.

I realized this means we can also significantly improve multigraded basis in this case. This is kind of already implemented in basis' in the Truncations package without any toric assumptions.

One problem is that the order of monomials found this way may be different than the engine algorithm. @mikestillman is this a problem? I recall running into this #2810 as well.

Also, should this be implemented in the top level, or is it worth changing basis0_multi_graded in matrix-kbasis.cpp to directly use Normaliz via rawHilbertBasis?

cc: @jkyang92

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