Avoid hermite_form in solve_right if possible #40276
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Documentation preview for this PR (built with commit c71f7c9; changes) is ready! 🎉 |
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Thanks for the reviews 🙂 |
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Well, once the code is implemented, we can revisit the comparison. ;) |
vbraun
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sagemathgh-40276: Avoid hermite_form in solve_right if possible Currently, hermite_form can be randomly very slow (sagemath#33418, flintlib/flint#389) When `rank()==ncols()`, the solution is uniquely determined, so that an alternative algorithm is to solve the system over the fraction field, then convert it back to the ring. And computing rank is much faster — the current default algorithm for ℤ picks a random prime p and compute rank modulo p. This PR detects the full-rank case and implement the alternative algorithm. ### 📝 Checklist <!-- Put an `x` in all the boxes that apply. --> - [x] The title is concise and informative. - [x] The description explains in detail what this PR is about. - [x] I have linked a relevant issue or discussion. - [x] I have created tests covering the changes. - [ ] I have updated the documentation and checked the documentation preview. ### ⌛ Dependencies <!-- List all open PRs that this PR logically depends on. For example, --> <!-- - sagemath#12345: short description why this is a dependency --> <!-- - sagemath#34567: ... --> URL: sagemath#40276 Reported by: user202729 Reviewer(s): Travis Scrimshaw
This was referenced Jul 28, 2025
vbraun
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Aug 1, 2025
sagemathgh-40497: Actually avoid hermite_form in solve_right if possible I tried to speed this up in sagemath#40276 , but there was some error in logic which makes it fail. ### 📝 Checklist <!-- Put an `x` in all the boxes that apply. --> - [ ] The title is concise and informative. - [ ] The description explains in detail what this PR is about. - [ ] I have linked a relevant issue or discussion. - [ ] I have created tests covering the changes. - [ ] I have updated the documentation and checked the documentation preview. ### ⌛ Dependencies <!-- List all open PRs that this PR logically depends on. For example, --> <!-- - sagemath#12345: short description why this is a dependency --> <!-- - sagemath#34567: ... --> URL: sagemath#40497 Reported by: user202729 Reviewer(s): user202729
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Currently, hermite_form can be randomly very slow (#33418, flintlib/flint#389)
When
rank()==ncols(), the solution is uniquely determined, so that an alternative algorithm is to solve the system over the fraction field, then convert it back to the ring. And computing rank is much faster — the current default algorithm for ℤ picks a random prime p and compute rank modulo p.This PR detects the full-rank case and implement the alternative algorithm.
📝 Checklist
⌛ Dependencies