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Speed up multimodular algorithm in bad case #39204

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Related to #39197.

Technically the algorithm doesn't deviate from @williamstein 's original book; however the original book doesn't say how many additional primes to add each time.

The original implementation roughly consider 3 more primes each time. This can be highly inefficient when there are more columns than rows, which makes the result's height much higher than the guess.

This increases the length of M by roughly a factor of 1.2 each time. Worst case it makes the algorithm slower by a (hopefully small) constant factor.

For the added test case, it appears to improve the performance. (Originally takes 40s, now takes <10s on my machine)

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github-actions bot commented Dec 25, 2024

Documentation preview for this PR (built with commit 25ab579; changes) is ready! 🎉
This preview will update shortly after each push to this PR.

@user202729 user202729 marked this pull request as draft January 22, 2025 05:57
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Since flint is fast now it may be better to just switch to flint entirely.

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