Raise exception when factoring zero polynomial #38720
Merged
Conversation
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
|
Documentation preview for this PR (built with commit e9b8e84; changes) is ready! 🎉 |
vbraun
pushed a commit
to vbraun/sage
that referenced
this pull request
Nov 2, 2024
sagemathgh-38722: Roots of polynomials mod n <!-- ^ Please provide a concise and informative title. --> <!-- ^ Don't put issue numbers in the title, do this in the PR description below. --> <!-- ^ For example, instead of "Fixes sagemath#12345" use "Introduce new method to calculate 1 + 2". --> <!-- v Describe your changes below in detail. --> <!-- v Why is this change required? What problem does it solve? --> <!-- v If this PR resolves an open issue, please link to it here. For example, "Fixes sagemath#12345". --> Presently, Sage implements root-finding over Z/n in a way that requires time exponential in e, where e is the largest exponent of a prime divisor of n. For example, while Sage is capable of the following, it takes 8 minutes and 40 seconds on the laptop I'm using: ```python R.<x> = Zmod(2^30)[] (x^2 - 1).roots(multiplicities=False) ``` This patch implements a better algorithm. Like the present one, it uses the Chinese Remainder Theorem to reduce to the case of prime powers. Unlike the present algorithm, it finds roots modulo prime powers using Hensel lifting. When the root is non-singular mod p, it uses Newton iteration and converges quadratically. When the root is singular, lifting is done one power at a time, and the running time is bounded by the product of e and the maximum number of roots modulo any p^d with d ≤ e. With this patch, the above code snippet takes 32 milliseconds; even lifting modulo 2^1000 takes less than a second. Depends on sagemath#38720. URL: sagemath#38722 Reported by: Kyle Hofmann Reviewer(s): Kyle Hofmann, Vincent Macri
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
3 participants
Add this suggestion to a batch that can be applied as a single commit.
This suggestion is invalid because no changes were made to the code.
Suggestions cannot be applied while the pull request is closed.
Suggestions cannot be applied while viewing a subset of changes.
Only one suggestion per line can be applied in a batch.
Add this suggestion to a batch that can be applied as a single commit.
Applying suggestions on deleted lines is not supported.
You must change the existing code in this line in order to create a valid suggestion.
Outdated suggestions cannot be applied.
This suggestion has been applied or marked resolved.
Suggestions cannot be applied from pending reviews.
Suggestions cannot be applied on multi-line comments.
Suggestions cannot be applied while the pull request is queued to merge.
Suggestion cannot be applied right now. Please check back later.
The zero polynomial doesn't have a factorization or square-free factorization, so
should raise errors instead of returning zero. This patch fixes this behavior.