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Record W4407385828 · doi:10.1145/3717582.3717595

Sparse Hensel Lifting Algorithms for Multivariate Polynomial Factorization

2024· article· en· W4407385828 on OpenAlex
Tian Chen

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueACM communications in computer algebra · 2024
Typearticle
Languageen
FieldComputer Science
TopicPolynomial and algebraic computation
Canadian institutionsSimon Fraser University
Fundersnot available
KeywordsMultivariate statisticsFactorizationPolynomialComputer scienceAlgorithmMathematicsMachine learning

Abstract

fetched live from OpenAlex

Let a be a polynomial in Z[x 1 , ... , x n ] that is represented by a black box. In this thesis, we have designed and implemented a new factorization algorithm that, on input of the black box, outputs the irreducible factors of a in the sparse representation. Our new algorithm based on sparse Hensel lifting applies equally well to general multivariate polynomials, both sparse and dense. We first designed the algorithm for a being monic in x 1 and square-free, then completed the factorization problem by considering a being non-monic, non-square-free, and non-primitive. Our algorithm first finds the factors of the primitive part of a , then the factors of the content of a in the main variable x 1 . We implemented our algorithm in Maple with some subroutines in C. A variety of timing benchmarks are presented. All our timings are much faster than the current best determinant and factorization algorithms in Maple and Magma. We also present a worst-case complexity analysis of our new black box factorization algorithm, along with a failure probability analysis. The case for large integer coefficients has also been considered.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Simulation or modeling · Consensus signal: none
GenreCandidate signal: Methods · Consensus signal: Methods
Teacher disagreement score0.935
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.001
Science and technology studies0.0000.000
Scholarly communication0.0010.001
Open science0.0040.002
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.066
GPT teacher head0.330
Teacher spread0.264 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it