A Maple Program to Factor Multivariate Polynomials Given by Black Boxes
Bibliographic record
Abstract
Let a be a polynomial in Z[ x 1 , x 2 , …,x n ]. Let α ∈ Z n and p be a large prime. Let B be a modular black box representation for a , that is, B : Z n × { p } → Z p such that B( α,p ) outputs a ( α ) mod p. In our implementation B is a Maple procedure. We present a Maple program CMBBSHL which on input of B outputs the irreducible factorization Π r i =1 f e i i of a ( x 1 ,…, x n ) with high probability. Our program is a combination of Maple codes and C codes where the main programs are implemented in Maple and several subroutines are implemented in C for increased efficiency. We present (1) a description of the algorithm, (2) a demonstration of the software, (3) a timing benchmark, and (4) some implementation details.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot 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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.006 | 0.005 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".