The Multivariate Power Series Package in Maple 2024.
Bibliographic record
Abstract
While symbolic computation is the realm of exact methods, this field was able to develop solutions to approximate problems, which can be used to provide approximate answers to problems that are either intractable or too expensive to solve exactly. A well-known example is the so-called symbolic Newton iteration method for approximating the solutions of algebraic equations. At the heart of these methods is the manipulation of formal multivariate power series.The MultivariatePowerSeries library in Maple provides formal, Laurent and Puiseux series in several variables. The implementation of those series is based on the paradigm of lazy evaluation (or call-by-need). Not only arithmetic operations (addition, multiplication, inversion) are offered, but univariate polynomial over multivariate series are provided by this library. The user can factorize such polynomials in a number of ways, using either Weierstrass Preparation Theorem, Hensel Lemma, Puiseux Theorem and the Extended Hensel Construction. In this talk, we will give a tour of these facilities and illustrate their usage with a number of applications.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.337 | 0.178 |
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 source (direct Gemma or distilled Codex), 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".