Recent Progress on Computing Groebner Bases
summary
Defines a module-level framework that turns Buchberger S-pair work into signature-based checks: a subset G generates a strong Gröbner basis for the module exactly when every computed J-pair is “covered” by G, so most S-polynomials can be discarded without reduction. Uses Faugère-style signature order and distinguishes regular/taut reductions, shows how module generators yield both a Gröbner basis and the syzygy (CZG) basis, and points out worst-case exponential output and sharp‑P hardness for some cubic cases.
AI-written summary · about
chapters (13)
- 0:00Start
- 0:38Gröbner Bases
- 1:50Remarks
- 2:52Monomial Orderings
- 3:57Top reductions
- 4:48S-polynomials
- 6:07Buchberger's Criterion (1965)
- 6:40Buchberger's Algorithm
- 7:51Detecting useless 5-polynomials
- 9:43Recent papers
- 10:26General framework
- 12:27Signatures
- 13:59Top-reductions
related talks
55mNon-commutative Computation
23mVerifying Graph Algorithms in Separation Logic: A Case for an Algebraic Approach
23mGenerating Programs for Polynomial Multiplication with Correctness Assurance
01h 19mTutorial 2: Algorithmic Invariant Theory
14mVerification of Algorithm and Code Generation for Signal Transforms
01h 01mTrue Complexity of Multilinear Systems
28mCertifying rings of integers in number fields
21mWell-founded recursion done right