Deterministic genericity for polynomial ideals. (English) Zbl 1446.13021
The authors deal, mainly from the algorithmic point of view, with the notion of genericity in the frame of commutative algebra, and more precisely in relation to polynomial ideals. More specifically, the paper emphasizes on generic positions related to Gröbner bases.
For this purpose, the authors define several stability notions using combinatorial descriptions. Algorithms for obtaining generic positions are provided.
Reviewer: Juan Rafael Sendra (Alcalá de Henares)
MSC:
| 13P10 | Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) |
| 68W30 | Symbolic computation and algebraic computation |
| 13-04 | Software, source code, etc. for problems pertaining to commutative algebra |
Keywords:
polynomial ideals; deterministic algorithms; Gröbner bases; Pommaret bases; generic positions; generic initial ideals; strongly stable ideals; stable ideals; quasi stable ideals; componentwise stability; \(\beta\)-maximal position; Noether positionReferences:
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