Localization and Primary Decomposition of Polynomial Ideals
β Scribed by Takeshi Shimoyama; Kazuhiro Yokoyama
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 828 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0747-7171
No coin nor oath required. For personal study only.
β¦ Synopsis
In this paper, we propose a new method for primary decomposition of a polynomial ideal, not necessarily zero-dimensional, and report on a detailed study for its practical implementation. In our method, we introduce two key techniques, effective localization and fast elimination of redundant components, by which we can get a good performance for several examples. The performance of our method is examined by comparison with other existing methods based on practical experiments.
π SIMILAR VOLUMES
Toric degenerations of polynomial ideals occur if one allows certain partial term orders in the theory of GrΓΆbner bases. We prove that the collection of toric degenerations of an ideal can be monotonically embedded into the complex closure of the GrΓΆbner fan. A process of geometric localization on t
We study the primary decomposition of lattice basis ideals. These ideals are binomial ideals with generators given by the elements of a basis of a saturated integer lattice. We show that the minimal primes of such an ideal are completely determined by the sign pattern of the basis elements, while th
Let K be an infinite perfect computable field and let I β K[x] be a zero-dimensional ideal represented by a GrΓΆbner basis. We derive a new algorithm for computing the reduced primary decomposition of I using only standard linear algebra and univariate polynomial factorization techniques. In practice