✦ LIBER ✦
From algebraic sets to monomial linear bases by means of combinatorial algorithms
✍ Scribed by L. Cerlienco; M. Mureddu
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 627 KB
- Volume
- 139
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
Let K be a field; let ~mK" be a finite set and let 3(N)mK[xl ..... x,] be the ideal of ~. A purely combinatorial algorithm to obtain a linear basis of the quotient algebra K Ix1 ..... x,]/3(~) is given. Such a basis is represented by an n-dimensional Ferrers diagram of monomials which is minimal with respect to the inverse lexicographical order ~<i.l.-It is also shown how this algorithm can be extended to the case in which ~ is an algebraic multiset. A few applications are stated (among them, how to determine a reduced Grfbner basis of 3(,~) with respect to %i.1. without using Buchberger's algorithm).