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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

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✦ 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).