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TitleComputing generators of the ideal of a smooth affine algebraic variety
Author(s) Cristina Blanco, Gabriela Jeronimo, P. Solernó
TypeArticle in Journal
AbstractLet K be an algebraically closed field, V⊂K^n be a smooth equidimensional algebraic variety and I(V)⊂K[x1,,xn] be the ideal of all polynomials vanishing on V. We show that there exists a system of generators f1,,fm of I(V) such that m≤(n−dimV)(1+dimV) and deg(fi)≤degV for i=1,,m. If char(K)=0 we present a probabilistic algorithm which computes the generators f1,,fm from a set-theoretical description of V. If V is given as the common zero locus of s polynomials of degrees bounded by d encoded by straight-line programs of length L, the algorithm obtains the generators of I(V) with error probability bounded by ε within complexity s(nd^n)^O(1)log^2(⌈1/ε⌉)L.
KeywordsNumber and degree of generators of polynomial ideals, Efficient generation of polynomial ideals, Computation of the radical of a regular ideal, Straight-line programs, Regular rings
ISSN0747-7171
URL http://www.sciencedirect.com/science/article/pii/S0747717104000288
LanguageEnglish
JournalJournal of Symbolic Computation
Volume38
Number1
Pages843 - 872
Year2004
Edition0
Translation No
Refereed No
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