Details:
Title  Computing generators of the ideal of a smooth affine algebraic variety  Author(s)  Cristina Blanco, Gabriela Jeronimo, P. Solernó  Type  Article in Journal  Abstract  Let 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 settheoretical description of V. If V is given as the common zero locus of s polynomials of degrees bounded by d encoded by straightline 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.  Keywords  Number and degree of generators of polynomial ideals, Efficient generation of polynomial ideals, Computation of the radical of a regular ideal, Straightline programs, Regular rings  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717104000288 
Language  English  Journal  Journal of Symbolic Computation  Volume  38  Number  1  Pages  843  872  Year  2004  Edition  0  Translation 
No  Refereed 
No 
