Name
Abstract | ||
|---|---|---|
Let f=(f1,…,fs) be a sequence of polynomials in Q[X1,…,Xn] of maximal degree D and V⊂Cn be the algebraic set defined by f and r be its dimension. The real radical 〈f〉re associated to f is the largest ideal which defines the real trace of V. When V is smooth, we show that 〈f〉re, has a finite set of generators with degrees bounded by degV. Moreover, we present a probabilistic algorithm of complexity (snDn)O(1) to compute the minimal primes of 〈f〉re. When V is not smooth, we give a probabilistic algorithm of complexity sO(1)(nD)O(nr2r) to compute rational parametrizations for all irreducible components of the real algebraic set V∩Rn. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.1016/j.jsc.2019.10.018 | Journal of Symbolic Computation |
Keywords | DocType | Volume |
Polynomial system,Real radical,S-radical ideal,Semi-algebraic set,Real algebraic geometry | Journal | 102 |
ISSN | Citations | PageRank |
0747-7171 | 0 | 0.34 |
References | Authors | |
0 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mohab Safey El Din | 1 | 450 | 35.64 |
| Zhi-Hong Yang | 2 | 0 | 0.34 |
| Lihong Zhi | 3 | 463 | 33.18 |