Name
Abstract | ||
|---|---|---|
Let f = (f(1), ..., f(s)) be a sequence of polynomials in Q[X-1, ..., X-n] of maximal degree D and V subset of C-n be the algebraic set defined by f and r be its dimension. The real radical re root < f > associated to f is the largest ideal which defines the real trace of V. When V is smooth, we show that re root < f >, has a finite set of generators with degrees bounded by degV. Moreover, we present a probabilistic algorithm of complexity (snD(n))(O(1)) to compute the minimal primes of re root < f > When V is not smooth, we give a probabilistic algorithm of complexity s(O(1)) (nD)(O(nr2r)) to compute rational parametrizations for all irreducible components of the real algebraic set V boolean AND R-n. Experiments are given to show the efficiency of our approaches. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1145/3208976.3209002 | ISSAC'18: PROCEEDINGS OF THE 2018 ACM INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION |
Keywords | Field | DocType |
Polynomial system, Real radical, Real Algebraic Geometry | Randomized algorithm,Discrete mathematics,Combinatorics,Finite set,Polynomial,Computer science,Algebraic set,Real algebraic geometry,Bounded function | Conference |
Citations | PageRank | References |
1 | 0.35 | 21 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mohab Safey El Din | 1 | 450 | 35.64 |
| Zhi-Hong Yang | 2 | 1 | 0.69 |
| Lihong Zhi | 3 | 463 | 33.18 |