Name
Title | ||
|---|---|---|
Decomposing polynomial sets into simple sets over finite fields: The zero-dimensional case |
Abstract | ||
|---|---|---|
This paper presents algorithms for decomposing any zero-dimensional polynomial set into simple sets over an arbitrary finite field, with an associated ideal or zero decomposition. As a key ingredient of these algorithms, we generalize the squarefree decomposition approach for univariate polynomials over a finite field to that over the field product determined by a simple set. As a subprocedure of the generalized squarefree decomposition approach, a method is proposed to extract the pth root of any element in the field product. Experiments with a preliminary implementation show the effectiveness of our algorithms. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1016/j.camwa.2010.09.059 | Computers & Mathematics with Applications |
Keywords | Field | DocType |
associated ideal,preliminary implementation,simple set,squarefree decomposition,p th root extraction,squarefree decomposition approach,regular set,key ingredient,finite field,polynomial set,arbitrary finite field,generalized squarefree decomposition approach,zero decomposition,field product,zero-dimensional case,p | Finite field,Radical of an ideal,Mathematical optimization,Square-free integer,Polynomial,Mathematical analysis,Simple set,Triangular decomposition,Subprocedure,Univariate,Mathematics | Journal |
Volume | Issue | ISSN |
60 | 11 | Computers and Mathematics with Applications |
Citations | PageRank | References |
6 | 0.45 | 13 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Xiaoliang Li | 1 | 28 | 7.12 |
| Chenqi Mou | 2 | 38 | 5.55 |
| Dongming Wang | 3 | 458 | 55.77 |