Scheme of cyclic 9-roots. A heuristic numerical-symbolic approach

作者：Sabeti Rostam^*

来源：Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie, 2015, 58(2): 199-209.

• Computational algebraic geometry
• components of solutions
• irreducible
• decomposition
• symbolic-numerical algorithm
• cyclic n-roots

In this paper, a new heuristic symbolic-numerical method to derive exact form of the generators of the ideals in minimal prime decomposition of the radical of an ideal is presented. We set up the method without monodromy grouping. Application of the method on cyclic 9-roots polynomial system is given. A proof of the primality of the ideals is presented. Among many proved results, we also consider the residue class field of a typical prime ideal as the collection of well defined quotient of the elements in the direct sum circle plus(9)(i=7) x(i)C[x(i)]circle plus C[x(7), x(8)] circle plus delta C[x(8), x(9)] circle plus sigma C[x(7), x(9)] circle plus C, where eta = x(7)x(8), delta =x(8)x(9) and sigma = x(7)x(9).

• 出版日期2015