Rostam Sabeti: Scheme of cyclic 9-roots. A heuristic numerical-symbolic approach, p.199-209

Abstract:

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 $$\bigoplus_{i=7}^9 x_i\mathbb{C}[x_i] \oplus \eta \mathbb{C}[x_7,x_... ...\delta \mathbb{C}[x_8,x_9] \oplus \sigma \mathbb{C}[x_7,x_9] \oplus \mathbb{C},$$ where $\eta=x_7x_8$, $\delta=x_8x_9$ and $\sigma=x_7x_9$.

Key Words: Computational algebraic geometry, components of solutions, irreducible decomposition, symbolic-numerical algorithm, cyclic $n$-roots.

2000 Mathematics Subject Classification: Primary: 14Q15;
Secondary: 65H10, 68W30, 13P05.

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