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Verifying KSY Condition By Elementary Matrix Transformations

Jinao He, Lei Huang

Abstract


Dixon’s method is a practical approach for computing the multivariate resultant in the quantifier elimination. The method is found to be quite restrictive as the Dixon matrix is singular always, and the Dixon resultant vanishes identically yielding no information about solutions for many algebraic and geometry problems. Kapur-Saxena-Yang extended Dixon’s method
for the case when the Dixon matrix is singular with the KSY condition. While the KSY condition is very difficult to be verified, so there has not any practical algorithm to do it yet. In this paper, we propose a new method to verify KSY condition by elementary matrix transformations directly.

Keywords


Singular Dixon Matrix, KSY Condition,Elementary Matrix Transformation, Dixon resultant.

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