Speaker: 肖方慧副教授 , 湖南师大

Inviter: 王定康研究员

Title: An extended GCD algorithm by computing comprehensive Groebner systems for modules

Language: Chinese

Time & Venue: 2024.12.11 19:00-20:00 腾讯会议：799-626-704

Abstract: This algorithm computes not only the GCD of parametric univariate polynomials in each constructible set but also the corresponding representation coefficients (or multipliers) for the GCD expressed as a linear combination of these parametric univariate polynomials. The key idea of this algorithm is that for non-parametric case the GCD of arbitrary finite number of univariate polynomials can be obtained by computing the minimal Groebner basis of the ideal generated by those polynomials. But instead of computing the Groebner basis of the ideal generated by those polynomials directly, we construct a special module by adding the unit vectors which can record the representation coefficients, then obtain the GCD and representation coefficients by computing a Groebner basis of the module. This method can be naturally generalized to the parametric case because of the comprehensive Groebner systems for modules. As a consequence, we obtain an extended GCD algorithm for parametric univariate polynomials.