On Computing the Elimination Ideal Using Resultants with Applications to Gröbner Bases

2013/07/19 by Gallet, Matteo, Rahkooy, Hamid, Zafeirakopoulos, Zafeirakis
#Commutative Algebra (math.AC) #FOS: Computer and information sciences #FOS: Mathematics #Symbolic Computation (cs.SC)

paper · doi:10.48550/arxiv.1307.5330

Abstract

Resultants and Gröbner bases are crucial tools in studying polynomial elimination theory. We investigate relations between the variety of the resultant of two polynomials and the variety of the ideal they generate. Then we focus on the bivariate case, in which the elimination ideal is principal. We study - by means of elementary tools - the difference between the multiplicity of the factors of the generator of the elimination ideal and the multiplicity of the factors of the resultant.

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