The resultant of an unmixed bivariate system

Authors:
Amit Khetan
Affiliations:
Department of Mathematics, UC Berkeley, Berkeley, CA
Venue:
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Year:
2003

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Abstract

This paper gives an explicit formula for computing the resultant of any sparse unmixed bivariate system with a given support. We construct square matrices whose determinant is exactly the resultant, with no extraneous factors. This is the first time that such matrices have been given for unmixed bivariate systems with arbitrary support. The matrices constructed are of hybrid Sylvester and Bézout type. The results extend previous work by the author by giving a complete combinatorial description of the matrix. We make use of the exterior algebra techniques of Eisenbud, Fløystad, and Schreyer.