Ruppert matrix as subresultant mapping

Authors:
Kosaku Nagasaka
Affiliations:
Kobe University, Japan
Venue:
CASC'07 Proceedings of the 10th international conference on Computer Algebra in Scientific Computing
Year:
2007

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Abstract

Ruppert and Sylvester matrices are very common for computing irreducible factors of bivariate polynomials and computing polynomial greatest common divisors, respectively. Since Ruppert matrix comes from Ruppert criterion for bivariate polynomial irreducibility testing and Sylvester matrix comes from the usual subresultant mapping, they are used for different purposes and their relations have not been focused yet. In this paper, we show some relations between Ruppert and Sylvester matrices as the usual subresultant mapping for computing (exact/approximate) polynomial GCDs, using Ruppert matrices.