Multiplicity Preserving Triangular Set Decomposition of Two Polynomials

Details Multiplicity Preserving Triangular Set Decomposition of Two Polynomials Multiplicity Preserving Triangular Set Decomposition of Two Polynomials

2011-01-19

arxiv.org/abs/1101.3603v1

Computer Science

Symbolic Computation

18 pages

Scientific paper

In this paper, a multiplicity preserving triangular set decomposition algorithm is proposed for a system of two polynomials. The algorithm decomposes the variety defined by the polynomial system into unmixed components represented by triangular sets, which may have negative multiplicities. In the bivariate case, we give a complete algorithm to decompose the system into multiplicity preserving triangular sets with positive multiplicities. We also analyze the complexity of the algorithm in the bivariate case. We implement our algorithm and show the effectiveness of the method with extensive experiments.

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