Subresultants in Recursive Polynomial Remainder Sequence

Details Subresultants in Recursive Polynomial Remainder Sequence Subresultants in Recursive Polynomial Remainder Sequence

2008-06-03

arxiv.org/abs/0806.0478v1

Proceedings of The 6th International Workshop on Computer Algebra in Scientific Computing: CASC 2003, Institute for Informatic

Mathematics

Commutative Algebra

13 pages. Presented at CASC 2003 (Passau, Germany, September 20-26, 2003)

Scientific paper

We introduce concepts of "recursive polynomial remainder sequence (PRS)" and "recursive subresultant," and investigate their properties. In calculating PRS, if there exists the GCD (greatest common divisor) of initial polynomials, we calculate "recursively" with new PRS for the GCD and its derivative, until a constant is derived. We call such a PRS a recursive PRS. We define recursive subresultants to be determinants representing the coefficients in recursive PRS by coefficients of initial polynomials. Finally, we discuss usage of recursive subresultants in approximate algebraic computation, which motivates the present work.

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