Recursive Polynomial Remainder Sequence and the Nested Subresultants

Details Recursive Polynomial Remainder Sequence and the Nested Subresultants Recursive Polynomial Remainder Sequence and the Nested Subresultants

2008-06-03

arxiv.org/abs/0806.0488v1

Computer Algebra in Scientific Computing (Proc. CASC 2005), Lecture Notes in Computer Science 3718, Springer, 2005, 445-456

Mathematics

Commutative Algebra

12 pages. Presented at CASC 2005 (Kalamata, Greece, Septermber 12-16, 2005)

Scientific paper

10.1007/11555964_38

We give two new expressions of subresultants, nested subresultant and reduced nested subresultant, for the recursive polynomial remainder sequence (PRS) which has been introduced by the author. The reduced nested subresultant reduces the size of the subresultant matrix drastically compared with the recursive subresultant proposed by the authors before, hence it is much more useful for investigation of the recursive PRS. Finally, we discuss usage of the reduced nested subresultant in approximate algebraic computation, which motivates the present work.

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