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TitleSymmetric subresultants and applications
Author(s) Cyril Brunie, Philippe Saux Picart
TypeArticle in Journal
AbstractSchurís transforms of a polynomial are used to count its roots in the unit disk. These are generalized then by introducing the sequence of symmetric subresultants of two polynomials. Although they do have a determinantal definition, we show that they satisfy a structure theorem which allows us to compute them with a type of Euclidean division. As a consequence, a fast algorithm based on a dichotomic process and FFT is designed. We prove also that these symmetric subresultants have a deep link with Toeplitz matrices. Finally, we propose a new algorithm of inversion for such matrices. It has the same cost as those already known; however it is fraction free and consequently well adapted to computer algebra.
KeywordsSubresultant, Toeplitz matrices, Matrix inversion, DFT, Fraction-free algorithm, Euclidean division
URL http://www.sciencedirect.com/science/article/pii/S0747717107000740
JournalJournal of Symbolic Computation
Pages884 - 919
Translation No
Refereed No