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TitleImproved polynomial remainder sequences for Ore polynomials
Author(s) Maximilian Jaroschek
TypeArticle in Journal
AbstractAbstract Polynomial remainder sequences contain the intermediate results of the Euclidean algorithm when applied to (non-)commutative polynomials. The running time of the algorithm is dependent on the size of the coefficients of the remainders. Different ways have been studied to make these as small as possible. The subresultant sequence of two polynomials is a polynomial remainder sequence in which the size of the coefficients is optimal in the generic case, but when taking the input from applications, the coefficients are often larger than necessary. We generalize two improvements of the subresultant sequence to Ore polynomials and derive a new bound for the minimal coefficient size. Our approach also yields a new proof for the results in the commutative case, providing a new point of view on the origin of the extraneous factors of the coefficients.
KeywordsOre polynomials, Greatest common right divisor, Polynomial remainder sequences, Subresultants
URL http://www.sciencedirect.com/science/article/pii/S0747717113000849
JournalJournal of Symbolic Computation
Pages64 - 76
Translation No
Refereed No