Details:
Title  Improved polynomial remainder sequences for Ore polynomials  Author(s)  Maximilian Jaroschek  Type  Article in Journal  Abstract  Abstract 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.  Keywords  Ore polynomials, Greatest common right divisor, Polynomial remainder sequences, Subresultants  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717113000849 
Language  English  Journal  Journal of Symbolic Computation  Volume  58  Number  0  Pages  64  76  Year  2013  Edition  0  Translation 
No  Refereed 
No 
