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(2018.08.17 15:00pm N202)Hoon Hong:Algorithm for computing mu-bases of univariate polynomials

Time:2018-08-15  Source:KLMM

Title                 Algorithm for computing mu-bases of univariate polynomials

Speaker           Hoon Hong North Carolina State University

Time&Venue   2018.08.17  15:00pm  N202

Abstract:          A "mu-basis" of polynomials is a certain nice generator of the syzygy module of the polynomials.

It was originally conceived by Cox, Sederberg and Chen about 20 years ago as an extension of rational parametrization of curves with the goal of making various geometric operations more efficient. However, now it is investigated for its own sake due to many interesting structural properties.
There are already several algorithms: by Cox, Sederberg, Chen, Zheng, Wang for three polynomials, and by Song and Goldman for an arbitrary many polynomials.
In this talk, we present another algorithm for arbitrary many polynomials. It is conceptually different from Song-Goldman algorithm in that it does not involve polynomial remaining (row operations on Sylvester-kind matrix).  It instead works on the "transpose" of the Sylvester-kind matrix, which has no counter-part in polynomial arithmetic. This brings out certain structural patterns to surface so that we can exploit it more readily.
Comparison with Song-Goldman algorithm will be given.
This is a joint work with Zachary Hough and Irina Kogan.

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