Santander/Cantabria ISSAC 2004

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Matrix Determinant Interpolator

Michael Brazier and Arthur D. Chtcherba



Commercial computer algebra systems have various sometimes contradictory goals when it comes to providing extended functionality as well as ease of use. Given their nature and objectives it is rarely that some subsystem is lightweight and fast. One of the challenging problems to symbolic packages is the most basic one, polynomial arithmetic. Computing for example the determinant of a polynomial matrix is a difficult problem. We provide a small tool for interpolating determinants of polynomial matrices. In its first release, it uses classic Zippel's spare probabilistic interpolation algorithm with a few improvements to extract the determinant of a given matrix. Even though a few similar tools exist for some time now our implementation has very little overhead and employs a few optimizing heuristics. This tool is primarily used for computing the projection operators from resultant matrices constructed in Maple.

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