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TitleA Speed-Up Algorithm for Computing Comprehensive Groebner Systems
Author(s) Katsusuke Nabeshima
TypeBook, Chapter in Book, Conference Proceeding
AbstractWe introduce a new algorithm for computing comprehensive Groebner systems. There exists the Suzuki-Sato algorithm for computing comprehensive Groebner systems. The Suzuki-Sato algorithm often creates overmuch cells of the parameter space for comprehensive Groebner systems. Therefore the computation becomes heavy. However, by using inequations (``not equal zero''), we can obtain different cells. In many cases, this number of cells of parameter space is smaller than that of Suzuki-Sato's. Therefore, our new algorithm is more efficient than Suzuki-Sato's one, and outputs a nice comprehensive Groebner system. Our new algorithm has been implemented in the computer algebra system Risa/Asir. We compare the runtime of our implementation with the Suzuki-Sato algorithm and find our algorithm superior in many cases.
URL http://www.risc.jku.at/publications/download/risc_3154/Issa2007_nabeshi.pdf
PublisherACM Press
EditorC. W. Brown
Translation No
Refereed No
ConferencenameISSAC 2007