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  • @inproceedings{RISC3154,
    author = {K. Nabeshima},
    title = {{A Speed-Up Algorithm for Computing Comprehensive Groebner Systems}},
    booktitle = {{ISSAC 2007}},
    language = {english},
    abstract = {We 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. },
    pages = {299--306},
    publisher = {ACM-press},
    isbn_issn = {978-1-59593-743-8},
    year = {2007},
    editor = {C. W. Brown},
    refereed = {yes},
    length = {8}
    }