Katsusuke Nabeshima,
"A Speed-Up Algorithm for Computing Comprehensive Groebner Systems"
, in C. W. Brown: ISSAC 2007, ACM-press, Seite(n) 299-306, 2007, ISBN: 978-1-59593-743-8
Original Titel:
A Speed-Up Algorithm for Computing Comprehensive Groebner Systems
Sprache des Titels:
Englisch
Original Buchtitel:
ISSAC 2007
Original Kurzfassung:
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.