Method and device for generating Grobner bases to reduce memory

Details Method and device for generating Grobner bases to reduce memory Method and device for generating Grobner bases to reduce memory

1994-11-17

1997-10-14

Bowler, Alyssa H.

Boots, shoes, and leggings

395500, 364602, 364608, 364718, 364735, 364808, 3642313, 364DIG1, G06F 500

Patent

active

056780559

ABSTRACT:
A method and device for generating the Grobner bases to reduce the memory usage and compute at a high speed. The method comprises the steps of a) selecting a prime number, b) computing the normalization format of the polynomial pair regarding p as the modulus, c) computing the normalization format on the rational number only when the normalization format in the modulus p is not 0, d) omitting the computation of the normalization format on the rational number regarding the normalization format on the rational number as 0, when the normalization format in the modulus p is 0, and e) obtaining the polynomial set F.sub.1 which is the Grobner basis candidate. Thus, the digits of the intermediate formula are reduced, the memory usage is saved and the computing speed is accelerated. It is also possible to execute the computing after homogenizing previously the polynomial set F which is an object and dehomogenizing it at the end.

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Shoup, "New Algorithms for Finding Irreducible Polynomial over Finite Fields". IEEE, pp. 283-332. 1988.
Qian, "A Polynomial Approach to Image Processing and Quadtrees", IEEE, pp. 596-600. 1989.
Borgne, "Polynomial Ideal Therory Methods in Discrete Event, and Hybrid Dynamical Systems" IEEE, pp. 2695-2700. 1989.

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