Shutaro Inoue

On the Computation of Elimination Ideals of Boolean Polynomial Rings

In order to compute an eliminate portion of a given polynomial ideal by a Grobner basis computation, we usually need to compute a Grobner basis of the whole ideal with respect to some proper term order. In a boolean polynomial ring, we show that we can compute an eliminate portion by computing Grobner bases in the boolean polynomial ring with the same coefficient ring that has the only variables which we want to eliminate. We also check the efficiency of our method through our implementation.

On the parallel computation of comprehensive Gröbner systems

We report on our implementation for parallel computations of comprehensive Gröbner systems (introduced by Weispfenning [7]) based on Suzuki-Sato algorithm. It is the first ever parallel implementation of comprehensive Gröbner systems.

On the Computation of Comprehensive Boolean Gröbner Bases

We show that a comprehensive Boolean Grobner basis of an ideal I in a Boolean polynomial ring B

An Implementation Method of Boolean Gröbner Bases and Comprehensive Boolean Gröbner Bases on General Computer Algebra Systems

(\bar A,\bar X)

On the Implementation of Boolean Gröbner Bases

with main variables

On QE Algorithms over an Algebraically Closed Field Based on Comprehensive Gröbner Systems

\bar X

A Mathematical Hierarchy of Sudoku Puzzles and Its Computation by Boolean Gröbner Bases

and parameters

Implementation of Boolean Gröbner bases in Risa/Asir

\bar A

Computation of inverses in residue class rings with parameters

can be obtained by simply computing a usual Boolean Grobner basis of I regarding both

Boolean Gröbner bases

\bar X