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We report on our implementation for parallel computations of comprehensive Gröbner systems (introduced by Weispfenning ) based on Suzuki-Sato algorithm. It is the first ever parallel implementation of comprehensive Gröbner systems.
A commutative ring B with an identity is called a boolean ring if every element of which is idempotent. A residue class ring B[X 1 ,. 2 n − X n also becomes a boolean ring, which is called a boolean polynomial ring. A Gröbner basis in a boolean polynomial ring, called a boolean Gröbner basis, is first introduced in [3, 4] with its computation algorithm in… (More)
X n ]. In order to decide whether p has an inverse in the residue class ring K[X 1 ,. .. , X n ]/I, there is a standard way to decide and compute it if exists. (See chapter 5 and 6 of  for example.) Step 1. Compute the reduced Gröbner basis G of the ideal p, These steps are simultaneously proceeded by so called extended Gröbner bases computations. It is… (More)