On Monomial Reduction and Polynomial Expressions with Respect to Binomial Ideals
Rostam Sabeti · Communications in Algebra · 2015
Let I ⊂ K[x 1,…, x n ] be an ideal and G be the reduced Gröbner basis of I with respect to lexicographic monomial order. We introduce the index of an expression of f ∈ K[x 1,…, x n ] with respect to G. A minimal expression is characterized as the one with zero G-index. In case where I is a binomial prime ideal, a new division algorithm with minimal and unique expression is presented. The application of our new method on benchmark polynomial systems cyclic-9 and cyclic-12 shows its superiority in comparison with the existing division algorithm.