Abstract
ABSTRACT Let be the Borel group of upper triangular matrices. In this paper we want to study the action of on the set of monomial ideals of ( a field of characteristic zero) from a computational point of view. More specifically, we show that the stabilizer of a monomial ideal in is a purely combinatorial object and we give an algorithm for computing it. Then we characterize the subgroups of that are stabilizers of monomial ideals, we give an algorithm which finds if a given ideal is in the orbit of a monomial ideal under the action of and in the affirmative case, finds the matrices such that . We show that the entries of can be directly obtained from the coefficients of the generators of , so in particular no solutions of polynomial equations are required.
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