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Involutive Divisions in Mathematica: Implementation and Some Applications

V. Gerdt
M. Berth
G. Czichowski
Journal / Anthology

submitted to the Sixth Rhein Workshop on Computer Science
Year: 1998

In this paper we consider different involutive divisions and describe their implementation in Mathematica together with algorithms for the construction of involutive bases for monomial ideals. As a straightforward application, we consider computation of the Hilbert function and the Hilbert polynomial for a monomial ideal, or for a polynomial one represented by its Gröbner basis. This allows one, in particular, to determine the index of regularity of the ideal.

*Mathematics > Algebra > Polynomials