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We consider computational and implementation issues for the completion ofmonomial sets to involution using different involutive divisions. Every ofthese divisions produces its own completion procedure. For the polynomial caseit yields an involutive basis which is a special form of a Groebner basis,generally redundant. We also compare our Mathematica implementation of Janetdivision to an implementation in C.

Construction of Involutive Monomial Sets for Different Involutive Divisions