Construction of Janet Bases I. Monomial Bases

Algorithms for computation of Janet bases for monomial ideals and implementation of these algorithms are presented. As data structures for finite monomial sets the binary trees called Janet trees are selected. An algorithm for construction of a Janet basis for the ideal generated by a finite monomial set is described. This algorithm contains as subalgorithms those to search for Janet divisor in a given tree and to insert monomials into the tree in the process of completion to involution. The algorithms presented have been implemented in C in the form of package for completion of monomial sets to Janet involutive ones. An example is given to illustrate practical efficiency of the monomial algorithms and their implementation.

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