Applications of Bar Code to involutive divisions and a greedy algorithm for complete sets
Abstract
In this paper, we describe how to get Janet decomposition for a finite set of terms and detect completeness of that set by means of the associated Bar Code. Moreover, we explain an algorithm to find a variable ordering (if it exists) s.t. a given set of terms is complete according to that ordering. The algorithm is greedy and constructs a Bar Code from the maximal to the minimal variable, adjusting the variable ordering with a sort of backtracking technique, thus allowing to construct the desired ordering without trying all the n! possible orderings
- Publication:
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arXiv e-prints
- Pub Date:
- October 2019
- DOI:
- 10.48550/arXiv.1910.02802
- arXiv:
- arXiv:1910.02802
- Bibcode:
- 2019arXiv191002802C
- Keywords:
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- Mathematics - Combinatorics;
- Mathematics - Commutative Algebra;
- 05E40;
- 13P10
- E-Print:
- arXiv admin note: text overlap with arXiv:1805.09165