Applications of Bar Code to Involutive Divisions and a “Greedy” Algorithm for Complete Sets

Given a finite set of terms U in n variables, we describe an algorithm which finds – if it exists – an ordering on the variables such that U is a complete set according to Janet involutive division. The algorithm, based on Bar Codes for monomial ideals, is able to adjust the variables ordering with...

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Bibliographic Details
Published inMathematics in computer science Vol. 16; no. 4
Main Author Ceria, Michela
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2022
Springer Nature B.V
Subjects
Bar codes
Computer Science
Greedy algorithms
Mathematics
Mathematics and Statistics
Janet division
Bar Codes
Completeness
Online AccessGet full text
ISSN1661-8270
1661-8289
DOI10.1007/s11786-022-00548-1

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Summary:Given a finite set of terms U in n variables, we describe an algorithm which finds – if it exists – an ordering on the variables such that U is a complete set according to Janet involutive division. The algorithm, based on Bar Codes for monomial ideals, is able to adjust the variables ordering with a sort of backtracking technique, thus allowing to find the desired ordering without trying all the n ! possible ones.
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ISSN:1661-8270
1661-8289
DOI:10.1007/s11786-022-00548-1