On μ -Symmetric Polynomials and D-Plus

Jing Yang, Chee K. Yap

Research output: Chapter in Book/Report/Conference proceedingConference contribution


We study functions of the roots of a univariate polynomial of degree n≥ 1 in which the roots have a given multiplicity structure μ, denoted by a partition of n. For this purpose, we introduce a theory of μ -symmetric polynomials which generalizes the classic theory of symmetric polynomials. We designed three algorithms for checking if a given root function is μ -symmetric: one based on Gröbner bases, another based on preprocessing and reduction, and the third based on solving linear equations. Experiments show that the latter two algorithms are significantly faster. We were originally motivated by a conjecture about the μ -symmetry of a certain root function D+(μ) called D-plus. This conjecture is proved to be true. But prior to the proof, we studied the conjecture experimentally using our algorithms.

Original languageEnglish (US)
Title of host publicationMathematical Software – ICMS 2018 - 6th International Conference, Proceedings
EditorsJames H. Davenport, George Labahn, Josef Urban, Manuel Kauers
PublisherSpringer Verlag
Number of pages10
ISBN (Print)9783319964171
StatePublished - 2018
Event6th International Conference on Mathematical Software, ICMS 2018 - South Bend, United States
Duration: Jul 24 2018Jul 27 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10931 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other6th International Conference on Mathematical Software, ICMS 2018
Country/TerritoryUnited States
CitySouth Bend

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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