On Multivariate Hermitian Quadratic Forms

Ryoya Fukasaku, Hidenao Iwane, Yosuke Sato

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

Multivariate Hermitian quadratic forms play an important role in the real quantifier elimination algorithm based on the computation of comprehensive Gröbner systems introduced by V. Weispfenning and further improved by us. Our algorithm needs the computation of a certain type of saturation ideal in a parametric polynomial ring. In this paper, we study multivariate Hermitian quadratic forms in more detail and show several facts which have special importance in a parametric polynomial ring. Our results enable us to have an efficient method to compute the saturation ideal, which brings us a drastic improvement of our real quantifier elimination software.

Original languageEnglish
Pages (from-to)79-93
Number of pages15
JournalMathematics in Computer Science
Volume13
Issue number1-2
DOIs
Publication statusPublished - Jun 1 2019
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

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