NC algorithms for real algebraic numbers

F. Cucker, H. Lanneau, Bhubaneswar Mishra, P. Pedersen, M. F. Roy

Research output: Contribution to journalArticle

Abstract

Characterizing real algebraic numbers by a sign-sequence (according to Thom's lemma), using a variant of Ben Or Kozan and Reif algorithm for reducing the solving of systems of polynomial inequalities to the problem of counting real zeroes satisfying one polynomial inequality, and using a multivariate Sturm theory generalizing Hermite quadratic forms method for counting real zeroes, we prove that the computations on real algebraic numbers are in NC.

Original languageEnglish (US)
Pages (from-to)79-98
Number of pages20
JournalApplicable Algebra in Engineering, Communication and Computing
Volume3
Issue number2
DOIs
StatePublished - Jun 1992

Fingerprint

Algebraic number
Counting
Polynomials
Polynomial
Zero
Hermite
Quadratic form
Lemma

Keywords

  • NC complexity
  • Parallel algebraic complexity
  • Real algebraic numbers
  • Sturm theory
  • Systems of polynomial inequalities
  • Thom's lemma

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Applied Mathematics
  • Computer Science Applications
  • Computational Theory and Mathematics

Cite this

NC algorithms for real algebraic numbers. / Cucker, F.; Lanneau, H.; Mishra, Bhubaneswar; Pedersen, P.; Roy, M. F.

In: Applicable Algebra in Engineering, Communication and Computing, Vol. 3, No. 2, 06.1992, p. 79-98.

Research output: Contribution to journalArticle

Cucker, F. ; Lanneau, H. ; Mishra, Bhubaneswar ; Pedersen, P. ; Roy, M. F. / NC algorithms for real algebraic numbers. In: Applicable Algebra in Engineering, Communication and Computing. 1992 ; Vol. 3, No. 2. pp. 79-98.
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