Explicit equivalence of quadratic forms over Fq(t)

Gábor Ivanyos, Péter Kutas, L. Rónyai

Research output: Contribution to journalArticle

Abstract

We propose a randomized polynomial time algorithm for computing non-trivial zeros of quadratic forms in 4 or more variables over Fq(t), where Fq is a finite field of odd characteristic. The algorithm is based on a suitable splitting of the form into two forms and finding a common value they both represent. We make use of an effective formula for the number of fixed degree irreducible polynomials in a given residue class. We apply our algorithms for computing a Witt decomposition of a quadratic form, for computing an explicit isometry between quadratic forms and finding zero divisors in quaternion algebras over quadratic extensions of Fq(t).

LanguageEnglish
Pages33-63
Number of pages31
JournalFinite Fields and their Applications
Volume55
DOIs
Publication statusPublished - Jan 1 2019

Fingerprint

Quadratic form
Equivalence
Computing
Polynomials
Quaternion Algebra
Zero-divisor
Irreducible polynomial
Randomized Algorithms
Isometry
Algebra
Polynomial-time Algorithm
Galois field
Odd
Decomposition
Decompose
Zero
Form
Class

Keywords

  • Function field
  • Polynomial time algorithm
  • Quadratic forms

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Algebra and Number Theory
  • Engineering(all)
  • Applied Mathematics

Cite this

Explicit equivalence of quadratic forms over Fq(t). / Ivanyos, Gábor; Kutas, Péter; Rónyai, L.

In: Finite Fields and their Applications, Vol. 55, 01.01.2019, p. 33-63.

Research output: Contribution to journalArticle

Ivanyos, Gábor ; Kutas, Péter ; Rónyai, L. / Explicit equivalence of quadratic forms over Fq(t). In: Finite Fields and their Applications. 2019 ; Vol. 55. pp. 33-63.
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