Explicit equivalence of quadratic forms over \mathbbF_q(t)

2016/10/27 by Gábor Ivanyos, Ivanyos, Gábor, Péter Kutas +3
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Coding theory and cryptography #Cryptography and Residue Arithmetic #FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT) #Rings and Algebras (math.RA) #Symbolic Computation (cs.SC)

paper · pdf · doi:10.48550/arxiv.1610.08671

openalex publication_date 2016/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a randomized polynomial time algorithm for computing nontrivial zeros of quadratic forms in 4 or more variables over \mathbbF_q(t), where \mathbbF_q 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 \mathbbF_q(t).

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