Explicit equivalence of quadratic forms over F_q(t)

10/27/2016

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by   Gábor Ivanyos, et al.

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