Finding Nontrivial Zeros of Quadratic Forms over Rational Function Fields of Characteristic 2
Finding Nontrivial Zeros of Quadratic Forms over Rational Function Fields of Characteristic 2
We propose polynomial-time algorithms for finding nontrivial zeros of quadratic forms with four variables over rational function fields of characteristic 2. We apply these results to find prescribed quadratic subfields of quaternion division algebras and zero divisors in $M_2(D)$, the full matrix algebra over a division algebra, given by structure …