Generating a Quadratic Forms from a Given Genus
  Given a non-empty genus in $n$ dimensions with determinant $d$, we give a randomized algorithm that outputs a quadratic form from this genus. The time complexity of the algorithm is poly$(n,\log d)$; assuming Generalized Riemann Hypothesis (GRH). 
Chandan Dubey and Thomas Holenstein
cs.DS math.NT math.RA