Algorithms for weakly nonnegative quadratic forms Original Research Article

Let q: Zn → Z with q(v) = ∑ni = 1 v(t)2 + ∑i < j aijv(i)v(j) be a unit form. We present an algorithm that allows one to check if q is weakly nonnegative [i.e., q(v) greater-or-equal, slanted 0 for any vector v set membership, variant Nn]. The algorithm also calculates the set of critical vectors of q. We sketch the relation of this problem to the representation theory of finite-dimensional algebras.