ALGORITHMS FOR WEAKLY NONNEGATIVE QUADRATIC-FORMS

Let q:Z(n) --> Z with q(upsilon) = Sigma(i=1)(n) upsilon(t)(2) + Sigma (i<j) a(ij)upsilon(i)upsilon(j) be a unit form. We present an algorith m that allows one to check if q is weakly nonnegative [i.e., q(upsilon ) greater than or equal to 0 for any vector upsilon is an element of N -n]. The algorithm also calculates the set of critical vectors of q. W e sketch the relation of this problem to the representation theory of finite-dimensional algebras.