It is well known that every non-degenerate quadratic form admits a decomposition into an orthogonal sum of its anisotropic part and hyperbolic form. This unique up to isometry. In this paper we present algorithm for constructing given with coefficients in arbitrary number field.

In this paper, we study the global dynamics of continuous piecewise quadratic Hamiltonian systems separated by straight line [Formula: see text], where these kinds have a nilpotent center at which comes from combination two cusps both systems. By Poincaré compactification classify phase portraits We must mention that it is extremely rare to find works studying center-focus problem in smooth wit...

The theorem in question gives a sufficient condition for a quadratic space over a local ring R to contain a hyperbolic plane over R. Our main aim in this paper is to prove the following result, which is a variant of the Springer theorem [La] for quadratic spaces over local rings. Theorem. Let R be a local Noetherian domain that has an infinite residue field of characteristic different from 2. L...