Algorithms for quadratic forms

We present algorithms for square classes, quadratic forms and Witt classes of quadratic forms over the eld of rational functions of one variable over the reals. The algorithms are capable of: nding the unique representative of a square class, deciding if a given function is a square or a sum of squares and deciding if a quadratic form is isotropic or hyperbolic. Moreover we propose a representation for Witt classes of quadratic forms. With this representation one can manipulate Witt classes without operating directly on their coe cients. We present algorithms both for computing this representation and manipulating Witt classes.