Emmy-Noether-Seminar: How to make equations nice

How to make equations nice

Michael Stoll (Bayreuth)

Abstract: Consider a homogeneous polynomial equation in three variables, F(X,Y,Z) = 0, with coefficients in the ring of integers. We will present an algorithm that finds an equivalent equation of the form G(X,Y,Z) := u F(aX+bY+cZ, dX+eY+fZ, gX+hY+iZ) = 0 , where u is a nonzero rational number and (a b c / d e f / g h i) is an invertible matrix with rational entries, such that G also has integral coefficients and the coefficients are more or less as small as possible.

This is joint work with Stephan Elsenhans (Würzburg).