Multiplication of non degenerated curves of second order

Abstract

In this paper we introduce two operations in the set of non degenerated curves of second order: a) multiplication of curves and b) inversion of a curve. The main result is that this set with these two operations is a commutative and associative group. We prove also the multiplication of the curves is independent of the rotation of the coordinate system. All calculation are done using Computer System Maple. So we demonstrate the power of this system.