Tenth World Congress on the Theory of Machines and Mechanisms

In many fields of engineering, for instance kinematic analysis, it is necessary to solve systems of polynomial equations. Mathematics software mostly uses the Buchberger Algorithm to find a lexicographic Gröbner Basis and subsequently compute the solutions. Although in theory the Buchberger Algorithm eventually terminates, the effort to compute Gröbner Bases from equations of higher degree or several unknowns grows rapidly. In fact for many problems it consumes so much performance, that powerful computers fail to produce results. This paper introduces the free software gfloat which numerically computes the Gröbner Basis and the solutions. It is suited for problems which have zero dimensional solutions i.e. there exists a finite set of solution points. Two techniques are used to reduce the demand of computer memory and processor time. These are (1) the use of floating point/modular arithmetic and (2) computing a lexicographic Gröbner Basis indirectly using a conversion algorithm. Section 6 demonstrates an application with a problem from kinematic synthesis.