A Fast Algorithm for Grobner Basis Conversion and its Applications

摘要

The grobner walk method converts a grobner basis by partitioning the computation of the basis into several smaller computations following a path in the Grobner fan of the ideal generalted by the system of equations. The method works with ideals of zero- dimension as well as positive dimensiona. Typically, the target point of the walking path lies on the intersection of very many cones, which ends up with initial forms of a consid- erable number of terms.