We present an algorithm which converts a given Grobner basis of a poly
nomial ideal I to a Grobner basis of I with respect to another term or
der. The conversion is done in several steps following a path in the G
robner fan of I. Each conversion step is based on the computation of a
Grobner basis of a toric degeneration of I. (C) 1997 Academic Press L
imited.