CGB: Computing Comprehensive Gr?bner Bases

IntroductionConsider the ideal basis F ={ax,x + y}. Treating a as a parameter, the callingsequencetorder({x,y},lex)$groebner{a*x,x+y};{x,y}yields{x,y} as reduced Grobner basis. This is, however, not correct under thespecialization a = 0. The reduced Grobner basis would then be{x+ y}. Takingthese results together, we obtain C ={x+ y, ax, ay}, which is correct wrt. all specializationsfor a including zero specializations. We call this set C a comprehensiveGrobner...