with(Groebner);Example to show that the order of the variables makes a big difference in the running time for computing Groebner bases.This example computes the hypersurface of osculating two-planes (spanned by velicity and acceleration vectors) to the "twisted quartic" (t,t^2,t^3,t^4) in affine 4-space. When the variables (x,y,z,w) are given in reverse order (R),then gbasis runs fine, in essentially no time. When the variables are in alphabetical order, on the other hand.... with(Ore_algebra);S := poly_algebra(s,t,u,v,x,y,z,w);T := termorder(S,plex(s,t,u,v,x,y,z,w));R := termorder(S,plex(u,t,s,v,w,z,y,x));GAcc := [x - t - s,y - t^2 - 2*s*t - 2*u,z - t^3 - 3*s*t^2 - 6*u*t,w - t^4 - 4*s*t^3 - 12*u*t^2];gbasis(GAcc,R);gbasis(GAcc,T);