//bsp 4
 
ring r = 0, (x,y,z) , lp;
ideal i = x5 + y5 - z5, x7 + y7 - z7;
groebner(i);
ring r = 0, (x,y,z), M(1,1,1,1,0,1,1,2,3);

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// IDEAL MEMBERSHIP PROBLEM (vgl Cox/Little/O'Shea 1992, S.94f)
 
ring r = (0,w) , (x,y,z) , lp;
minpoly = w2 + 1;                    //C[x,y,z]
ideal i = xz - y2, x3 -z2;
std(i);
poly f = -4*x2*y2*z2 + y6 + 3*z5;    //f Element von i
reduce(f,std(i));
poly g = xy - 5*z2 + x;       //g nicht Element von i
reduce(g,std(i));