The univariatepoly command computes the univariate polynomial in Z from a grevlex basis A in the variables X modulo P. The system must have a finite number of solutions, that is, its hilbert dimension must be zero. Progress information is available by setting info().
sys = [x^2+y, x*y-1]; G = groebnerbasis(sys,[x,y],[],0); univariatepoly(y,G,[x,y],0); 1+y^3