Use Mathematica to compute a Grbner basis for the set of polynomials {y2 x3 + x,

Use Mathematica to compute a Gröbner basis for the set of polynomials

{y2 − x3 + x, y3 − x2}

under lexicographical, degree lexicographical, and degree reverse lexicographical ordering, respectively. Solve the simultaneous equations y2−x3+

x = 0, y3 − x2 = 0 for x and y.