T := lexdeg([y1,y2,y3], [x1,x2,x3,x4], [b,c,d,e]): G := Groebner[Basis]([ y1-a*(x1+x2-x3-x4), y2-a*(x1-x2+x3-x4), y3-a*(x1-x2-x3+x4), b-(-a*(x1+x2+x3+x4)), c-(a*(x1*x2+x1*x3+x1*x4+x2*x3+x2*x4+x3*x4)), d-(-a*(x1*x2*x3+x1*x2*x4+x1*x3*x4+x2*x3*x4)), e-(a*(x1*x2*x3*x4))], T): Groebner[Reduce](y1^2+y2^2+y3^2, G, T); Groebner[Reduce](y1^2*y2^2+y1^2*y3^2+y2^2*y3^2, G, T); Groebner[Reduce](y1*y2*y3, G, T);