LIB "schubert.lib";
variety G = Grassmannian(3,5);
def r = G.baseRing;
setring r;
sheaf S = makeSheaf(G,subBundle);
sheaf B = dualSheaf(S)^2;
variety PB = projectiveBundle(B);
PB;
==> A variety of dimension 11
==> 
def R = PB.baseRing;
setring R;
QuotientBundle;
==> 1/1995840*z^5*q(2)^3-1/120960*z^5*q(1)*q(2)^2+1/20160*z^5*q(1)^2*q(2)+1/4\
   0320*z^5*q(2)^2-1/10080*z^5*q(1)^3-1/2688*z^5*q(1)*q(2)+1/840*z^5*q(1)^2+\
   1/1008*z^5*q(2)-1/180*z^5*q(1)+1/120*z^5-1/36288*z^4*q(2)^3+5/12096*z^4*q\
   (1)*q(2)^2-1/448*z^4*q(1)^2*q(2)+5/8064*z^4*q(2)^2+1/252*z^4*q(1)^3+1/100\
   8*z^4*q(1)*q(2)-1/72*z^4*q(1)^2+1/144*z^4*q(2)+1/24*z^4+43/72576*z^3*q(2)\
   ^3-47/8064*z^3*q(1)*q(2)^2+11/504*z^3*q(1)^2*q(2)-1/84*z^3*q(2)^2-1/36*z^\
   3*q(1)^3+5/144*z^3*q(1)*q(2)+1/6*z^3-1/192*z^2*q(2)^3+1/36*z^2*q(1)*q(2)^\
   2-1/24*z^2*q(1)^2*q(2)+1/36*z^2*q(2)^2+1/2*z^2+1/63*z*q(2)^3-1/36*z*q(1)*\
   q(2)^2+z+1
ChowRing(PB);
==> // coefficients: QQ
==> // number of vars : 3
==> //        block   1 : ordering wp
==> //                  : names    z
==> //                  : weights  1
==> //        block   2 : ordering wp
==> //                  : names    q(1) q(2)
==> //                  : weights     1    2
==> //        block   3 : ordering C
==> // quotient ring from ideal ...