restart:with(schubert):
n:=7;F:=n+1;
k:=n-3;#k linear forms + one of deg d
#change n,k as you like
grass(k,F,q,all);
S:=dual(Qq):chern(1,S);chern(2,S);
nvezes:=k*n*(n-k+1);#presumed degree of closed formula
#actual calculation of deg of component 11..1d
#for several values of d
for ii from 2 to 2*nvezes do
d:=ii;
Fdd,Sd:=symm(d,F),symm(d,S):
cd:=chern(0,DIM,Sd);
N:=rank(Fdd)-rank(Sd)-1:dim:=N+DIM;
sum(binomial(dim,i)*(cd[DIM-i+1]*q1^(i)),i=0..DIM):
Nd[d]:=integral(%):
od:

#postulate polynomial and solve for its coeffs
fd:=sum('cat(a,i)*t^i','i'=0..nvezes+2):
So:=solve({seq(subs(t=j,fd)-Nd[j],j=2..nvezes+5)}):
indets([seq(rhs(So[i]),i=1..nops(So))]);
Fd[n]:=z->subs(t=z,subs(So,fd)):
unassign('d');
factor(Fd[n](d)):degree(%);#ifactor(denom(%%));
#writeto(`11d_out`):n,k,%%%,%%,%;
#writeto(terminal):
#check polynomial against actual values computed
{seq(Fd[n](nvezes+i)-Nd[nvezes+i],i=1..nvezes)};