#restart:
with(schubert):   #Katz&Stromme Package 
n:=5;#change as you like
binomial(n+2,2);
grass(3,%,q); #Grass
DIM;
where();
chern(Qq);
#eval(Gq);
#Word of caution: schubert plays with the quotient Qq.
#We need -c1(dual(Qq))=q1, so no harm working with this convention.

d:=(q1-e)^DIM; #Pullback of hypln  class under  G-->Fol
d:=q1^DIM+collect(d-mtaylor(d,e,DIM-2*(n-1)),e);
#clean up terms of too small codim-->0
grass(2,n+1,c); #indeterm. locus, blowup center, veronese in G(3,S2)
TGc:=tangentbundle(Gc):
setvariety(Gc);DIM;
mtaylor(Hom(n+1-Qc,Qc)-TGc,t,DIM+1);
#TGq:=tangentbundle(Gq):# smarter:
DIM;
Qq:=bundle(3,q):
#Restriction of TG(3,S2F) ato TG(2,F)

TGqc:=mtaylor(subs(seq(chern(i,Qq)=
chern(i,symm(2,Qc)),i=1..3),
Hom(binomial(n+2,2)-Qq,Qq)),t,DIM+1):

N:=TGqc-TGc:     # normal bundle
d;
d0:=integral(Gq,subs(e=0,d));#n=4--->2861142656400
#Contribution off  indeterminacy locus
d:=d-subs(e=0,d); #Remaining contribs
sN:=chern(0,2*(n-1),-N);#chern(-N);
Gq[dimension_];
cod:=Gq[dimension_]-Gc[dimension_];
dim:=Gq[dimension_];
p:=0;
for i from cod to dim do     
p:=p+(-1)^(i-1)*coeff(d,e,i)*
sN[i-cod+1]    
od;        #direct image in Gc
indets(p);

p:=subs(q1=chern(1,symm(2,Qc)),p);
integral(%);
d0+%;
ifactor(%);
#check [n=4,2860923458080],[n=5,243661972980477736263],[n=6,728440733705107831789517245858];