> grass(2,4,b,all):
i1 : Gb = flagBundle({2,2}, base n, VariableNames => {,b})
o1 = Gb
o1 : a flag bundle with subquotient ranks {2:2}
|
i2 : Qb = last bundles Gb
o2 = Qb
o2 : an abstract sheaf of rank 2 on Gb
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> chi(Gb,Symm(n,Qb));
2 3
n + 1 + 1/6 n + 11/6 n
i3 : chi symmetricPower_n Qb
1 3 2 11
o3 = -n + n + --n + 1
6 6
o3 : QQ[n]
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> chi(Gb,o(n*b1));
4 3 23 2
1/12 n + 2/3 n + ---- n + 7/3 n + 1
12
i4 : chi OO_Gb(n*b_1)
1 4 2 3 23 2 7
o4 = --n + -n + --n + -n + 1
12 3 12 3
o4 : QQ[n]
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>
## This should be a quadric in P5:
>
> proj(5,H,all): chi(o(n*H)-o((n-2)*H));
4 3 23 2
1/12 n + 2/3 n + ---- n + 7/3 n + 1
12
i5 : P5 = abstractProjectiveSpace'(5,base n,VariableName=>H)
warning: clearing value of symbol H to allow access to subscripted variables based on it
: debug with expression debug 204 or with command line option --debug 204
o5 = P5
o5 : a flag bundle with subquotient ranks {5, 1}
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i6 : chi(OO(n*H)-OO((n-2)*H))
1 4 2 3 23 2 7
o6 = --n + -n + --n + -n + 1
12 3 12 3
o6 : QQ[n]
|