> 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 |
> 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] |
> 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] |
> ## 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 = projectiveSpace'(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} |
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] |