Riemann-Roch on a curve

i1 : X = abstractVariety(1,QQ[r,s,e_1,f_1,D,K,Degrees=>{2:0,4:1}])

o1 = X

o1 : an abstract variety of dimension 1

i2 : X.TangentBundle = abstractSheaf(X,Rank=>1,ChernClass=>1-K)

o2 = a sheaf

o2 : an abstract sheaf of rank 1 on X

i3 : chi OO_X

                1
o3 = integral(- -K)
                2

o3 : Expression of class Adjacent

i4 : chi OO(D)

                  1
o4 = integral(D - -K)
                  2

o4 : Expression of class Adjacent

i5 : E = abstractSheaf(X,Rank => r, ChernClass => 1+e_1)

o5 = E

o5 : an abstract sheaf of rank r on X

i6 : F = abstractSheaf(X,Rank => s, ChernClass => 1+f_1)

o6 = F

o6 : an abstract sheaf of rank s on X

i7 : chi Hom(E,F)

                1
o7 = integral(- -r*s*K - s*e  + r*f )
                2           1      1

o7 : Expression of class Adjacent