M = R^{i,j,k,...}
i1 : R = QQ[a..d]/(a*b*c*d) o1 = R o1 : QuotientRing
i2 : X = Proj R o2 = X o2 : ProjectiveVariety
i3 : OO_X^{-1,-2,3} 1 1 1 o3 = OO (-1) ++ OO (-2) ++ OO (3) X X X o3 : coherent sheaf on X, free of rank 3
i4 : Y = Proj (QQ[x,y,z,Degrees=>{{1,0},{1,-1},{1,-2}}]) o4 = Y o4 : ProjectiveVariety
i5 : OO_Y^{{1,2},{-1,3}} 1 1 o5 = OO (1, 2) ++ OO (-1, 3) Y Y o5 : coherent sheaf on Y, free of rank 2
i6 : degrees oo o6 = {{-1, -2}, {1, -3}} o6 : List