The behavior of IsGraded=>false is documented in ramificationDivisor. If the option IsGraded is set to true, then the function will assume that the source of f is affine, and the target is projective over the source. In this case, the coefficient ring of the target must be equal to the source ring. This can be useful when computing things like relative canonical divisors over regular bases (it may not give the expected answer over non-regular bases). For example, this is useful if you want to compute the relative canonical divisor of a blowup.
i1 : R = QQ[x,y]; |
i2 : S = reesAlgebra(ideal(x,y^2)); |
i3 : f = map(S, R); o3 : RingMap S <--- R |
i4 : ramificationDivisor(f,IsGraded=>true) o4 = 2*Div(y, x) o4 : WeilDivisor on S |