coefficient(Ideal,BasicDivisor) -- get the coefficient of an ideal for a fixed divisor

Synopsis

Function: coefficient
Usage:

coefficient(P, D)
Inputs:
- P, an ideal, the height one prime ideal that we want to find the coefficient of
- D, an instance of the type BasicDivisor, the divisor in question
Outputs:
- a number,

This function returns the coefficient of $D$ along the prime divisor associated to $P$.

i1 : R = QQ[x,y,u,v]/ideal(x*y-u*v);

i2 : D = divisor(x)

o2 = Div(v, x) + Div(u, x)

o2 : WeilDivisor on R

i3 : coefficient(ideal(x,u), D)

o3 = 1

i4 : E = divisor(x*u)

o4 = Div(v, x) + Div(u, y) + 2*Div(u, x)

o4 : WeilDivisor on R

i5 : coefficient(ideal(x,u), E)

o5 = 2