BasicDivisor + BasicDivisor -- add or subtract two divisors, or negate a divisor

Synopsis

Operator: +
Usage:

A + B

A - B

-A
Inputs:
- A, an instance of the type BasicDivisor,
- B, an instance of the type BasicDivisor,
Outputs:
- an instance of the type BasicDivisor,

We can add or subtract two divisors:

i1 : R = QQ[x, y, z];

i2 : D1 = divisor({1, 3, 2}, {ideal(x), ideal(y), ideal(z)})

o2 = 3*Div(y) + 2*Div(z) + Div(x)

o2 : WeilDivisor on R

i3 : D2 = divisor({-2, 3, -5}, {ideal(z), ideal(y), ideal(x)})

o3 = -2*Div(z) + 3*Div(y) + -5*Div(x)

o3 : WeilDivisor on R

i4 : D1 + D2

o4 = 6*Div(y) + -4*Div(x)

o4 : WeilDivisor on R

i5 : D1 - D2

o5 = 4*Div(z) + 6*Div(x)

o5 : WeilDivisor on R

We can also add or subtract divisors with different coefficients.

i6 : R = QQ[x,y];

i7 : D1 = divisor({3, 1}, {ideal(x), ideal(y)})

o7 = 3*Div(x) + Div(y)

o7 : WeilDivisor on R

i8 : D2 = divisor({3/2, -1}, {ideal(x), ideal(y)}, CoefficientType=>QQ)

o8 = 3/2*Div(x) + -Div(y)

o8 : QWeilDivisor on R

i9 : D3 = divisor({1.25}, {ideal(x)}, CoefficientType=>RR)

o9 = 1.25*Div(x)

o9 : RWeilDivisor on R

i10 : D1+D2

o10 = 9/2*Div(x)

o10 : QWeilDivisor on R

i11 : D1+D3

o11 = Div(y) + 4.25*Div(x)

o11 : RWeilDivisor on R

i12 : D2+D3

o12 = -Div(y) + 2.75*Div(x)

o12 : RWeilDivisor on R

Finally, we can negate a divisor.

i13 : R = ZZ/3[x,y,z]/ideal(x^2-y*z);

i14 : D = divisor({3, 0, -1}, {ideal(x,z), ideal(y,z), ideal(x-y, x-z)})

o14 = 0*Div(y, z) + -Div(x-y, x-z) + 3*Div(x, z)

o14 : WeilDivisor on R

i15 : -D

o15 = Div(x-y, x-z) + -3*Div(x, z)

o15 : WeilDivisor on R

i16 : E = divisor({3/2, -2/3}, {ideal(x, z), ideal(y, z)})

o16 = -2/3*Div(y, z) + 3/2*Div(x, z)

o16 : WeilDivisor on R

i17 : -E

o17 = 2/3*Div(y, z) + -3/2*Div(x, z)

o17 : WeilDivisor on R