The set of torus-invariant Weil divisors forms an abelian group under addition. The basic operations arising from this structure, including addition, subtraction, negation, and scalar multiplication by integers, are available.
We illustrate a few of the possibilities on one variety.
i1 : X = normalToricVariety(id_(ZZ^3) | -id_(ZZ^3)); |
i2 : # rays X o2 = 8 |
i3 : D = toricDivisor({2,-7,3,0,7,5,8,-8}, X)
o3 = 2*X - 7*X + 3*X + 7*X + 5*X + 8*X - 8*X
0 1 2 4 5 6 7
o3 : ToricDivisor on X
|
i4 : K = toricDivisor X
o4 = - X - X - X - X - X - X - X - X
0 1 2 3 4 5 6 7
o4 : ToricDivisor on X
|
i5 : D + K
o5 = X - 8*X + 2*X - X + 6*X + 4*X + 7*X - 9*X
0 1 2 3 4 5 6 7
o5 : ToricDivisor on X
|
i6 : assert(D + K == K + D) |
i7 : D - K
o7 = 3*X - 6*X + 4*X + X + 8*X + 6*X + 9*X - 7*X
0 1 2 3 4 5 6 7
o7 : ToricDivisor on X
|
i8 : assert(D - K == -(K-D)) |
i9 : - K
o9 = X + X + X + X + X + X + X + X
0 1 2 3 4 5 6 7
o9 : ToricDivisor on X
|
i10 : assert(-K == (-1)*K) |
i11 : 7*D
o11 = 14*X - 49*X + 21*X + 49*X + 35*X + 56*X - 56*X
0 1 2 4 5 6 7
o11 : ToricDivisor on X
|
i12 : assert(7*D == (3+4)*D) |
i13 : assert(7*D == 3*D + 4*D) |
i14 : -3*D + 7*K
o14 = - 13*X + 14*X - 16*X - 7*X - 28*X - 22*X - 31*X + 17*X
0 1 2 3 4 5 6 7
o14 : ToricDivisor on X
|
i15 : assert(-3*D+7*K == (-2*D+8*K) + (-D-K)) |