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NormalToricVarieties :: ToricDivisor + ToricDivisor

ToricDivisor + ToricDivisor -- arithmetic of toric divisors

Synopsis

Description

The set of torus-invariant Weil divisors form an abelian group under addition. The basic operations arising from this structure, including addition, substraction, negation, and scalar multplication by integers, are available.
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*D  - 7*D  + 3*D  + 7*D  + 5*D  + 8*D  - 8*D
        0      1      2      4      5      6      7

o3 : ToricDivisor on X
i4 : K = toricDivisor X

o4 = - D  - D  - D  - D  - D  - D  - D  - D
        0    1    2    3    4    5    6    7

o4 : ToricDivisor on X
i5 : D+K

o5 = D  - 8*D  + 2*D  - D  + 6*D  + 4*D  + 7*D  - 9*D
      0      1      2    3      4      5      6      7

o5 : ToricDivisor on X
i6 : D+K === K+D

o6 = true
i7 : D-K

o7 = 3*D  - 6*D  + 4*D  + D  + 8*D  + 6*D  + 9*D  - 7*D
        0      1      2    3      4      5      6      7

o7 : ToricDivisor on X
i8 : D-K === -(K-D)

o8 = true
i9 : -K

o9 = D  + D  + D  + D  + D  + D  + D  + D
      0    1    2    3    4    5    6    7

o9 : ToricDivisor on X
i10 : -K === (-1)*K

o10 = true
i11 : 7*D

o11 = 14*D  - 49*D  + 21*D  + 49*D  + 35*D  + 56*D  - 56*D
          0       1       2       4       5       6       7

o11 : ToricDivisor on X
i12 : 7*D === (3+4)*D

o12 = true
i13 : -3*D+7*K    

o13 = - 13*D  + 14*D  - 16*D  - 7*D  - 28*D  - 22*D  - 31*D  + 17*D
            0       1       2      3       4       5       6       7

o13 : ToricDivisor on X
i14 : -3*D+7*K === (-2*D+8*K) + (-D-K)

o14 = true

See also