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NormalToricVarieties :: ToricDivisor

ToricDivisor -- the class of all torus-invariant Weil divisors

Description

A torus-invariant Weil divisor on a normal toric variety is an integral linear combination of the torus-invariant prime divisors. The torus-invariant prime divisors correspond to the rays. In this package, the rays are ordered and indexed by the nonnegative integers.

The first examples illustrates some torus-invariant Weil divisors on projective 2-space

i1 : PP2 = projectiveSpace 2;
i2 : D1 = toricDivisor({2,-7,3},PP2) 

o2 = 2*D  - 7*D  + 3*D
        0      1      2

o2 : ToricDivisor on PP2
i3 : D2 = 2*PP2_0 + 4*PP2_2

o3 = 2*D  + 4*D
        0      2

o3 : ToricDivisor on PP2
i4 : D1+D2

o4 = 4*D  - 7*D  + 7*D
        0      1      2

o4 : ToricDivisor on PP2
i5 : D1-D2

o5 = - 7*D  - D
          1    2

o5 : ToricDivisor on PP2
i6 : K = toricDivisor PP2  

o6 = - D  - D  - D
        0    1    2

o6 : ToricDivisor on PP2
One can easily extract individual coefficients or the vector of coefficients
i7 : D1#0

o7 = 2
i8 : D1#1

o8 = -7
i9 : D1#2

o9 = 3
i10 : vector D1

o10 = | 2  |
      | -7 |
      | 3  |

        3
o10 : ZZ
i11 : vector K

o11 = | -1 |
      | -1 |
      | -1 |

        3
o11 : ZZ

See also

Functions and methods returning a toric divisor :

Methods that use a toric divisor :

For the programmer

The object ToricDivisor is a type, with ancestor classes HashTable < Thing.