toricCycle -- Creates a ToricCycle

Usage:

toricCycle(L,X)

toricCycle(D)
Inputs:
- L, a list, a list of options (sigma => d) where d is the coefficient of the cycle associated to the cone sigma
- X, a normal toric variety, the variety the cycle lives on
Outputs:
- a toric cycle,

Description

Toric cycles can be created with the constructor, and as they form an abelian group under addition, arithmetic can be done with them.

i1 : rayList={{1,0},{0,1},{-1,-1},{0,-1}}

o1 = {{1, 0}, {0, 1}, {-1, -1}, {0, -1}}

o1 : List

i2 : coneList={{0,1},{1,2},{2,3},{3,0}}

o2 = {{0, 1}, {1, 2}, {2, 3}, {3, 0}}

o2 : List

i3 : X = normalToricVariety(rayList,coneList)

o3 = X

o3 : NormalToricVariety

i4 : cyc = toricCycle({{2,3} =>1,{3,0} => 4},X)

o4 = X       + 4*X
      {2, 3}      {3, 0}

o4 : ToricCycle on X

i5 : altcyc = (-2)*cyc

o5 = - 2*X       - 8*X
          {2, 3}      {3, 0}

o5 : ToricCycle on X

i6 : cyc + altcyc

o6 = - X       - 4*X
        {2, 3}      {3, 0}

o6 : ToricCycle on X

i7 : cyc - altcyc

o7 = 3*X       + 12*X
        {2, 3}       {3, 0}

o7 : ToricCycle on X

i8 : -cyc

o8 = - X       - 4*X
        {2, 3}      {3, 0}

o8 : ToricCycle on X

toricCycle(List,List,NormalToricVariety)
toricCycle(List,NormalToricVariety)
toricCycle(ToricCycle) -- see toricCycle(ToricDivisor) -- Creates a ToricCycle from a ToricDivisor
toricCycle(ToricDivisor) -- Creates a ToricCycle from a ToricDivisor

The source of this document is in TropicalToric/ToricCycleDoc.m2:106:0.