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toricCycle -- Creates a ToricCycle

Synopsis

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

See also

Ways to use toricCycle :

For the programmer

The object toricCycle is a method function.