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# toricCycle -- Creates a ToricCycle

## Synopsis

• 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, , the variety the cycle lives on
• Outputs:
• ,

## 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