The set of torus-invariant cycles forms an abelian group under addition. The basic operations arising from this structure, including addition, subtraction, negation, and scalar multplication by integers, are available.
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
|
i9 : X_{0} + X_{1}
o9 = X + X
{0} {1}
o9 : ToricCycle on X
|
i10 : 2*X_{0,1} - X_{0,2}
o10 = 2*X - X
{0, 1} {0, 2}
o10 : ToricCycle on X
|