Working with fans - Part 2

Now we construct a new fan to show some other functions.

i1 : C1 = coneFromVData matrix {{1,1,-1,-1},{1,-1,1,-1},{1,1,1,1}};

i2 : C2 = coneFromVData matrix {{1,1,1},{0,1,-1},{-1,1,1}};

i3 : C3 = coneFromVData matrix {{-1,-1,-1},{0,1,-1},{-1,1,1}};

i4 : C4 = coneFromVData matrix {{1,-1},{0,0},{-1,-1}};

i5 : F = fan {C1,C2,C3,C4}

o5 = F

o5 : Fan

This is not a ''very nice'' fan, as it is neither complete nor of pure dimension:

i6 : isComplete F

o6 = false

i7 : isPure F

o7 = false

If we add two more cones the fan becomes complete.

i8 : C5 = coneFromVData matrix {{1,-1,1,-1},{-1,-1,0,0},{1,1,-1,-1}};

i9 : C6 = coneFromVData matrix {{1,-1,1,-1},{1,1,0,0},{1,1,-1,-1}};

i10 : F = addCone({C5,C6},F)

o10 = F

o10 : Fan

i11 : isComplete F

o11 = true

For a complete fan we can check if it is projective:

i12 : isPolytopal F

o12 = true

If the fan is projective, the function returns a polyhedron such that the fan is its normal fan, otherwise it returns the empty polyhedron. This means our fan is projective.