isBalanced -- checks whether a tropical cycle is balanced

i1 : QQ[x,y,z]

o1 = QQ[x..z]

o1 : PolynomialRing

i2 : V = tropicalVariety(ideal(x+y+z))

o2 = V

o2 : TropicalCycle

i3 : isBalanced V

o3 = true

i4 : F = fan {posHull matrix {{1},{0},{0}}, posHull matrix {{0},{1},{0}}, posHull matrix {{0},{0},{1}}, posHull matrix {{-1},{-1},{-1}}}

o4 = F

o4 : Fan

i5 : mult = {1,2,-3,1}

o5 = {1, 2, -3, 1}

o5 : List

i6 : isBalanced (tropicalCycle(F, mult))

o6 = false