euler -- compute the Euler characteristic of a moment-angle complex

i1 : needsPackage "SimplicialComplexes"

o1 = SimplicialComplexes

o1 : Package

i2 : R = QQ[a..d]

o2 = R

o2 : PolynomialRing

i3 : K0 = simplicialComplex {a*b, b*c, c*d, d*a}

o3 = simplicialComplex | cd ad bc ab |

o3 : SimplicialComplex

i4 : Z0 = momentAngleComplex K0

o4 = MomentAngleComplex{MACSimplicialComplex => simplicialComplex | cd ad bc ab |}

o4 : MomentAngleComplex

i5 : euler Z0

o5 = 0

i6 : K1 = simplicialComplex {a*b*c*d}

o6 = simplicialComplex | abcd |

o6 : SimplicialComplex

i7 : Z1 = momentAngleComplex K1

o7 = MomentAngleComplex{MACSimplicialComplex => simplicialComplex | abcd |}

o7 : MomentAngleComplex

i8 : euler Z1

o8 = 1