isSquareFree -- whether something is square free monomial ideal

i1 : QQ[x,y,z];

i2 : J = monomialIdeal(x^3*y^5*z, y^5*z^4, y^3*z^5, 
     	       x*y*z^5, x^2*z^5, x^4*z^3, x^4*y^2*z^2, 
     	       x^4*y^4*z)

                     4 4    3 5    4 2 2   4 3   5 4   2 5       5   3 5
o2 = monomialIdeal (x y z, x y z, x y z , x z , y z , x z , x*y*z , y z )

o2 : MonomialIdeal of QQ[x..z]

i3 : isSquareFree J

o3 = false

i4 : radical J

o4 = monomialIdeal (x*z, y*z)

o4 : MonomialIdeal of QQ[x..z]

i5 : isSquareFree radical J

o5 = true

i6 : needsPackage "SimplicialComplexes"

o6 = SimplicialComplexes

o6 : Package

i7 : R = QQ[a..d]

o7 = R

o7 : PolynomialRing

i8 : D = simplicialComplex {a*b*c,a*b*d,a*c*d,b*c*d}

o8 = simplicialComplex | bcd acd abd abc |

o8 : SimplicialComplex

i9 : I = monomialIdeal D

o9 = monomialIdeal(a*b*c*d)

o9 : MonomialIdeal of R

i10 : isSquareFree I

o10 = true