# isSquareFree -- whether something is square free monomial ideal

## Description

A square free monomial ideal is an ideal generated by products of variables; in other words, a radical 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
Square free monomial ideals correspond both to simplicial complexes and to unions of coordinate subspaces.
 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 = | 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

Implemented by Greg Smith.