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Macaulay2Doc :: isSquareFree

isSquareFree -- whether something is square free monomial ideal

Synopsis

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.

See also

Ways to use isSquareFree :

For the programmer

The object isSquareFree is a method function.