isSquareFree MonomialIdeal -- whether a monomial ideal is square free

isSquareFree MonomialIdeal -- whether a monomial ideal is square free

Synopsis:

Function: isSquareFree

Input:

an instance of class MonomialIdeal.

Output:

an instance of class Boolean.

A square free monomial ideal is an ideal generated by products of variables; in other words, a radical monomial ideal.

Square free monomial ideals correspond both to simplicial complexes and to unions of coordinate subspaces.

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, y, z]

i3 : isSquareFree J



o3 = false

i4 : isSquareFree radical J



o4 = true

Implemented by Greg Smith.

Code:

     -- ../../../Macaulay2/m2/monideal.m2:311
     isSquareFree MonomialIdeal := (I) -> all(first entries gens I, m -> all(first exponents m, i -> i<2))