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--- status: Draft
--- author(s): Gregory G. Smith
--- notes:
document {
Key => {isSquareFree,
(isSquareFree, MonomialIdeal),
(isSquareFree, Ideal),
(isSquareFree, Module)},
Headline => "whether something is square free monomial ideal",
Usage => "isSquareFree I",
Inputs => {
"I" => MonomialIdeal
},
Outputs => {
Boolean => {TO "true", " if ", TT "I", " is a square free ",
TO2("MonomialIdeal", "monomial ideal"),
" and ", TO "false", " otherwise"}
},
"A square free ", TO2("MonomialIdeal", "monomial ideal"), " is an ideal generated
by products of variables; in other words, a radical
monomial ideal.",
EXAMPLE {
"QQ[x,y,z];",
"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)",
"isSquareFree J",
"radical J",
"isSquareFree radical J"
},
"Square free monomial ideals correspond both to
simplicial complexes and to unions of coordinate
subspaces.",
EXAMPLE {
"needsPackage \"SimplicialComplexes\"",
"R = QQ[a..d]",
"D = simplicialComplex {a*b*c,a*b*d,a*c*d,b*c*d}",
"I = monomialIdeal D",
"isSquareFree I"
},
PARA{},
"Implemented by Greg Smith.",
SeeAlso => {"MinimalPrimes::radical", "PrimaryDecomposition::associatedPrimes", "SimplicialComplexes::SimplicialComplexes"}
}
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