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<head><title>isSquareFree -- whether something is square free monomial ideal</title>
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<div><h1>isSquareFree -- whether something is square free monomial ideal</h1>
<div class="single"><h2>Synopsis</h2>
<ul><li><div class="list"><dl class="element"><dt class="heading">Usage: </dt><dd class="value"><div><tt>isSquareFree I</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>I</tt>, <span>a <a href="___Monomial__Ideal.html">monomial ideal</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Boolean.html">Boolean value</a></span>, <a href="_true.html" title="">true</a> if <tt>I</tt> is a square free <a href="___Monomial__Ideal.html">monomial ideal</a> and <a href="_false.html" title="">false</a> otherwise</span></li>
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<div class="single"><h2>Description</h2>
<div>A square free <a href="___Monomial__Ideal.html">monomial ideal</a> is an ideal generated by products of variables; in other words, a radical monomial ideal.<table class="examples"><tr><td><pre>i1 : QQ[x,y,z];</pre>
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<tr><td><pre>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]</pre>
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<tr><td><pre>i3 : isSquareFree J
o3 = false</pre>
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<tr><td><pre>i4 : radical J
o4 = monomialIdeal (x*z, y*z)
o4 : MonomialIdeal of QQ[x, y, z]</pre>
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<tr><td><pre>i5 : isSquareFree radical J
o5 = true</pre>
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Square free monomial ideals correspond both to simplicial complexes and to unions of coordinate subspaces.<table class="examples"><tr><td><pre>i6 : needsPackage "SimplicialComplexes"
o6 = SimplicialComplexes
o6 : Package</pre>
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<tr><td><pre>i7 : R = QQ[a..d]
o7 = R
o7 : PolynomialRing</pre>
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<tr><td><pre>i8 : D = simplicialComplex {a*b*c,a*b*d,a*c*d,b*c*d}
o8 = | bcd acd abd abc |
o8 : SimplicialComplex</pre>
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<tr><td><pre>i9 : I = monomialIdeal D
o9 = monomialIdeal(a*b*c*d)
o9 : MonomialIdeal of R</pre>
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<tr><td><pre>i10 : isSquareFree I
o10 = true</pre>
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Implemented by Greg Smith.</div>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_radical.html" title="the radical of an ideal">radical</a> -- the radical of an ideal</span></li>
<li><span><a href="_associated__Primes.html" title="find the associated primes of an ideal">associatedPrimes</a> -- find the associated primes of an ideal</span></li>
<li><span><a href="../../SimplicialComplexes/html/index.html" title="simplicial complexes">SimplicialComplexes</a> -- simplicial complexes</span></li>
</ul>
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<div class="waystouse"><h2>Ways to use <tt>isSquareFree</tt> :</h2>
<ul><li>isSquareFree(MonomialIdeal)</li>
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