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<head><title>SimplicialComplexes -- simplicial complexes</title>
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<div><h1>SimplicialComplexes -- simplicial complexes</h1>
<div class="single"><h2>Description</h2>
<div><em>SimplicialComplexes</em> is a package for manipulating simplicial complexes.<p/>
A simplicial complex on a set of vertices is a collection of subsets <tt>D</tt> of these vertices, such that if <tt>F</tt> is in <tt>D</tt>, then every subset of <tt>F</tt> is also in <tt>D</tt>. In Macaulay2, the vertices are variables in a polynomial ring, and each subset is represented as a product of the corresponding variables.<p/>
There is a bijection between simplicial complexes and squarefree monomial ideals. This package exploits this correspondence by using commutative algebra routines to perform most of the necessary computations.<p/>
This package includes the following functions:<ul><li><span><a href="_boundary.html" title="boundary operator">boundary</a> -- boundary operator</span></li>
<li><span><a href="_buchberger__Complex.html" title="Buchberger complex of a monomial ideal">buchbergerComplex</a> -- Buchberger complex of a monomial ideal</span></li>
<li><span><tt>chainComplex(SimplicialComplex)</tt> (missing documentation<!-- tag: (chainComplex,SimplicialComplex) -->)</span></li>
<li><span><a href="_coefficient__Ring_lp__Simplicial__Complex_rp.html" title="get the coefficient ring">coefficientRing(SimplicialComplex)</a> -- get the coefficient ring</span></li>
<li><span><a href="_dim_lp__Simplicial__Complex_rp.html" title="dimension of a simplicial complex">dim(SimplicialComplex)</a> -- dimension of a simplicial complex</span></li>
<li><span><a href="_dual_lp__Simplicial__Complex_rp.html" title="the Alexander dual of a simplicial complex">dual(SimplicialComplex)</a> -- the Alexander dual of a simplicial complex</span></li>
<li><span><a href="_faces.html" title="the i-faces of a simplicial complex ">faces</a> -- the i-faces of a simplicial complex </span></li>
<li><span><a href="_facets.html" title="the facets of a simplicial complex">facets</a> -- the facets of a simplicial complex</span></li>
<li><span><a href="_f__Vector.html" title="the f-vector of a simplicial complex">fVector</a> -- the f-vector of a simplicial complex</span></li>
<li><span><tt>HH SimplicialComplex</tt> (missing documentation<!-- tag: (homology,SimplicialComplex) -->)</span></li>
<li><span><a href="_ideal_lp__Simplicial__Complex_rp.html" title="the ideal of minimal nonfaces (the Stanley-Reisner ideal)">ideal(SimplicialComplex)</a> -- the ideal of minimal nonfaces (the Stanley-Reisner ideal)</span></li>
<li><span><a href="_is__Pure.html" title="whether the facets are equidimensional">isPure</a> -- whether the facets are equidimensional</span></li>
<li><span><a href="_label.html" title="labels with monomials the faces of simplicial complex">label</a> -- labels with monomials the faces of simplicial complex</span></li>
<li><span><a href="_lyubeznik__Complex.html" title="Simplicial complex supporting the Lyubeznik resolution of a monomial ideal">lyubeznikComplex</a> -- Simplicial complex supporting the Lyubeznik resolution of a monomial ideal</span></li>
<li><span><a href="_monomial__Ideal_lp__Simplicial__Complex_rp.html" title="the monomial ideal of minimal nonfaces (the Stanley-Reisner ideal)">monomialIdeal(SimplicialComplex)</a> -- the monomial ideal of minimal nonfaces (the Stanley-Reisner ideal)</span></li>
<li><span><a href="_ring_lp__Simplicial__Complex_rp.html" title="get the associated ring of an object">ring(SimplicialComplex)</a> -- get the associated ring of an object</span></li>
<li><span><a href="_simplicial__Complex.html" title="create a simplicial complex">simplicialComplex</a> -- create a simplicial complex</span></li>
<li><span><tt>simplicialChainComplex</tt> (missing documentation<!-- tag: simplicialChainComplex -->)</span></li>
<li><span><a href="_superficial__Complex.html" title="Simplicial complex supporting a superficial resolution of a monomial ideal">superficialComplex</a> -- Simplicial complex supporting a superficial resolution of a monomial ideal</span></li>
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<div class="single"><h2>Authors</h2>
<ul><li><div class="single"><a href="http://www.math.sunysb.edu/~sorin/">Sorin Popescu</a><span> <<a href="mailto:sorin@math.sunysb.edu">sorin@math.sunysb.edu</a>></span></div>
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<li><div class="single"><a href="http://www.mast.queensu.ca/~ggsmith">Gregory G. Smith</a><span> <<a href="mailto:ggsmith@mast.queensu.ca">ggsmith@mast.queensu.ca</a>></span></div>
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<li><div class="single"><a href="http://www.math.cornell.edu/~mike">Mike Stillman</a><span> <<a href="mailto:mike@math.cornell.edu">mike@math.cornell.edu</a>></span></div>
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<div class="single"><h2>Version</h2>
This documentation describes version <b>1.1</b> of SimplicialComplexes.</div>
<div class="single"><h2>Source code</h2>
The source code from which this documentation is derived is in the file <a href="../../../../Macaulay2/SimplicialComplexes.m2">SimplicialComplexes.m2</a>.</div>
<div class="single"><h2>Exports</h2>
<ul><li><div class="single">Types<ul><li><span><a href="___Simplicial__Complex.html" title="">SimplicialComplex</a></span></li>
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<li><div class="single">Functions<ul><li><span><a href="_boundary.html" title="boundary operator">boundary</a> -- boundary operator</span></li>
<li><span><a href="_buchberger__Complex.html" title="Buchberger complex of a monomial ideal">buchbergerComplex</a> -- Buchberger complex of a monomial ideal</span></li>
<li><span><a href="_faces.html" title="the i-faces of a simplicial complex ">faces</a> -- the i-faces of a simplicial complex </span></li>
<li><span><a href="_facets.html" title="the facets of a simplicial complex">facets</a> -- the facets of a simplicial complex</span></li>
<li><span><a href="_f__Vector.html" title="the f-vector of a simplicial complex">fVector</a> -- the f-vector of a simplicial complex</span></li>
<li><span><a href="_is__Pure.html" title="whether the facets are equidimensional">isPure</a> -- whether the facets are equidimensional</span></li>
<li><span><a href="_label.html" title="labels with monomials the faces of simplicial complex">label</a> -- labels with monomials the faces of simplicial complex</span></li>
<li><span><a href="_link.html" title="link of a face in a simplicial complex">link</a> -- link of a face in a simplicial complex</span></li>
<li><span><a href="_lyubeznik__Complex.html" title="Simplicial complex supporting the Lyubeznik resolution of a monomial ideal">lyubeznikComplex</a> -- Simplicial complex supporting the Lyubeznik resolution of a monomial ideal</span></li>
<li><span><tt>simplicialChainComplex</tt> (missing documentation<!-- tag: simplicialChainComplex -->)</span></li>
<li><span><a href="_simplicial__Complex.html" title="create a simplicial complex">simplicialComplex</a> -- create a simplicial complex</span></li>
<li><span><a href="_superficial__Complex.html" title="Simplicial complex supporting a superficial resolution of a monomial ideal">superficialComplex</a> -- Simplicial complex supporting a superficial resolution of a monomial ideal</span></li>
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<li><div class="single">Methods<ul><li><span><a href="_boundary_lp__Z__Z_cm__Simplicial__Complex_rp.html" title="the boundary map from i-faces to (i-1)-faces">boundary(ZZ,SimplicialComplex)</a> -- the boundary map from i-faces to (i-1)-faces</span></li>
<li><span>faces(ZZ,SimplicialComplex), see <span><a href="_faces.html" title="the i-faces of a simplicial complex ">faces</a> -- the i-faces of a simplicial complex </span></span></li>
<li><span><tt>HH_ZZ SimplicialComplex</tt> (missing documentation<!-- tag: (homology,ZZ,SimplicialComplex) -->)</span></li>
<li><span><tt>HH_ZZ(SimplicialComplex,Ring)</tt> (missing documentation<!-- tag: (homology,ZZ,SimplicialComplex,Ring) -->)</span></li>
<li><span><tt>homology(Nothing,SimplicialComplex)</tt> (missing documentation<!-- tag: (homology,Nothing,SimplicialComplex) -->)</span></li>
<li><span><tt>homology(Nothing,SimplicialComplex,Ring)</tt> (missing documentation<!-- tag: (homology,Nothing,SimplicialComplex,Ring) -->)</span></li>
<li><span><tt>homology(SimplicialComplex,Ring)</tt> (missing documentation<!-- tag: (homology,SimplicialComplex,Ring) -->)</span></li>
<li><span>label(SimplicialComplex,List), see <span><a href="_label.html" title="labels with monomials the faces of simplicial complex">label</a> -- labels with monomials the faces of simplicial complex</span></span></li>
<li><span>link(SimplicialComplex,RingElement), see <span><a href="_link.html" title="link of a face in a simplicial complex">link</a> -- link of a face in a simplicial complex</span></span></li>
<li><span><tt>simplicialChainComplex(List,SimplicialComplex)</tt> (missing documentation<!-- tag: (simplicialChainComplex,List,SimplicialComplex) -->)</span></li>
<li><span><tt>SimplicialComplex == SimplicialComplex</tt> (missing documentation<!-- tag: (==,SimplicialComplex,SimplicialComplex) -->)</span></li>
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