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<head><title>Flat -- intersection of hyperplanes</title>
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<div><h1>Flat -- intersection of hyperplanes</h1>
<div class="single"><h2>Description</h2>
<div><p/>
A flat is a set of hyperplanes, maximal with respect to the property that they contain a given subspace. In this package, flats are treated as lists of indices of hyperplanes in the arrangement.</div>
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<div class="waystouse"><h2>Functions and methods returning an intersection of hyperplane(s) :</h2>
<ul><li><span><a href="_closure.html" title="closure operation in the intersection lattice">closure</a> -- closure operation in the intersection lattice</span></li>
<li><span>closure(Arrangement,List), see <span><a href="_closure.html" title="closure operation in the intersection lattice">closure</a> -- closure operation in the intersection lattice</span></span></li>
<li><span><tt>closure(Arrangement,Arrangement)</tt> (missing documentation<!-- tag: (closure,Arrangement,Arrangement) -->)</span></li>
<li><span><tt>closure(Arrangement,Ideal)</tt> (missing documentation<!-- tag: (closure,Arrangement,Ideal) -->)</span></li>
<li><span><a href="_flat.html" title="make a flat from a list of indices">flat</a> -- make a flat from a list of indices</span></li>
<li><span>flat(Arrangement,List), see <span><a href="_flat.html" title="make a flat from a list of indices">flat</a> -- make a flat from a list of indices</span></span></li>
<li><span><a href="___Flat_sp^_sp__Flat.html" title="meet operation in intersection lattice">Flat ^ Flat</a> -- meet operation in intersection lattice</span></li>
<li><span><a href="___Flat_sp_vb_sp__Flat.html" title="join operation in intersection lattice">Flat | Flat</a> -- join operation in intersection lattice</span></li>
<li><span><a href="_meet.html" title="meet operation in intersection lattice">meet</a> -- meet operation in intersection lattice</span></li>
<li><span>meet(Flat,Flat), see <span><a href="_meet.html" title="meet operation in intersection lattice">meet</a> -- meet operation in intersection lattice</span></span></li>
<li><span><a href="_vee.html" title="join operation in intersection lattice">vee</a> -- join operation in intersection lattice</span></li>
<li><span>vee(Flat,Flat), see <span><a href="_vee.html" title="join operation in intersection lattice">vee</a> -- join operation in intersection lattice</span></span></li>
</ul>
<h2>Methods that use an intersection of hyperplane(s) :</h2>
<ul><li><span><a href="___Arrangement_sp^_sp__Flat.html" title="restriction of arrangement to flat">Arrangement ^ Flat</a> -- restriction of arrangement to flat</span></li>
<li><span><a href="___Arrangement_sp_us_sp__Flat.html" title="Subarrangement containing a fixed flat">Arrangement _ Flat</a> -- Subarrangement containing a fixed flat</span></li>
<li><span><tt>arrangement(Flat)</tt> (missing documentation<!-- tag: (arrangement,Flat) -->)</span></li>
<li><span><a href="_euler_lp__Flat_rp.html" title="Euler characteristic">euler(Flat)</a> -- Euler characteristic</span></li>
<li><span><tt>expression(Flat)</tt> (missing documentation<!-- tag: (expression,Flat) -->)</span></li>
<li><span><tt>net(Flat)</tt> (missing documentation<!-- tag: (net,Flat) -->)</span></li>
<li><span><tt>rank(Flat)</tt> (missing documentation<!-- tag: (rank,Flat) -->)</span></li>
<li><span>restriction(Arrangement,Flat), see <span><a href="_restriction.html" title="restriction of arrangement to flat/hyperplane">restriction</a> -- restriction of arrangement to flat/hyperplane</span></span></li>
<li><span>restriction(Flat), see <span><a href="_restriction.html" title="restriction of arrangement to flat/hyperplane">restriction</a> -- restriction of arrangement to flat/hyperplane</span></span></li>
<li><span>subArrangement(Arrangement,Flat), see <span><a href="_sub__Arrangement.html" title="Subarrangement containing a fixed flat">subArrangement</a> -- Subarrangement containing a fixed flat</span></span></li>
<li><span>subArrangement(Flat), see <span><a href="_sub__Arrangement.html" title="Subarrangement containing a fixed flat">subArrangement</a> -- Subarrangement containing a fixed flat</span></span></li>
<li><span><tt>tolist(Flat)</tt> (missing documentation<!-- tag: (tolist,Flat) -->)</span></li>
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<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="___Flat.html" title="intersection of hyperplanes">Flat</a> is <span>a <a href="../../Macaulay2Doc/html/___Type.html">type</a></span>, with ancestor classes <a href="../../Macaulay2Doc/html/___Hash__Table.html" title="the class of all hash tables">HashTable</a> < <a href="../../Macaulay2Doc/html/___Thing.html" title="the class of all things">Thing</a>.</p>
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