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<div><h1>HyperplaneArrangements -- hyperplane arrangements</h1>
<div class="single"><h2>Description</h2>
<div><em>HyperplaneArrangement</em> is a package for manipulating hyperplane arrangements.<p/>
A hyperplane arrangement is a finite set of hyperplanes in an affine or projective space. In this package, an arrangement is expressed as a list of (linear) defining equations for the hyperplanes. The tools provided allow the user to create new arrangements from old, and to compute various algebraic invariants of arrangements.</div>
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<div class="single"><h2>Authors</h2>
<ul><li><div class="single"><a href="http://www.math.uwo.ca/~gdenham/">Graham Denham</a></div>
</li>
<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>
</li>
</ul>
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<div class="single"><h2>Version</h2>
This documentation describes version <b>0.5</b> of HyperplaneArrangements.</div>
<div class="single"><h2>Source code</h2>
The source code from which this documentation is derived is in the file <a href="../../../../Macaulay2/HyperplaneArrangements.m2">HyperplaneArrangements.m2</a>.</div>
<div class="single"><h2>Exports</h2>
<ul><li><div class="single">Types<ul><li><span><a href="___Arrangement.html" title="class of hyperplane arrangements">Arrangement</a> -- class of hyperplane arrangements</span></li>
<li><span><a href="___Flat.html" title="intersection of hyperplanes">Flat</a> -- intersection of hyperplanes</span></li>
</ul>
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</li>
<li><div class="single">Functions<ul><li><span><a href="_arrangement.html" title="create a hyperplane arrangement">arrangement</a> -- create a hyperplane arrangement</span></li>
<li><span><tt>arrangementSum</tt> (missing documentation<!-- tag: arrangementSum -->)</span></li>
<li><span><tt>changeRing</tt> (missing documentation<!-- tag: changeRing -->)</span></li>
<li><span><a href="_circuits.html" title="list the circuits of an arrangement">circuits</a> -- list the circuits of an arrangement</span></li>
<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><a href="_deletion.html" title="subarrangement given by deleting a hyperplane">deletion</a> -- subarrangement given by deleting a hyperplane</span></li>
<li><span><a href="_der.html" title="Module of logarithmic derivations">der</a> -- Module of logarithmic derivations</span></li>
<li><span><a href="___E__P__Y.html" title="compute the Eisenbud-Popescu-Yuzvinsky module of an arrangement">EPY</a> -- compute the Eisenbud-Popescu-Yuzvinsky module of an arrangement</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><a href="_flats.html" title="list the flats of an arrangement of given rank">flats</a> -- list the flats of an arrangement of given rank</span></li>
<li><span><a href="_graphic.html" title="Make a graphic arrangement">graphic</a> -- Make a graphic arrangement</span></li>
<li><span><a href="_is__Decomposable.html" title="test if an arrangement is decomposable">isDecomposable</a> -- test if an arrangement is decomposable</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><a href="_mult__Ideal.html" title="compute a multiplier ideal">multIdeal</a> -- compute a multiplier ideal</span></li>
<li><span><a href="_orlik__Solomon.html" title="defining ideal for the Orlik-Solomon algebra">orlikSolomon</a> -- defining ideal for the Orlik-Solomon algebra</span></li>
<li><span><a href="_random__Arrangement.html" title="generate an arrangement at random">randomArrangement</a> -- generate an arrangement at random</span></li>
<li><span><a href="_restriction.html" title="restriction of arrangement to flat/hyperplane">restriction</a> -- restriction of arrangement to flat/hyperplane</span></li>
<li><span><a href="_sub__Arrangement.html" title="Subarrangement containing a fixed flat">subArrangement</a> -- Subarrangement containing a fixed flat</span></li>
<li><span><tt>tolist</tt> (missing documentation<!-- tag: tolist -->)</span></li>
<li><span><a href="_type__A.html" title="Type A reflection arrangement">typeA</a> -- Type A reflection arrangement</span></li>
<li><span><a href="_type__B.html" title="Type B reflection arrangement">typeB</a> -- Type B reflection arrangement</span></li>
<li><span><a href="_type__D.html" title="Type D reflection arrangement">typeD</a> -- Type D reflection arrangement</span></li>
<li><span><a href="_vee.html" title="join operation in intersection lattice">vee</a> -- join operation in intersection lattice</span></li>
</ul>
</div>
</li>
<li><div class="single">Methods<ul><li><span>arrangement(Arrangement,Ring), see <span><a href="_arrangement.html" title="create a hyperplane arrangement">arrangement</a> -- create a hyperplane arrangement</span></span></li>
<li><span><tt>Arrangement ** Arrangement</tt> (missing documentation<!-- tag: (**,Arrangement,Arrangement) -->)</span></li>
<li><span><tt>Arrangement ** Ring</tt> (missing documentation<!-- tag: (**,Arrangement,Ring) -->)</span></li>
<li><span><tt>Arrangement == Arrangement</tt> (missing documentation<!-- tag: (==,Arrangement,Arrangement) -->)</span></li>
<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>arrangementSum(Arrangement,Arrangement)</tt> (missing documentation<!-- tag: (arrangementSum,Arrangement,Arrangement) -->)</span></li>
<li><span><tt>changeRing(Arrangement,Ring)</tt> (missing documentation<!-- tag: (changeRing,Arrangement,Ring) -->)</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><tt>cone(Arrangement,RingElement)</tt> (missing documentation<!-- tag: (cone,Arrangement,RingElement) -->)</span></li>
<li><span><tt>cone(Arrangement,Symbol)</tt> (missing documentation<!-- tag: (cone,Arrangement,Symbol) -->)</span></li>
<li><span>deletion(Arrangement,RingElement), see <span><a href="_deletion.html" title="subarrangement given by deleting a hyperplane">deletion</a> -- subarrangement given by deleting a hyperplane</span></span></li>
<li><span>der(Arrangement,List), see <span><a href="_der.html" title="Module of logarithmic derivations">der</a> -- Module of logarithmic derivations</span></span></li>
<li><span><tt>dlogPhi(Arrangement,List)</tt> (missing documentation<!-- tag: (dlogPhi,Arrangement,List) -->)</span></li>
<li><span>EPY(Arrangement,PolynomialRing), see <span><a href="___E__P__Y.html" title="compute the Eisenbud-Popescu-Yuzvinsky module of an arrangement">EPY</a> -- compute the Eisenbud-Popescu-Yuzvinsky module of an arrangement</span></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>flats(ZZ,Arrangement), see <span><a href="_flats.html" title="list the flats of an arrangement of given rank">flats</a> -- list the flats of an arrangement of given rank</span></span></li>
<li><span><tt>freeDlogPhi(Arrangement,List)</tt> (missing documentation<!-- tag: (freeDlogPhi,Arrangement,List) -->)</span></li>
<li><span>isDecomposable(Arrangement,Ring), see <span><a href="_is__Decomposable.html" title="test if an arrangement is decomposable">isDecomposable</a> -- test if an arrangement is decomposable</span></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>multIdeal(Number,Arrangement), see <span><a href="_mult__Ideal.html" title="compute a multiplier ideal">multIdeal</a> -- compute a multiplier ideal</span></span></li>
<li><span>multIdeal(Number,Arrangement,List), see <span><a href="_mult__Ideal.html" title="compute a multiplier ideal">multIdeal</a> -- compute a multiplier ideal</span></span></li>
<li><span>multIdeal(RR,Arrangement), see <span><a href="_mult__Ideal.html" title="compute a multiplier ideal">multIdeal</a> -- compute a multiplier ideal</span></span></li>
<li><span>multIdeal(RR,Arrangement,List), see <span><a href="_mult__Ideal.html" title="compute a multiplier ideal">multIdeal</a> -- compute a multiplier ideal</span></span></li>
<li><span>orlikSolomon(Arrangement,Ring), see <span><a href="_orlik__Solomon.html" title="defining ideal for the Orlik-Solomon algebra">orlikSolomon</a> -- defining ideal for the Orlik-Solomon algebra</span></span></li>
<li><span>orlikSolomon(Arrangement,Symbol), see <span><a href="_orlik__Solomon.html" title="defining ideal for the Orlik-Solomon algebra">orlikSolomon</a> -- defining ideal for the Orlik-Solomon algebra</span></span></li>
<li><span><tt>orlikSolomon(Arrangement,PolynomialRing)</tt> (missing documentation<!-- tag: (orlikSolomon,Arrangement,PolynomialRing) -->)</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(Arrangement,Ideal), 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(Arrangement,RingElement), 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>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>
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</li>
<li><div class="single">Symbols<ul><li><span><tt>HypAtInfinity</tt> (missing documentation<!-- tag: HypAtInfinity -->)</span></li>
</ul>
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</li>
<li><div class="single">Other things<ul><li><span><tt>arrangementLibrary</tt> (missing documentation<!-- tag: arrangementLibrary -->)</span></li>
</ul>
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</li>
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