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<head><title>changeRing -- replaces vertices with variables of a different ring</title>
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<div><h1>changeRing -- replaces vertices with variables of a different ring</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>G = changeRing(H,R,L)</tt><br/><tt>G = changeRing(H,R,L, MaximalEdges => B)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>H</tt>, <span>a <a href="___Hyper__Graph.html">hypergraph</a></span></span></li>
<li><span><tt>R</tt>, <span>a <a href="../../Macaulay2Doc/html/___Polynomial__Ring.html">polynomial ring</a></span>, containing the new vertices as variables</span></li>
<li><span><tt>L</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, of substitutions, one variable in R for each vertex of H</span></li>
<li><span><tt>B</tt>, <span>a <a href="../../Macaulay2Doc/html/___Boolean.html">Boolean value</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>G</tt>, <span>a <a href="___Hyper__Graph.html">hypergraph</a></span>, over the ring R with edges obtained by making substitutions into the edges of H</span></li>
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<li><div class="single"><a href="../../Macaulay2Doc/html/_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><a href="_change__Ring_lp..._cm_sp__Maximal__Edges_sp_eq_gt_sp..._rp.html">MaximalEdges => ...</a>, -- optional argument for changeRing</span></li>
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<div class="single"><h2>Description</h2>
<div><div>This method is meant for moving a <a href="___Hyper__Graph.html" title="a class for hypergraphs">HyperGraph</a> that is defined over one ring to another ring R. The parameter L must be a list containing variables of R that should replace the vertices of H. For the most basic way to use this method, see the first example:</div>
<table class="examples"><tr><td><pre>i1 : P = QQ[a,b,c];</pre>
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<tr><td><pre>i2 : H = hyperGraph({a*b,b*c});</pre>
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<tr><td><pre>i3 : S = QQ[x,y,z,w];</pre>
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<tr><td><pre>i4 : changeRing(H,S,{x,z,y})
o4 = HyperGraph{edges => {{y, z}, {z, x}}}
ring => S
vertices => {x, y, z, w}
o4 : HyperGraph</pre>
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<div>In the example above, <tt>a</tt> is replaced with <tt>x</tt>, <tt>b</tt> is replaced with <tt>z</tt>, and <tt>c</tt> is replaced with <tt>y</tt>. A more complex situation arises when two vertices of <tt>H</tt> are replaced by the same variable.</div>
<table class="examples"><tr><td><pre>i5 : P = QQ[a,b,c];</pre>
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<tr><td><pre>i6 : H = hyperGraph({a*b*c});</pre>
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<tr><td><pre>i7 : G = hyperGraph({a*b,b*c});</pre>
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<tr><td><pre>i8 : S = QQ[x,y,z,w];</pre>
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<tr><td><pre>i9 : changeRing(H,S,{x,y,x})
o9 = HyperGraph{edges => {{y, x}} }
ring => S
vertices => {x, y, z, w}
o9 : HyperGraph</pre>
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<tr><td><pre>i10 : changeRing(G,S,{x,y,x})
o10 = HyperGraph{edges => {{y, x}} }
ring => S
vertices => {x, y, z, w}
o10 : HyperGraph</pre>
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<div>Note that duplicate variables are removed from edges after substitution. Duplicate edges are also reduced to a single edge. As all HyperGraphs in this package have the property that no edge is a subset of any other edge, some edges may need to be dropped after substitution. This happens in the next example.</div>
<table class="examples"><tr><td><pre>i11 : P = QQ[a,b,c];</pre>
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<tr><td><pre>i12 : H = hyperGraph({a*b,b*c});</pre>
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<tr><td><pre>i13 : S = QQ[x,y];</pre>
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<tr><td><pre>i14 : changeRing(H,S,{x,y,y})
o14 = HyperGraph{edges => {{y}} }
ring => S
vertices => {x, y}
o14 : HyperGraph</pre>
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<tr><td><pre>i15 : changeRing(H,S,{x,y,y},MaximalEdges=>true)
o15 = HyperGraph{edges => {{y, x}} }
ring => S
vertices => {x, y}
o15 : HyperGraph</pre>
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<div>By default, <tt>changeRing</tt> uses minimal edges that appear after substitution to construct its output. The optional argument <a href="___Maximal__Edges.html" title="optional argument for changeRing">MaximalEdges</a> allows one to get the maximal edges instead.</div>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_induced__Hyper__Graph.html" title="returns the induced subgraph of a (hyper)graph">inducedHyperGraph</a> -- returns the induced subgraph of a (hyper)graph</span></li>
</ul>
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<div class="waystouse"><h2>Ways to use <tt>changeRing</tt> :</h2>
<ul><li>changeRing(HyperGraph,PolynomialRing,List)</li>
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