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<head><title>graphRing(RingMap) -- the coordinate ring of the graph of the regular map corresponding to a ring map</title>
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<div><a href="index.html" title="">Macaulay2Doc</a> > <a href="_substitution_spand_spmaps_spbetween_springs.html" title="">substitution and maps between rings</a> > <a href="_graph__Ring_lp__Ring__Map_rp.html" title="the coordinate ring of the graph of the regular map corresponding to a ring map">graphRing(RingMap)</a></div>
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<div><h1>graphRing(RingMap) -- the coordinate ring of the graph of the regular map corresponding to a ring map</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>graphRing f</tt></div>
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<li><span>Function: <a href="_graph__Ring_lp__Ring__Map_rp.html" title="the coordinate ring of the graph of the regular map corresponding to a ring map">graphRing</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>f</tt>, <span>a <a href="___Ring__Map.html">ring map</a></span></span></li>
</ul>
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</li>
<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Quotient__Ring.html">quotient ring</a></span>, the coordinate ring of the graph of regular map corresponding to <tt>f</tt></span></li>
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<li><div class="single"><a href="_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><tt>MonomialOrder => </tt><span><span>default value {GRevLex, Position => Up}</span>, a monomial ordering, see <a href="_monomial_sporderings.html" title="">monomial orderings</a></span></span></li>
<li><span><tt>MonomialSize => </tt><span><span>an <a href="___Z__Z.html">integer</a></span>, <span>default value 32</span>, the monomial size, see <a href="___Monomial__Size.html" title="name for an optional argument">MonomialSize</a></span></span></li>
<li><span><tt>VariableBaseName => </tt><span><span>a <a href="___Symbol.html">symbol</a></span>, <span>default value p</span>, the variable base name, see <a href="_monoid.html" title="make or retrieve a monoid">VariableBaseName</a></span></span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : R = QQ[x,y]
o1 = R
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : S = QQ[s,t,u]
o2 = S
o2 : PolynomialRing</pre>
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<tr><td><pre>i3 : f = map(R,S,{x^2,x*y,y^2})
2 2
o3 = map(R,S,{x , x*y, y })
o3 : RingMap R <--- S</pre>
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<tr><td><pre>i4 : graphRing f
QQ[p , p , p , p , p ]
0 1 2 3 4
o4 = -----------------------------------
2 2
(- p + p , - p p + p , - p + p )
0 2 0 1 3 1 4
o4 : QuotientRing</pre>
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<tr><td><pre>i5 : Spec oo
/ QQ[p , p , p , p , p ] \
| 0 1 2 3 4 |
o5 = Spec|-----------------------------------|
| 2 2 |
|(- p + p , - p p + p , - p + p )|
\ 0 2 0 1 3 1 4 /
o5 : AffineVariety</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_graph__Ideal_lp__Ring__Map_rp.html" title="the ideal of the graph of the regular map corresponding to a ring map">graphIdeal</a> -- the ideal of the graph of the regular map corresponding to a ring map</span></li>
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