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<head><title>ringFromFractions -- find presentation for f.g. ring</title>
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<div><h1>ringFromFractions -- find presentation for f.g. 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>(F,G) = ringFromFractions(H,f)</tt></div>
</dd></dl>
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</li>
<li><div class="single">Inputs:<ul><li><span><tt>H</tt>, <span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span>, a one row matrix over a ring <i>R</i></span></li>
<li><span><tt>f</tt>, <span>a <a href="../../Macaulay2Doc/html/___Ring__Element.html">ring element</a></span></span></li>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span><tt>F</tt>, <span>a <a href="../../Macaulay2Doc/html/___Ring__Map.html">ring map</a></span>, <i>R →S</i>, where <i>S</i> is the extension ring of <i>R</i> generated by the fractions <i>1/f H</i></span></li>
<li><span><tt>G</tt>, <span>a <a href="../../Macaulay2Doc/html/___Ring__Map.html">ring map</a></span>, <i>frac S →frac R</i>, the fractions</span></li>
</ul>
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</li>
<li><div class="single"><a href="../../Macaulay2Doc/html/_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><tt>Index => ...</tt> (missing documentation<!-- tag: ringFromFractions(..., Index => ...) -->), </span></li>
<li><span><tt>Variable => ...</tt> (missing documentation<!-- tag: ringFromFractions(..., Variable => ...) -->), </span></li>
<li><span><tt>Verbosity => ...</tt> (missing documentation<!-- tag: ringFromFractions(..., Verbosity => ...) -->), </span></li>
</ul>
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<div class="single"><h2>Description</h2>
<div><div>Serious restriction: It is assumed that this ring R[1/f H] is an endomorphism ring of an ideal in <i>R</i>. This means that the Groebner basis, in a product order, will have lead terms all quadratic monomials in the new variables, together with other elements which are degree 0 or 1 in the new variables.</div>
<table class="examples"><tr><td><pre>i1 : R = QQ[x,y]/(y^2-x^3)
o1 = R
o1 : QuotientRing</pre>
</td></tr>
<tr><td><pre>i2 : H = (y * ideal(x,y)) : ideal(x,y)
2
o2 = ideal (y, x )
o2 : Ideal of R</pre>
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<tr><td><pre>i3 : (F,G) = ringFromFractions(((gens H)_{1}), H_0);</pre>
</td></tr>
<tr><td><pre>i4 : S = target F
o4 = S
o4 : QuotientRing</pre>
</td></tr>
<tr><td><pre>i5 : F
o5 = map(S,R,{x, y})
o5 : RingMap S <--- R</pre>
</td></tr>
<tr><td><pre>i6 : G
y
o6 = map(frac(R),frac(S),{-, x, y})
x
o6 : RingMap frac(R) <--- frac(S)</pre>
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<div class="waystouse"><h2>Ways to use <tt>ringFromFractions</tt> :</h2>
<ul><li>ringFromFractions(Matrix,RingElement)</li>
</ul>
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