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<head><title>addCokerGrading -- Stores a cokernel grading in a polynomial ring.</title>
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<div><h1>addCokerGrading -- Stores a cokernel grading in a polynomial 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>addCokerGrading(R)</tt><br/><tt>addCokerGrading(R,A)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>R</tt>, <span>a <a href="../../Macaulay2Doc/html/___Polynomial__Ring.html">polynomial ring</a></span></span></li>
<li><span><tt>A</tt>, <span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span>, the integer grading matrix.</span></li>
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<div class="single"><h2>Description</h2>
<div><p>Stores a cokernel grading (Cox grading) in a polynomial ring. This data is accessed by <a href="___First__Order__Deformation.html" title="The class of all first order deformations of monomial ideals.">FirstOrderDeformation</a> to compute the small torus <a href="_degree_lp__First__Order__Deformation_rp.html" title="The small torus degree of a deformation.">degree(FirstOrderDeformation)</a> of a deformation, and by <a href="___Complex.html" title="The class of all embedded complexes.">Complex</a> and <a href="___Co__Complex.html" title="The class of all embedded co-complexes.">CoComplex</a> to store the vertices.</p>
<p>The number or rows of A has to match the number of variables of R.</p>
<p>If A is not specified, <a href="_rays__P__Pn.html" title="The rays of the standard fan of projective space.">raysPPn</a> R is used.</p>
<p>This command does not change the behaviour of R with respect to the standard Macaualy2 image grading, which we want to use independently.</p>
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<table class="examples"><tr><td><pre>i1 : R=QQ[x_0..x_4];</pre>
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<tr><td><pre>i2 : addCokerGrading(R);
5 4
o2 : Matrix ZZ <--- ZZ</pre>
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<tr><td><pre>i3 : R.grading
o3 = | -1 -1 -1 -1 |
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 1 0 |
| 0 0 0 1 |
5 4
o3 : Matrix ZZ <--- ZZ</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="___First__Order__Deformation.html" title="The class of all first order deformations of monomial ideals.">FirstOrderDeformation</a> -- The class of all first order deformations of monomial ideals.</span></li>
<li><span><a href="_rays__P__Pn.html" title="The rays of the standard fan of projective space.">raysPPn</a> -- The rays of the standard fan of projective space.</span></li>
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<div class="waystouse"><h2>Ways to use <tt>addCokerGrading</tt> :</h2>
<ul><li>addCokerGrading(PolynomialRing)</li>
<li>addCokerGrading(PolynomialRing,Matrix)</li>
</ul>
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