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<head><title>macaulayRep -- the Macaulay representation of an integer</title>
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<div><h1>macaulayRep -- the Macaulay representation of an integer</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>h=macaulayRep(a,d)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>a</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, a nonnegative integer</span></li>
<li><span><tt>d</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, a positive integer</span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>L</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, a list of pairs i,j of integers such that j <= d for all terms, and a is the sum of the <tt>binomial(i,j)</tt>.</span></li>
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<div class="single"><h2>Description</h2>
<div><div>Yields the <tt>d</tt>-th Macaulay representation of the integer <tt>a</tt>. Given a positive integer <tt>d</tt>, each positive integer a can be uniquely represented as a sum of binomials <tt>binomial(b<sub>d</sub>,d) + binomial(b<sub>d-1</sub>,d-1) + ... + binomial(b<sub>1</sub>,1)</tt>, where <tt>b<sub>d</sub> > b<sub>d-1</sub> > ... > b<sub>1</sub> >= 0</tt>.</div>
<table class="examples"><tr><td><pre>i1 : macaulayRep(100,4)
o1 = {{8, 4}, {6, 3}, {5, 2}}
o1 : List</pre>
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<tr><td><pre>i2 : macaulayRep(10,5)
o2 = {{6, 5}, {4, 4}, {3, 3}, {2, 2}, {1, 1}}
o2 : List</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_macaulay__Bound.html" title="the bound on the growth of a Hilbert function from Macaulay's Theorem">macaulayBound</a> -- the bound on the growth of a Hilbert function from Macaulay's Theorem</span></li>
<li><span><a href="_is__H__F.html" title="is a finite list a Hilbert function of a polynomial ring mod a homogeneous ideal">isHF</a> -- is a finite list a Hilbert function of a polynomial ring mod a homogeneous ideal</span></li>
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<div class="waystouse"><h2>Ways to use <tt>macaulayRep</tt> :</h2>
<ul><li>macaulayRep(ZZ,ZZ)</li>
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