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<head><title>pureFree -- computes a GL(V)-equivariant map whose resolution is pure, or the reduction mod p of such a map</title>
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<div><h1>pureFree -- computes a GL(V)-equivariant map whose resolution is pure, or the reduction mod p of such a 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>pureFree(d, P)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>d</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, a list of degrees (increasing numbers)</span></li>
<li><span><tt>P</tt>, <span>a <a href="../../Macaulay2Doc/html/___Polynomial__Ring.html">polynomial ring</a></span>, a polynomial ring over a field K in n variables</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>, A map whose cokernel has Betti diagram with degree sequence d if K has characteristic 0. If K has positive characteristic p, then the corresponding map is calculated over QQ and is lifted to a ZZ-form which is then reduced mod p.</span></li>
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<div class="single"><h2>Description</h2>
<div>The function translates the data of a degree sequence d for a desired pure free resolution into the data of a Pieri map according to the formula of Eisenbud-Fl\o ystad-Weyman and then applies the function <a href="_pieri.html" title="computes a matrix representation for a Pieri inclusion of representations of a general linear group">pieri</a>.<table class="examples"><tr><td><pre>i1 : betti res coker pureFree({0,1,2,4}, QQ[a,b,c]) -- degree sequence {0,1,2,4}
0 1 2 3
o1 = total: 3 8 6 1
0: 3 8 6 .
1: . . . 1
o1 : BettiTally</pre>
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<tr><td><pre>i2 : betti res coker pureFree({0,1,2,4}, ZZ/2[a,b,c]) -- same map, but reduced mod 2
0 1 2 3
o2 = total: 3 8 6 1
0: 3 8 6 .
1: . . . 1
o2 : BettiTally</pre>
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<tr><td><pre>i3 : betti res coker pureFree({0,1,2,4}, GF(4)[a,b,c]) -- can also use non prime fields
0 1 2 3
o3 = total: 3 8 6 1
0: 3 8 6 .
1: . . . 1
o3 : BettiTally</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_pieri.html" title="computes a matrix representation for a Pieri inclusion of representations of a general linear group">pieri</a> -- computes a matrix representation for a Pieri inclusion of representations of a general linear group</span></li>
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<div class="waystouse"><h2>Ways to use <tt>pureFree</tt> :</h2>
<ul><li>pureFree(List,PolynomialRing)</li>
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