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<head><title>generateLPPs -- return all LPP ideals corresponding to a given Hilbert function</title>
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<div><h1>generateLPPs -- return all LPP ideals corresponding to a given Hilbert function</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>li=generateLPPs(R,hilb)</tt></div>
</dd></dl>
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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>hilb</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, a Hilbert function as a list</span></li>
</ul>
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</li>
<li><div class="single">Outputs:<ul><li><span><tt>li</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, a list of the form powers, LPP ideal, powers, LPP ideal, ...</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><a href="_generate__L__P__Ps_lp..._cm_sp__Print__Ideals_sp_eq_gt_sp..._rp.html">PrintIdeals => ...</a>, -- print LPP ideals nicely on the screen</span></li>
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<div class="single"><h2>Description</h2>
<div><div>Given a polynomial ring <tt>R</tt> and a Hilbert function <tt>hilb</tt> for <tt>R</tt> modulo a homogeneous ideal, <tt>generateLPPs</tt> generates all the LPP ideals corresponding to <tt>hilb</tt>. The power sequences and ideals are returned in a list. If the user sets the <tt>PrintIdeals</tt> option to <tt>true</tt>, the power sequences and ideals are printed on the screen in a nice format.</div>
<table class="examples"><tr><td><pre>i1 : R=ZZ/32003[a..c];</pre>
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<tr><td><pre>i2 : generateLPPs(R,{1,3,4,3,2})
2 2 4 2 2 5
o2 = {{{2, 2, 4}, ideal (a , b , c , a*b*c)}, {{2, 2, 5}, ideal (a , b , c ,
------------------------------------------------------------------------
3 4 2 3 4 2 2 3
a*b*c, a*c , b*c )}, {{2, 3, 4}, ideal (a , b , c , a*b, a*c , b c )},
------------------------------------------------------------------------
2 3 5 2 2 2 4
{{2, 3, 5}, ideal (a , b , c , a*b, a*c , b c , b*c )}}
o2 : List</pre>
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<div>Same example with the <tt>PrintIdeals</tt> option set to <tt>true</tt>:</div>
<table class="examples"><tr><td><pre>i3 : generateLPPs(R,{1,3,4,3,2},PrintIdeals=>true)
2 2 4
{2, 2, 4} ideal (a , b , c , a*b*c)
2 2 5 3 4
{2, 2, 5} ideal (a , b , c , a*b*c, a*c , b*c )
2 3 4 2 2 3
{2, 3, 4} ideal (a , b , c , a*b, a*c , b c )
2 3 5 2 2 2 4
{2, 3, 5} ideal (a , b , c , a*b, a*c , b c , b*c )
2 2 4 2 2 5
o3 = {{{2, 2, 4}, ideal (a , b , c , a*b*c)}, {{2, 2, 5}, ideal (a , b , c ,
------------------------------------------------------------------------
3 4 2 3 4 2 2 3
a*b*c, a*c , b*c )}, {{2, 3, 4}, ideal (a , b , c , a*b, a*c , b c )},
------------------------------------------------------------------------
2 3 5 2 2 2 4
{{2, 3, 5}, ideal (a , b , c , a*b, a*c , b c , b*c )}}
o3 : List</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="___L__P__P.html" title="return the lex-plus-powers (LPP) ideal corresponding to a given Hilbert function and power sequence">LPP</a> -- return the lex-plus-powers (LPP) ideal corresponding to a given Hilbert function and power sequence</span></li>
<li><span><a href="_is__L__P__P.html" title="determine whether an ideal is an LPP ideal">isLPP</a> -- determine whether an ideal is an LPP ideal</span></li>
</ul>
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<div class="waystouse"><h2>Ways to use <tt>generateLPPs</tt> :</h2>
<ul><li>generateLPPs(PolynomialRing,List)</li>
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