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<h1>LieRing</h1>


<h2>Computing with finitely presented Lie rings</h2>

<p>
    Version 2.4.2</p>

<p>
    10 February 2022
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<p><b>
    Serena Cicalò



  </b>
<br />Email: <span class="URL"><a href="mailto:cicalo@science.unitn.it">cicalo@science.unitn.it</a></span>
<br />Address: <br />Serena Cicalò<br /> Dipartimento di Matematica e Informatica<br /> Via Ospedale 72<br /> Italy<br />
</p><p><b>
    Willem Adriaan de Graaf



  </b>
<br />Email: <span class="URL"><a href="mailto:degraaf@science.unitn.it">degraaf@science.unitn.it</a></span>
<br />Homepage: <span class="URL"><a href="http://www.science.unitn.it/~degraaf">http://www.science.unitn.it/~degraaf</a></span>
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<h3>Abstract</h3>
<p>This package provides functions for constructing and working with Lie rings. There are functions for dealing with finitely-presented Lie rings, and for performing the Lazard correspondence. The package also contains a small database of finitely-generated Lie rings satisfying an Engel condition.</p>

<p><a id="X81488B807F2A1CF1" name="X81488B807F2A1CF1"></a></p>
<h3>Copyright</h3>
<p>© 2016 Serena Cicalò and Willem de Graaf</p>

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<h3>Contents<a id="contents" name="contents"></a></h3>

<div class="ContChap"><a href="chap1.html#X7DFB63A97E67C0A1">1 <span class="Heading">Introduction</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X8749E1888244CC3D">1.1 <span class="Heading">Preliminaries</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X865892E97C9D1E6D">1.2 <span class="Heading">The free Lie ring </span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X7994DA6587ABDA2D">1.3 <span class="Heading">The Lazard correspondence </span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap2.html#X8173135A7D187358">2 <span class="Heading">The functions</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X865892E97C9D1E6D">2.1 <span class="Heading">The free Lie ring</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7E52D2B884457822">2.1-1 FreeLieRing</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X826A861E7E7D944E">2.1-2 Degree</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X7BDAF9F47EBC6C0E">2.2 <span class="Heading"> Creating Lie rings </span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X784B8B28809EAC37">2.2-1 IsLieRing</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7DEFFA797BB7E432">2.2-2 LieRingByStructureConstants</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7D58E7AB7B2788D2">2.2-3 FpLieRing</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7D2CC3FF80F73EF8">2.2-4 FpLieAlgebra</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X7876A08584CBABAE">2.3 <span class="Heading"> Working with Lie rings </span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X837BE54C80DE368E">2.3-1 Basis</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X804ADF0280F67CDC">2.3-2 StructureConstantsTable</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7BF95CA07861A1AF">2.3-3 Torsion</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X80B32F667BF6AFD8">2.3-4 Coefficients</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7BC3398686B25634">2.3-5 SubLieRing</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7E97DBD778358F19">2.3-6 LieRingIdeal</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X83D53D98809EC461">2.3-7 NaturalHomomorphismByIdeal</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7900D17E7BA26A48">2.3-8 LieLowerCentralSeries</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X790A24857D0E559A">2.3-9 LieLowerPCentralSeries</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X8111F58E7DE3E25C">2.3-10 LieCentre</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X819C15027E16E335">2.3-11 TensorWithField</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X7994DA6587ABDA2D">2.4 <span class="Heading">The Lazard correspondence</span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X81FC256983DC2A94">2.4-1 PGroupToLieRing</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7E683E5F80B27375">2.4-2 LieRingToPGroup</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X7CB9E82C84258435">2.5 <span class="Heading">The database of <span class="SimpleMath">n</span>-Engel Lie rings</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7F6C2B1D82E381D0">2.5-1 SmallNEngelLieRing</a></span>
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<div class="ContChap"><a href="chapBib.html"><span class="Heading">References</span></a></div>
<div class="ContChap"><a href="chapInd.html"><span class="Heading">Index</span></a></div>
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