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<div class="chlinktop"><span class="chlink1">Goto Chapter: </span><a href="chap0_mj.html">Top</a>  <a href="chap1_mj.html">1</a>  <a href="chap2_mj.html">2</a>  <a href="chap3_mj.html">3</a>  <a href="chap4_mj.html">4</a>  <a href="chapBib_mj.html">Bib</a>  <a href="chapInd_mj.html">Ind</a>  </div>

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<h1><strong class="pkg">StandardFF</strong></h1>

<p>( Version 
1.0

 )</p>

<p>September 2023</p>

</div>
<p><b> Frank Lübeck 
    
    
  </b>
<br />Email: <span class="URL"><a href="mailto:Frank.Luebeck@Math.RWTH-Aachen.De">Frank.Luebeck@Math.RWTH-Aachen.De</a></span>
<br />Homepage: <span class="URL"><a href="https://www.math.rwth-aachen.de/~Frank.Luebeck">https://www.math.rwth-aachen.de/~Frank.Luebeck</a></span>
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<p><a id="X81488B807F2A1CF1" name="X81488B807F2A1CF1"></a></p>
<h3>Copyright</h3>
<p>© 2020- by Frank Lübeck</p>

<p>This package may be distributed under the terms and conditions of the GNU Public License Version 3 or later, see <span class="URL"><a href="https://www.gnu.org/licenses">https://www.gnu.org/licenses</a></span>.</p>

<p><a id="X7982162280BC7A61" name="X7982162280BC7A61"></a></p>
<h3>Colophon</h3>
<p>This package implements the constructions in the paper <a href="chapBib_mj.html#biBStdFFCyc">[Lüb23]</a>, that is it provides relatively easy to reproduce generators of finite fields and compatible generators of their multiplicative cyclic subgroups.</p>

<p><a id="X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8"></a></p>

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

<div class="ContChap"><a href="chap1_mj.html#X7BC4C7287FDF6602">1 <span class="Heading">Introduction to <strong class="pkg">StandardFF</strong> package</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X8599E5B885932EEC">1.1 <span class="Heading">Aim</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap2_mj.html#X7D1270E8831F128E">2 <span class="Heading">Standard finite fields</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X7F9D926586E030D9">2.1 <span class="Heading">Definition of standard finite fields</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X82D368EB8718370E">2.2 <span class="Heading">Creating standard finite fields</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X80DCBB4F84F04DDB">2.2-1 <span class="Heading">Constructing standard finite fields</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7DD6C7C3867D84B8">2.2-2 <span class="Heading">Filters for standard fields</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X84ED04C57C4BB25B">2.3 <span class="Heading">Elements in standard finite fields</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X8569D7B1786AE5FC">2.3-1 <span class="Heading">Maps for elements of standard finite fields</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X7F3D740F80F68F74">2.4 <span class="Heading">Embeddings of standard finite fields</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X85BC2EF17DA2E707">2.4-1 SteinitzPair</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X851FD36881708D5E">2.4-2 Embedding</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X800EE1C5800EE1C5">2.4-3 ZZ</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X839220E3865258DA">2.4-4 MoveToSmallestStandardField</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7ECCD8D27FBA9505">2.4-5 StandardIsomorphismGF</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap3_mj.html#X7C788F1583FB8544">3 <span class="Heading">Standard generators of cyclic groups</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X864390D67EA526FA">3.1 <span class="Heading">Generators of multiplicative groups</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X79D3165F833F28DA">3.1-1 StandardCyclicGenerator</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap4_mj.html#X7B7EC1DC7BF3A7BD">4 <span class="Heading">Utilities from the <strong class="pkg">StandardFF</strong> package</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X7BFCD0EA853203E8">4.1 <span class="Heading">A simple bijection on a range</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X85113F358019E11C">4.1-1 StandardAffineShift</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X845FFCBC7CE095A6">4.2 <span class="Heading">Finding linear combinations</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7F1ABC6E83E257A3">4.2-1 FindLinearCombination</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X876B131786C80F86">4.3 <span class="Heading">Irreducibility over finite fields</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7F7C09C3860AF01D">4.3-1 IsIrreducibleCoeffList</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X86D4E7A6830D51D3">4.4 <span class="Heading">Connection to Conway polynomials</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7E781D7B7CB1DFF4">4.4-1 FindConjugateZeroes</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7C00A74780A75A10">4.4-2 ZeroesConway</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X784E128A811F5C91">4.4-3 SteinitzPairConwayGenerator</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X846AF3D08713D57A">4.5 <span class="Heading">Discrete logarithms</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X84A138947E8C49A8">4.5-1 DLog</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X83936E9986D475BA">4.6 <span class="Heading">Minimal polynomials of sequences</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7E978CBD81D69FA2">4.6-1 InvModCoeffs</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7CE85678790D8967">4.6-2 BerlekampMassey</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7BBC9E097F02B26E">4.6-3 MinimalPolynomialByBerlekampMassey</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X7C69EBE885DA1B15">4.7 <span class="Heading">Brauer characters with respect to different lifts</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X86408E6883916C5D">4.7-1 StandardValuesBrauerCharacter</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X814BE20A81F82969">4.7-2 <span class="Heading">Frobenius character values</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X78ED090878CEE6AA">4.8 <span class="Heading">Known factorizations of multiplicative group orders</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7BAF533D86DAD073">4.8-1 CANFACT</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X7D85D01D7F846000">4.9 <span class="Heading">Some loops for  <strong class="pkg">StandardFF</strong></span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X788898E979B9E9D9">4.9-1 <span class="Heading">Computing all fields in various ranges</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X7EA72E8A78A4ADE2">4.10 <span class="Heading">Undocumented features</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chapBib_mj.html"><span class="Heading">References</span></a></div>
<div class="ContChap"><a href="chapInd_mj.html"><span class="Heading">Index</span></a></div>
<br />
</div>

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