<?xml version="1.0" encoding="UTF-8" ?>DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd " >html xmlns="http://www.w3.org/1999/xhtml " xml:lang="en" >head >title >GAP (StandardFF) - Contents</title >meta http-equiv="content-type" content="text/html; charset=UTF-8" />meta name="generator" content="GAPDoc2HTML" />link rel="stylesheet" type="text/css" href="manual.css" />script src="manual.js" type="text/javascript" ></script >script type="text/javascript" >overwriteStyle();</script >head >body class="chap0" onload="jscontent()" >div class="chlinktop" ><span class="chlink1" >Goto Chapter: </span ><a href="chap0.html" >Top</a> <a href="chap1.html" >1</a> <a href="chap2.html" >2</a> <a href="chap3.html" >3</a> <a href="chap4.html" >4</a> <a href="chapBib.html" >Bib</a> <a href="chapInd.html" >Ind</a> </div >div class="chlinkprevnexttop" > <a href="chap0.html" >[Top of Book]</a> <a href="chap0.html#contents" >[Contents]</a> <a href="chap1.html" >[Next Chapter]</a> </div >"mathjaxlink" class="pcenter" ><a href="chap0_mj.html" >[MathJax on]</a></p>"X7D2C85EC87DD46E5" name="X7D2C85EC87DD46E5" ></a></p>div class="pcenter" >h1 ><strong class="pkg" >StandardFF</strong ></h1 >div >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 >"X81488B807F2A1CF1" name="X81488B807F2A1CF1" ></a></p>on 3 or later, see <span class="URL" ><a href="https://www.gnu.org/licenses " >https://www.gnu.org/licenses</a></span >.</p>"X7982162280BC7A61" name="X7982162280BC7A61" ></a></p>"chapBib.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>"X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8" ></a></p>div class="contents" >"contents" name="contents" ></a></h3>div class="ContChap" ><a href="chap1.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.html#X8599E5B885932EEC" >1.1 <span class="Heading" >Aim</span ></a>span >div >div >div class="ContChap" ><a href="chap2.html#X7D1270E8831F128E" >2 <span class="Heading" >Standard finite fields</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2.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.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.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.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.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.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.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.html#X85BC2EF17DA2E707" >2.4-1 SteinitzPair</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X851FD36881708D5E" >2.4-2 Embedding</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X800EE1C5800EE1C5" >2.4-3 ZZ</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X839220E3865258DA" >2.4-4 MoveToSmallestStandardField</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X7ECCD8D27FBA9505" >2.4-5 StandardIsomorphismGF</a></span >div ></div >div >div class="ContChap" ><a href="chap3.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.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.html#X79D3165F833F28DA" >3.1-1 StandardCyclicGenerator</a></span >div ></div >div >div class="ContChap" ><a href="chap4.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.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.html#X85113F358019E11C" >4.1-1 StandardAffineShift</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.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.html#X7F1ABC6E83E257A3" >4.2-1 FindLinearCombination</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.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.html#X7F7C09C3860AF01D" >4.3-1 IsIrreducibleCoeffList</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.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.html#X7E781D7B7CB1DFF4" >4.4-1 FindConjugateZeroes</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7C00A74780A75A10" >4.4-2 ZeroesConway</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X784E128A811F5C91" >4.4-3 SteinitzPairConwayGenerator</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.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.html#X84A138947E8C49A8" >4.5-1 DLog</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.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.html#X7E978CBD81D69FA2" >4.6-1 InvModCoeffs</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7CE85678790D8967" >4.6-2 BerlekampMassey</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7BBC9E097F02B26E" >4.6-3 MinimalPolynomialByBerlekampMassey</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.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.html#X86408E6883916C5D" >4.7-1 StandardValuesBrauerCharacter</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.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.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.html#X7BAF533D86DAD073" >4.8-1 CANFACT</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.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.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.html#X7EA72E8A78A4ADE2" >4.10 <span class="Heading" >Undocumented features</span ></a>span >div >div >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 >br />div >div class="chlinkprevnextbot" > <a href="chap0.html" >[Top of Book]</a> <a href="chap0.html#contents" >[Contents]</a> <a href="chap1.html" >[Next Chapter]</a> </div >div class="chlinkbot" ><span class="chlink1" >Goto Chapter: </span ><a 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