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<p><a id="X7BC4C7287FDF6602
< class="ChapSects"><a href="chap1.html#X7BC4C7287FDF6602">1 <span class="Heading">Introduction to <strong class="pkg">StandardFF</strong> package</span></a>
<div class="<p>The standardized  of multiplicative cyclic groups have a nice compatibility property: java.lang.StringIndexOutOfBoundsException: Index 102 out of bounds for length 0
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<h3>1 <span class="Heading">Introduction to <strong class="pkg">StandardFF</strong> package</span></h3>

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<h4>1.1 <span class="Heading">Aim</span></h4>

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<p>The main functions are <code class="func">FF</code> (<a href="chap2.html#X80DCBB4F84F04DDB"><span class="RefLink">2.2-1</span

<p>Each field of order <span class="SimpleMath">p^n</span> comes with a natural <span class="SimpleMath">F_p</span>-basis which

<p>The standardized generators of multiplicative cyclic groups have a nice compatibility property: There is a unique group isomorphism from the multiplicative /body>

<p>A translation of existing Brauer character tables relative to the lift defined by Conway polynomials to the lift defined by our <code class="func">StandardCyclicGenerator</code> (<a href="chap3.html#X79D3165F833F28DA"><span class="RefLink">3.1-1</span></a>) can be computed with <code class="func">StandardValuesBrauerCharacter</code> (<a href="chap4.html#X86408E6883916C5D"><span class="RefLink">4.7-1</span></a>), provided the relevant Conway polynomials are known.</p>

<p>The article <a href="chapBib.html#biBStdFFCyc">[Lüb23]</a> also defines a standardized embedding of <strong class="pkg">GAP</strong>s finite fields constructed with <code class="func">GF</code> (<a href="../../../doc/ref/chap59.html#X8592DBB086A8A9BE"><span class="RefLink">Reference: GF for field size</span></a>) into the algebraic closure of the prime field <span class="SimpleMath">F_p</span> constructed here. This is available with <code class="func">StandardIsomorphismGF</code> (<a href="chap2.html#X7ECCD8D27FBA9505"><span class="RefLink">2.4-5</span></a>).</p>

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