new version of mws harvests

cc452130 · m-iancu · d18a32f8 · cc452130 · cc452130 · cc452130
Commit cc452130 authored 8 years ago by m-iancu
--- a/export/mwscrawler/1.html
+++ b/export/mwscrawler/1.html
 <html> 
      <head>
-        <title>TODO</title>
+        <title>2.5 Entities and Special Characters</title>
-        <meta name="url" content="http://www.gap-system.org/Manuals/doc/ref/TODO#X7F10E951789D6EDF"></meta>
+        <meta name="url" content="http://www.gap-system.org/Manuals/doc/ref/TODO#X83A355E68485D6D1"></meta>
      </head>
-      <body> <h4 xmlns="http://www.w3.org/1999/xhtml">2.4 <span class="Heading">Lists and Tables</span></h4><p xmlns="http://www.w3.org/1999/xhtml">[→ <a shape="rect" href="chapB_mj.html#X7BB822947F626E1A"><span class="RefLink">B.9</span></a>]</p><p xmlns="http://www.w3.org/1999/xhtml">There are</p><ul xmlns="http://www.w3.org/1999/xhtml"><li><p>lists</p>
+      <body> <h4 xmlns="http://www.w3.org/1999/xhtml">2.5 <span class="Heading">Entities and Special Characters</span></h4><p xmlns="http://www.w3.org/1999/xhtml">[→ <a shape="rect" href="chapB_mj.html#X80B478CD7E584F6F"><span class="RefLink">B.10</span></a>]</p><p xmlns="http://www.w3.org/1999/xhtml">Here is a table of special characters, the first two are special for XML and must be typed in by entities in <strong class="pkg">GAPDoc</strong> documents. The other characters are special for LaTeX but in <strong class="pkg">GAPDoc</strong> they can be typed directly.</p><div class="pcenter" xmlns="http://www.w3.org/1999/xhtml"><table class="GAPDocTable"><caption class="GAPDocTable"><b>Table: </b>Special characters in character data</caption><tbody><tr><td colspan="1" rowspan="1" class="tdcenter"><code class="code">&amp;</code></td><td colspan="1" rowspan="1" class="tdcenter"><code class="code">&lt;</code></td><td colspan="1" rowspan="1" class="tdcenter"><code class="code">&gt;</code></td><td colspan="1" rowspan="1" class="tdcenter"><code class="code">#</code></td><td colspan="1" rowspan="1" class="tdcenter"><code class="code">$</code></td><td colspan="1" rowspan="1" class="tdcenter"><code class="code">%</code></td><td colspan="1" rowspan="1" class="tdcenter"><code class="code">~</code></td><td colspan="1" rowspan="1" class="tdcenter"><code class="code">\</code></td><td colspan="1" rowspan="1" class="tdcenter"><code class="code">{</code></td><td colspan="1" rowspan="1" class="tdcenter"><code class="code">}</code></td><td colspan="1" rowspan="1" class="tdcenter"><code class="code">_</code></td><td colspan="1" rowspan="1" class="tdcenter"><code class="code">^</code></td><td colspan="1" rowspan="1" class="tdcenter"><code class="code"> </code></td></tr></tbody></table><br/><p> </p><br/>
+</div><p xmlns="http://www.w3.org/1999/xhtml">And here are the predefined entities in <strong class="pkg">GAPDoc</strong>:</p><div class="pcenter" xmlns="http://www.w3.org/1999/xhtml"><table class="GAPDocTable"><caption class="GAPDocTable"><b>Table: </b>Predefined Entities in the <strong class="pkg">GAPDoc</strong> system</caption><tbody><tr><td colspan="1" rowspan="1" class="tdleft"><code class="code">&amp;GAP;</code></td><td colspan="1" rowspan="1" class="tdleft"><strong class="pkg">GAP</strong></td></tr><tr><td colspan="1" rowspan="1" class="tdleft"><code class="code">&amp;GAPDoc;</code></td><td colspan="1" rowspan="1" class="tdleft"><strong class="pkg">GAPDoc</strong></td></tr><tr><td colspan="1" rowspan="1" class="tdleft"><code class="code">&amp;TeX;</code></td><td colspan="1" rowspan="1" class="tdleft">TeX</td></tr><tr><td colspan="1" rowspan="1" class="tdleft"><code class="code">&amp;LaTeX;</code></td><td colspan="1" rowspan="1" class="tdleft">LaTeX</td></tr><tr><td colspan="1" rowspan="1" class="tdleft"><code class="code">&amp;BibTeX;</code></td><td colspan="1" rowspan="1" class="tdleft">BibTeX</td></tr><tr><td colspan="1" rowspan="1" class="tdleft"><code class="code">&amp;MeatAxe;</code></td><td colspan="1" rowspan="1" class="tdleft"><strong class="pkg">MeatAxe</strong></td></tr><tr><td colspan="1" rowspan="1" class="tdleft"><code class="code">&amp;XGAP;</code></td><td colspan="1" rowspan="1" class="tdleft"><strong class="pkg">XGAP</strong></td></tr><tr><td colspan="1" rowspan="1" class="tdleft"><code class="code">&amp;copyright;</code></td><td colspan="1" rowspan="1" class="tdleft">©</td></tr></tbody></table><br/><p> </p><br/>
-</li><li><p>enumerations, and</p>
+</div><p xmlns="http://www.w3.org/1999/xhtml">And some more for mathematical symbols: ℂ, ℤ, ℕ, ℙ, ℚ, ℍ, ℝ.</p><div class="chlinkprevnextbot" xmlns="http://www.w3.org/1999/xhtml"> <a shape="rect" href="chap0_mj.html">[Top of Book]</a>   <a shape="rect" href="chap0_mj.html#contents">[Contents]</a>    <a shape="rect" href="chap1_mj.html">[Previous Chapter]</a>    <a shape="rect" href="chapA_mj.html">[Next Chapter]</a>   </div><div class="chlinkbot" xmlns="http://www.w3.org/1999/xhtml"><span class="chlink1">Goto Chapter: </span><a shape="rect" href="chap0_mj.html">Top</a>  <a shape="rect" href="chap1_mj.html">1</a>  <a shape="rect" href="chap2_mj.html">2</a>  <a shape="rect" href="chapA_mj.html">A</a>  <a shape="rect" href="chapB_mj.html">B</a>  <a shape="rect" href="chapBib_mj.html">Bib</a>  <a shape="rect" href="chapInd_mj.html">Ind</a>  </div><hr xmlns="http://www.w3.org/1999/xhtml"/><p class="foot" xmlns="http://www.w3.org/1999/xhtml">generated by <a shape="rect" href="http://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc">GAPDoc2HTML</a></p> </body>
-</li><li><p>tables</p>
-</li></ul><p xmlns="http://www.w3.org/1999/xhtml">or:</p><ol xmlns="http://www.w3.org/1999/xhtml"><li><p>lists</p>
-</li><li><p>enumerations, and</p>
-</li><li><p>tables</p>
-</li></ol><p xmlns="http://www.w3.org/1999/xhtml">or with marks:</p><dl xmlns="http://www.w3.org/1999/xhtml"><dt><strong class="Mark">lists:</strong></dt><dd><p>not numbered</p>
-</dd><dt><strong class="Mark">enumerations:</strong></dt><dd><p>numbered</p>
-</dd><dt><strong class="Mark">tables:</strong></dt><dd><p>two-dimensional</p>
-</dd></dl><p xmlns="http://www.w3.org/1999/xhtml">Lists can also be nested:</p><ol xmlns="http://www.w3.org/1999/xhtml"><li><ol><li><p>first item of inner enumeration</p>
-</li><li><p>second item of inner enumeration</p>
-</li></ol>
-</li><li>
-<ul><li><p>first item of inner list</p>
-</li><li><p>second item of inner list</p>
-</li></ul>
-</li></ol><p xmlns="http://www.w3.org/1999/xhtml">Here is a <em>table</em>:</p><div class="pcenter" xmlns="http://www.w3.org/1999/xhtml"><table class="GAPDocTable"><caption class="GAPDocTable"><b>Table: </b>Prices</caption><tbody><tr><td colspan="1" rowspan="1" class="tdright">Object</td><td colspan="1" rowspan="1" class="tdcenter">Price</td><td colspan="1" rowspan="1" class="tdleft">available</td></tr><tr><td colspan="1" rowspan="1" class="tdright">Shoe</td><td colspan="1" rowspan="1" class="tdcenter">$1,00</td><td colspan="1" rowspan="1" class="tdleft">there</td></tr><tr><td colspan="1" rowspan="1" class="tdright">Hat</td><td colspan="1" rowspan="1" class="tdcenter">$2,00</td><td colspan="1" rowspan="1" class="tdleft">not there</td></tr></tbody></table><br/><p> </p><br/>
-</div> </body>
    </html>
\ No newline at end of file
--- a/export/mwscrawler/10.html
+++ b/export/mwscrawler/10.html
+<html> 
+      <head>
+        <title>60.4-2 ANFAutomorphism</title>
+        <meta name="url" content="http://www.gap-system.org/Manuals/doc/ref/TODO#X8643D4B47A827D9D"></meta>
+      </head>
+      <body> <h5 xmlns="http://www.w3.org/1999/xhtml">60.4-2 ANFAutomorphism</h5><div class="func" xmlns="http://www.w3.org/1999/xhtml"><table width="100%" class="func"><tbody><tr><td colspan="1" rowspan="1" class="tdleft"><code class="func">‣ ANFAutomorphism</code>( <var class="Arg">F</var>, <var class="Arg">k</var> )</td><td colspan="1" rowspan="1" class="tdright">( function )</td></tr></tbody></table></div><p xmlns="http://www.w3.org/1999/xhtml">Let <var class="Arg">F</var> be an abelian number field and <var class="Arg">k</var> be an integer that is coprime to the conductor (see <code class="func">Conductor</code> (<a shape="rect" href="chap18_mj.html#X815D6EC57CBA9827"><span class="RefLink">18.1-7</span></a>)) of <var class="Arg">F</var>. Then <code class="func">ANFAutomorphism</code> returns the automorphism of <var class="Arg">F</var> that is defined as the linear extension of the map that raises each root of unity in <var class="Arg">F</var> to its <var class="Arg">k</var>-th power.</p><div class="example" xmlns="http://www.w3.org/1999/xhtml"><pre xml:space="preserve">
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">f:= CF(25);</span>
+CF(25)
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">alpha:= ANFAutomorphism( f, 2 );</span>
+ANFAutomorphism( CF(25), 2 )
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">alpha^2;</span>
+ANFAutomorphism( CF(25), 4 )
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">Order( alpha );</span>
+20
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">E(5)^alpha;</span>
+E(5)^2
+</pre></div> </body>
+    </html>
\ No newline at end of file
--- a/export/mwscrawler/11.html
+++ b/export/mwscrawler/11.html
--- a/export/mwscrawler/12.html
+++ b/export/mwscrawler/12.html
+<html> 
+      <head>
+        <title>60.4 Galois Groups of Abelian Number Fields</title>
+        <meta name="url" content="http://www.gap-system.org/Manuals/doc/ref/TODO#X7E4AB4B17C7BA10C"></meta>
+      </head>
+      <body> <h4 xmlns="http://www.w3.org/1999/xhtml">60.4 <span class="Heading">Galois Groups of Abelian Number Fields</span></h4><p xmlns="http://www.w3.org/1999/xhtml">The field automorphisms of the cyclotomic field <math id="-8226334041509413860" display="inline" alttext="?_{n}" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <msub xref="p1.1.m1.1.3.cmml" id="p1.1.m1.1.3">
+      <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1" mathvariant="normal">?</mi>
+      <mi xref="p1.1.m1.1.2.1.cmml" id="p1.1.m1.1.2.1">n</mi>
+    </msub>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <apply xref="p1.1.m1.1.3" id="p1.1.m1.1.3.cmml">
+        <csymbol id="p1.1.m1.1.3.1.cmml" cd="ambiguous">subscript</csymbol>
+        <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">?</ci>
+        <ci xref="p1.1.m1.1.2.1" id="p1.1.m1.1.2.1.cmml">𝑛</ci>
+      </apply>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">?_{n}</annotation>
+  </semantics>
+</math> (see Chapter <a shape="rect" href="chap18_mj.html#X7DFC03C187DE4841"><span class="RefLink">18</span></a>) are given by the linear maps <math id="-91427219792583270" display="inline" alttext="*k" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mrow xref="p1.1.m1.1.3.cmml" id="p1.1.m1.1.3">
+      <mi xref="p1.1.m1.1.3.1.cmml" id="p1.1.m1.1.3.1"/>
+      <mo xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1">*</mo>
+      <mi xref="p1.1.m1.1.2.cmml" id="p1.1.m1.1.2">k</mi>
+    </mrow>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <apply xref="p1.1.m1.1.3" id="p1.1.m1.1.3.cmml">
+        <times xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml"/>
+        <csymbol xref="p1.1.m1.1.3.1" id="p1.1.m1.1.3.1.cmml" cd="latexml">absent</csymbol>
+        <ci xref="p1.1.m1.1.2" id="p1.1.m1.1.2.cmml">𝑘</ci>
+      </apply>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">*k</annotation>
+  </semantics>
+</math> on <math id="7662179593224293755" display="inline" alttext="?_{n}" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <msub xref="p1.1.m1.1.3.cmml" id="p1.1.m1.1.3">
+      <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1" mathvariant="normal">?</mi>
+      <mi xref="p1.1.m1.1.2.1.cmml" id="p1.1.m1.1.2.1">n</mi>
+    </msub>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <apply xref="p1.1.m1.1.3" id="p1.1.m1.1.3.cmml">
+        <csymbol id="p1.1.m1.1.3.1.cmml" cd="ambiguous">subscript</csymbol>
+        <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">?</ci>
+        <ci xref="p1.1.m1.1.2.1" id="p1.1.m1.1.2.1.cmml">𝑛</ci>
+      </apply>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">?_{n}</annotation>
+  </semantics>
+</math> that are defined by <code class="code">E</code><math id="-3240071424451291920" display="inline" alttext="(n)^{{*k}}=" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mrow xref="p1.1.m1.1.6.cmml" id="p1.1.m1.1.6">
+      <msup xref="p1.1.m1.1.6.1.cmml" id="p1.1.m1.1.6.1">
+        <mrow id="p1.1.m1.1.6.1.2">
+          <mo id="p1.1.m1.1.1" stretchy="false">(</mo>
+          <mi xref="p1.1.m1.1.2.cmml" id="p1.1.m1.1.2">n</mi>
+          <mo id="p1.1.m1.1.3" stretchy="false">)</mo>
+        </mrow>
+        <mrow xref="p1.1.m1.1.4.1.cmml" id="p1.1.m1.1.4.1">
+          <mi xref="p1.1.m1.1.4.1.3.cmml" id="p1.1.m1.1.4.1.3"/>
+          <mo xref="p1.1.m1.1.4.1.1.cmml" id="p1.1.m1.1.4.1.1">*</mo>
+          <mi xref="p1.1.m1.1.4.1.2.cmml" id="p1.1.m1.1.4.1.2">k</mi>
+        </mrow>
+      </msup>
+      <mo xref="p1.1.m1.1.5.cmml" id="p1.1.m1.1.5">=</mo>
+      <mi xref="p1.1.m1.1.6.2.cmml" id="p1.1.m1.1.6.2"/>
+    </mrow>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <apply xref="p1.1.m1.1.6" id="p1.1.m1.1.6.cmml">
+        <eq xref="p1.1.m1.1.5" id="p1.1.m1.1.5.cmml"/>
+        <apply xref="p1.1.m1.1.6.1" id="p1.1.m1.1.6.1.cmml">
+          <csymbol id="p1.1.m1.1.6.1.1.cmml" cd="ambiguous">superscript</csymbol>
+          <ci xref="p1.1.m1.1.2" id="p1.1.m1.1.2.cmml">𝑛</ci>
+          <apply xref="p1.1.m1.1.4.1" id="p1.1.m1.1.4.1.cmml">
+            <times xref="p1.1.m1.1.4.1.1" id="p1.1.m1.1.4.1.1.cmml"/>
+            <csymbol xref="p1.1.m1.1.4.1.3" id="p1.1.m1.1.4.1.3.cmml" cd="latexml">absent</csymbol>
+            <ci xref="p1.1.m1.1.4.1.2" id="p1.1.m1.1.4.1.2.cmml">𝑘</ci>
+          </apply>
+        </apply>
+        <csymbol xref="p1.1.m1.1.6.2" id="p1.1.m1.1.6.2.cmml" cd="latexml">absent</csymbol>
+      </apply>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">(n)^{{*k}}=</annotation>
+  </semantics>
+</math><code class="code">E</code><math id="-7031209855940056214" display="inline" alttext="(n)^{k}" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <msup xref="p1.1.m1.1.5.cmml" id="p1.1.m1.1.5">
+      <mrow id="p1.1.m1.1.5.2">
+        <mo id="p1.1.m1.1.1" stretchy="false">(</mo>
+        <mi xref="p1.1.m1.1.2.cmml" id="p1.1.m1.1.2">n</mi>
+        <mo id="p1.1.m1.1.3" stretchy="false">)</mo>
+      </mrow>
+      <mi xref="p1.1.m1.1.4.1.cmml" id="p1.1.m1.1.4.1">k</mi>
+    </msup>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <apply xref="p1.1.m1.1.5" id="p1.1.m1.1.5.cmml">
+        <csymbol id="p1.1.m1.1.5.1.cmml" cd="ambiguous">superscript</csymbol>
+        <ci xref="p1.1.m1.1.2" id="p1.1.m1.1.2.cmml">𝑛</ci>
+        <ci xref="p1.1.m1.1.4.1" id="p1.1.m1.1.4.1.cmml">𝑘</ci>
+      </apply>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">(n)^{k}</annotation>
+  </semantics>
+</math>, where <math id="2685378551882520261" display="inline" alttext="1\leq k&amp;lt;n" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mrow xref="p1.1.m1.1.9.cmml" id="p1.1.m1.1.9">
+      <mn xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1">1</mn>
+      <mo xref="p1.1.m1.1.2.cmml" id="p1.1.m1.1.2">≤</mo>
+      <mrow xref="p1.1.m1.1.9.1.1.cmml" id="p1.1.m1.1.9.1">
+        <mrow xref="p1.1.m1.1.9.1.1.cmml" id="p1.1.m1.1.9.1.2">
+          <mi xref="p1.1.m1.1.3.cmml" id="p1.1.m1.1.3">k</mi>
+          <mo xref="p1.1.m1.1.9.1.2.1.cmml" id="p1.1.m1.1.9.1.2.1">⁢</mo>
+          <mi xref="p1.1.m1.1.4.cmml" id="p1.1.m1.1.4" mathvariant="normal">&amp;</mi>
+          <mo xref="p1.1.m1.1.9.1.2.1.cmml" id="p1.1.m1.1.9.1.2.1a">⁢</mo>
+          <mi xref="p1.1.m1.1.5.cmml" id="p1.1.m1.1.5">l</mi>
+          <mo xref="p1.1.m1.1.9.1.2.1.cmml" id="p1.1.m1.1.9.1.2.1b">⁢</mo>
+          <mi xref="p1.1.m1.1.6.cmml" id="p1.1.m1.1.6">t</mi>
+        </mrow>
+        <mo id="p1.1.m1.1.7">;</mo>
+        <mi xref="p1.1.m1.1.8.cmml" id="p1.1.m1.1.8">n</mi>
+      </mrow>
+    </mrow>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <apply xref="p1.1.m1.1.9" id="p1.1.m1.1.9.cmml">
+        <leq xref="p1.1.m1.1.2" id="p1.1.m1.1.2.cmml"/>
+        <cn xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml" type="integer">1</cn>
+        <list xref="p1.1.m1.1.9.1" id="p1.1.m1.1.9.1.1.cmml">
+          <apply xref="p1.1.m1.1.9.1" id="p1.1.m1.1.9.1.2.cmml">
+            <times xref="p1.1.m1.1.9.1.2.1" id="p1.1.m1.1.9.1.2.1.cmml"/>
+            <ci xref="p1.1.m1.1.3" id="p1.1.m1.1.3.cmml">𝑘</ci>
+            <ci xref="p1.1.m1.1.4" id="p1.1.m1.1.4.cmml">&amp;</ci>
+            <ci xref="p1.1.m1.1.5" id="p1.1.m1.1.5.cmml">𝑙</ci>
+            <ci xref="p1.1.m1.1.6" id="p1.1.m1.1.6.cmml">𝑡</ci>
+          </apply>
+          <ci xref="p1.1.m1.1.8" id="p1.1.m1.1.8.cmml">𝑛</ci>
+        </list>
+      </apply>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">1\leq k&amp;lt;n</annotation>
+  </semantics>
+</math> and <code class="code">Gcd</code><math id="351920092830706621" display="inline" alttext="(n,k)=1" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mrow xref="p1.1.m1.1.8.cmml" id="p1.1.m1.1.8">
+      <mrow xref="p1.1.m1.1.8.1.1.cmml" id="p1.1.m1.1.8.1">
+        <mo id="p1.1.m1.1.1" stretchy="false">(</mo>
+        <mi xref="p1.1.m1.1.2.cmml" id="p1.1.m1.1.2">n</mi>
+        <mo id="p1.1.m1.1.3">,</mo>
+        <mi xref="p1.1.m1.1.4.cmml" id="p1.1.m1.1.4">k</mi>
+        <mo id="p1.1.m1.1.5" stretchy="false">)</mo>
+      </mrow>
+      <mo xref="p1.1.m1.1.6.cmml" id="p1.1.m1.1.6">=</mo>
+      <mn xref="p1.1.m1.1.7.cmml" id="p1.1.m1.1.7">1</mn>
+    </mrow>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <apply xref="p1.1.m1.1.8" id="p1.1.m1.1.8.cmml">
+        <eq xref="p1.1.m1.1.6" id="p1.1.m1.1.6.cmml"/>
+        <interval xref="p1.1.m1.1.8.1" id="p1.1.m1.1.8.1.1.cmml" closure="open">
+          <ci xref="p1.1.m1.1.2" id="p1.1.m1.1.2.cmml">𝑛</ci>
+          <ci xref="p1.1.m1.1.4" id="p1.1.m1.1.4.cmml">𝑘</ci>
+        </interval>
+        <cn xref="p1.1.m1.1.7" id="p1.1.m1.1.7.cmml" type="integer">1</cn>
+      </apply>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">(n,k)=1</annotation>
+  </semantics>
+</math> hold (see <code class="func">GaloisCyc</code> (<a shape="rect" href="chap18_mj.html#X79EE9097783128C4"><span class="RefLink">18.5-1</span></a>)). Note that this action is <em>not</em> equal to exponentiation of cyclotomics, i.e., for general cyclotomics <math id="-54504977581366215" display="inline" alttext="z" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1">z</mi>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">𝑧</ci>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">z</annotation>
+  </semantics>
+</math>, <math id="1610307170891981444" display="inline" alttext="z^{{*k}}" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <msup xref="p1.1.m1.1.3.cmml" id="p1.1.m1.1.3">
+      <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1">z</mi>
+      <mrow xref="p1.1.m1.1.2.1.cmml" id="p1.1.m1.1.2.1">
+        <mi xref="p1.1.m1.1.2.1.3.cmml" id="p1.1.m1.1.2.1.3"/>
+        <mo xref="p1.1.m1.1.2.1.1.cmml" id="p1.1.m1.1.2.1.1">*</mo>
+        <mi xref="p1.1.m1.1.2.1.2.cmml" id="p1.1.m1.1.2.1.2">k</mi>
+      </mrow>
+    </msup>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <apply xref="p1.1.m1.1.3" id="p1.1.m1.1.3.cmml">
+        <csymbol id="p1.1.m1.1.3.1.cmml" cd="ambiguous">superscript</csymbol>
+        <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">𝑧</ci>
+        <apply xref="p1.1.m1.1.2.1" id="p1.1.m1.1.2.1.cmml">
+          <times xref="p1.1.m1.1.2.1.1" id="p1.1.m1.1.2.1.1.cmml"/>
+          <csymbol xref="p1.1.m1.1.2.1.3" id="p1.1.m1.1.2.1.3.cmml" cd="latexml">absent</csymbol>
+          <ci xref="p1.1.m1.1.2.1.2" id="p1.1.m1.1.2.1.2.cmml">𝑘</ci>
+        </apply>
+      </apply>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">z^{{*k}}</annotation>
+  </semantics>
+</math> is different from <math id="5745742262325779948" display="inline" alttext="z^{k}" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <msup xref="p1.1.m1.1.3.cmml" id="p1.1.m1.1.3">
+      <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1">z</mi>
+      <mi xref="p1.1.m1.1.2.1.cmml" id="p1.1.m1.1.2.1">k</mi>
+    </msup>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <apply xref="p1.1.m1.1.3" id="p1.1.m1.1.3.cmml">
+        <csymbol id="p1.1.m1.1.3.1.cmml" cd="ambiguous">superscript</csymbol>
+        <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">𝑧</ci>
+        <ci xref="p1.1.m1.1.2.1" id="p1.1.m1.1.2.1.cmml">𝑘</ci>
+      </apply>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">z^{k}</annotation>
+  </semantics>
+</math>.</p><p xmlns="http://www.w3.org/1999/xhtml">(In <strong class="pkg">GAP</strong>, the image of a cyclotomic <math id="-6251623302427837955" display="inline" alttext="z" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1">z</mi>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">𝑧</ci>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">z</annotation>
+  </semantics>
+</math> under <math id="3460160945755555129" display="inline" alttext="*k" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mrow xref="p1.1.m1.1.3.cmml" id="p1.1.m1.1.3">
+      <mi xref="p1.1.m1.1.3.1.cmml" id="p1.1.m1.1.3.1"/>
+      <mo xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1">*</mo>
+      <mi xref="p1.1.m1.1.2.cmml" id="p1.1.m1.1.2">k</mi>
+    </mrow>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <apply xref="p1.1.m1.1.3" id="p1.1.m1.1.3.cmml">
+        <times xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml"/>
+        <csymbol xref="p1.1.m1.1.3.1" id="p1.1.m1.1.3.1.cmml" cd="latexml">absent</csymbol>
+        <ci xref="p1.1.m1.1.2" id="p1.1.m1.1.2.cmml">𝑘</ci>
+      </apply>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">*k</annotation>
+  </semantics>
+</math> can be computed as <code class="code">GaloisCyc( </code><math id="7378789492007022656" display="inline" alttext="z,k" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mrow xref="p1.1.m1.1.4.1.cmml" id="p1.1.m1.1.4">
+      <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1">z</mi>
+      <mo id="p1.1.m1.1.2">,</mo>
+      <mi xref="p1.1.m1.1.3.cmml" id="p1.1.m1.1.3">k</mi>
+    </mrow>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <list xref="p1.1.m1.1.4" id="p1.1.m1.1.4.1.cmml">
+        <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">𝑧</ci>
+        <ci xref="p1.1.m1.1.3" id="p1.1.m1.1.3.cmml">𝑘</ci>
+      </list>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">z,k</annotation>
+  </semantics>
+</math><code class="code"> )</code>.)</p><div class="example" xmlns="http://www.w3.org/1999/xhtml"><pre xml:space="preserve">
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">( E(5) + E(5)^4 )^2; GaloisCyc( E(5) + E(5)^4, 2 );</span>
+-2*E(5)-E(5)^2-E(5)^3-2*E(5)^4
+E(5)^2+E(5)^3
+</pre></div><p xmlns="http://www.w3.org/1999/xhtml">For <code class="code">Gcd</code><math id="2429103618119238021" display="inline" alttext="(n,k)\neq 1" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mrow xref="p1.1.m1.1.8.cmml" id="p1.1.m1.1.8">
+      <mrow xref="p1.1.m1.1.8.1.1.cmml" id="p1.1.m1.1.8.1">
+        <mo id="p1.1.m1.1.1" stretchy="false">(</mo>
+        <mi xref="p1.1.m1.1.2.cmml" id="p1.1.m1.1.2">n</mi>
+        <mo id="p1.1.m1.1.3">,</mo>
+        <mi xref="p1.1.m1.1.4.cmml" id="p1.1.m1.1.4">k</mi>
+        <mo id="p1.1.m1.1.5" stretchy="false">)</mo>
+      </mrow>
+      <mo xref="p1.1.m1.1.6.cmml" id="p1.1.m1.1.6">≠</mo>
+      <mn xref="p1.1.m1.1.7.cmml" id="p1.1.m1.1.7">1</mn>
+    </mrow>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <apply xref="p1.1.m1.1.8" id="p1.1.m1.1.8.cmml">
+        <neq xref="p1.1.m1.1.6" id="p1.1.m1.1.6.cmml"/>
+        <interval xref="p1.1.m1.1.8.1" id="p1.1.m1.1.8.1.1.cmml" closure="open">
+          <ci xref="p1.1.m1.1.2" id="p1.1.m1.1.2.cmml">𝑛</ci>
+          <ci xref="p1.1.m1.1.4" id="p1.1.m1.1.4.cmml">𝑘</ci>
+        </interval>
+        <cn xref="p1.1.m1.1.7" id="p1.1.m1.1.7.cmml" type="integer">1</cn>
+      </apply>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">(n,k)\neq 1</annotation>
+  </semantics>
+</math>, the map <code class="code">E</code><math id="-17755269626048527" display="inline" alttext="(n)\mapsto" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mrow xref="p1.1.m1.1.5.cmml" id="p1.1.m1.1.5">
+      <mrow id="p1.1.m1.1.5.1">
+        <mo id="p1.1.m1.1.1" stretchy="false">(</mo>
+        <mi xref="p1.1.m1.1.2.cmml" id="p1.1.m1.1.2">n</mi>
+        <mo id="p1.1.m1.1.3" stretchy="false">)</mo>
+      </mrow>
+      <mo xref="p1.1.m1.1.4.cmml" id="p1.1.m1.1.4">↦</mo>
+      <mi xref="p1.1.m1.1.5.2.cmml" id="p1.1.m1.1.5.2"/>
+    </mrow>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <apply xref="p1.1.m1.1.5" id="p1.1.m1.1.5.cmml">
+        <csymbol xref="p1.1.m1.1.4" id="p1.1.m1.1.4.cmml" cd="latexml">maps-to</csymbol>
+        <ci xref="p1.1.m1.1.2" id="p1.1.m1.1.2.cmml">𝑛</ci>
+        <csymbol xref="p1.1.m1.1.5.2" id="p1.1.m1.1.5.2.cmml" cd="latexml">absent</csymbol>
+      </apply>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">(n)\mapsto</annotation>
+  </semantics>
+</math> <code class="code">E</code><math id="7936211141160956024" display="inline" alttext="(n)^{k}" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <msup xref="p1.1.m1.1.5.cmml" id="p1.1.m1.1.5">
+      <mrow id="p1.1.m1.1.5.2">
+        <mo id="p1.1.m1.1.1" stretchy="false">(</mo>
+        <mi xref="p1.1.m1.1.2.cmml" id="p1.1.m1.1.2">n</mi>
+        <mo id="p1.1.m1.1.3" stretchy="false">)</mo>
+      </mrow>
+      <mi xref="p1.1.m1.1.4.1.cmml" id="p1.1.m1.1.4.1">k</mi>
+    </msup>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <apply xref="p1.1.m1.1.5" id="p1.1.m1.1.5.cmml">
+        <csymbol id="p1.1.m1.1.5.1.cmml" cd="ambiguous">superscript</csymbol>
+        <ci xref="p1.1.m1.1.2" id="p1.1.m1.1.2.cmml">𝑛</ci>
+        <ci xref="p1.1.m1.1.4.1" id="p1.1.m1.1.4.1.cmml">𝑘</ci>
+      </apply>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">(n)^{k}</annotation>
+  </semantics>
+</math> does <em>not</em> define a field automorphism of <math id="4830811453257139423" display="inline" alttext="?_{n}" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <msub xref="p1.1.m1.1.3.cmml" id="p1.1.m1.1.3">
+      <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1" mathvariant="normal">?</mi>
+      <mi xref="p1.1.m1.1.2.1.cmml" id="p1.1.m1.1.2.1">n</mi>
+    </msub>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <apply xref="p1.1.m1.1.3" id="p1.1.m1.1.3.cmml">
+        <csymbol id="p1.1.m1.1.3.1.cmml" cd="ambiguous">subscript</csymbol>
+        <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">?</ci>
+        <ci xref="p1.1.m1.1.2.1" id="p1.1.m1.1.2.1.cmml">𝑛</ci>
+      </apply>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">?_{n}</annotation>
+  </semantics>
+</math> but only a <math id="-5246741972512659832" display="inline" alttext="?" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1" mathvariant="normal">?</mi>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">?</ci>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">?</annotation>
+  </semantics>
+</math>-linear map.</p><div class="example" xmlns="http://www.w3.org/1999/xhtml"><pre xml:space="preserve">
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">GaloisCyc( E(5)+E(5)^4, 5 ); GaloisCyc( ( E(5)+E(5)^4 )^2, 5 );</span>
+2
+-6
+</pre></div> </body>
+    </html>
\ No newline at end of file
--- a/export/mwscrawler/13.html
+++ b/export/mwscrawler/13.html
+<html> 
+      <head>
+        <title>60.3-2 LenstraBase</title>
+        <meta name="url" content="http://www.gap-system.org/Manuals/doc/ref/TODO#X87DB9C2C858B722A"></meta>
+      </head>
+      <body> <h5 xmlns="http://www.w3.org/1999/xhtml">60.3-2 LenstraBase</h5><div class="func" xmlns="http://www.w3.org/1999/xhtml"><table width="100%" class="func"><tbody><tr><td colspan="1" rowspan="1" class="tdleft"><code class="func">‣ LenstraBase</code>( <var class="Arg">n</var>, <var class="Arg">stabilizer</var>, <var class="Arg">super</var>, <var class="Arg">m</var> )</td><td colspan="1" rowspan="1" class="tdright">( function )</td></tr></tbody></table></div><p xmlns="http://www.w3.org/1999/xhtml">Let <var class="Arg">n</var> and <var class="Arg">m</var> be positive integers such that <var class="Arg">m</var> divides <var class="Arg">n</var>, <var class="Arg">stabilizer</var> be a list of prime residues modulo <var class="Arg">n</var>, which describes a subfield of the <var class="Arg">n</var>-th cyclotomic field (see <code class="func">GaloisStabilizer</code> (<a shape="rect" href="chap60_mj.html#X87E7313D8070B9CC"><span class="RefLink">60.2-5</span></a>)), and <var class="Arg">super</var> be a list representing a supergroup of the group given by <var class="Arg">stabilizer</var>.</p><p xmlns="http://www.w3.org/1999/xhtml"><code class="func">LenstraBase</code> returns a list <math id="1208490429264458309" display="inline" alttext="[b_{1},b_{2},\ldots,b_{k}]" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mrow xref="p1.1.m1.1.13.1.cmml" id="p1.1.m1.1.13">
+      <mo id="p1.1.m1.1.1" stretchy="false">[</mo>
+      <msub xref="p1.1.m1.1.13.1.cmml" id="p1.1.m1.1.13.2">
+        <mi xref="p1.1.m1.1.2.cmml" id="p1.1.m1.1.2">b</mi>
+        <mn xref="p1.1.m1.1.3.1.cmml" id="p1.1.m1.1.3.1">1</mn>
+      </msub>
+      <mo id="p1.1.m1.1.4">,</mo>
+      <msub xref="p1.1.m1.1.13.1.cmml" id="p1.1.m1.1.13.3">
+        <mi xref="p1.1.m1.1.5.cmml" id="p1.1.m1.1.5">b</mi>
+        <mn xref="p1.1.m1.1.6.1.cmml" id="p1.1.m1.1.6.1">2</mn>
+      </msub>
+      <mo id="p1.1.m1.1.7">,</mo>
+      <mi xref="p1.1.m1.1.8.cmml" id="p1.1.m1.1.8" mathvariant="normal">…</mi>
+      <mo id="p1.1.m1.1.9">,</mo>
+      <msub xref="p1.1.m1.1.13.1.cmml" id="p1.1.m1.1.13.4">
+        <mi xref="p1.1.m1.1.10.cmml" id="p1.1.m1.1.10">b</mi>
+        <mi xref="p1.1.m1.1.11.1.cmml" id="p1.1.m1.1.11.1">k</mi>
+      </msub>
+      <mo id="p1.1.m1.1.12" stretchy="false">]</mo>
+    </mrow>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <list xref="p1.1.m1.1.13" id="p1.1.m1.1.13.1.cmml">
+        <apply xref="p1.1.m1.1.13" id="p1.1.m1.1.13.2.cmml">
+          <csymbol id="p1.1.m1.1.13.2.1.cmml" cd="ambiguous">subscript</csymbol>
+          <ci xref="p1.1.m1.1.2" id="p1.1.m1.1.2.cmml">𝑏</ci>
+          <cn xref="p1.1.m1.1.3.1" id="p1.1.m1.1.3.1.cmml" type="integer">1</cn>
+        </apply>
+        <apply xref="p1.1.m1.1.13" id="p1.1.m1.1.13.3.cmml">
+          <csymbol id="p1.1.m1.1.13.3.1.cmml" cd="ambiguous">subscript</csymbol>
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+        </apply>
+        <ci xref="p1.1.m1.1.8" id="p1.1.m1.1.8.cmml">…</ci>
+        <apply xref="p1.1.m1.1.13" id="p1.1.m1.1.13.4.cmml">
+          <csymbol id="p1.1.m1.1.13.4.1.cmml" cd="ambiguous">subscript</csymbol>
+          <ci xref="p1.1.m1.1.10" id="p1.1.m1.1.10.cmml">𝑏</ci>
+          <ci xref="p1.1.m1.1.11.1" id="p1.1.m1.1.11.1.cmml">𝑘</ci>
+        </apply>
+      </list>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">[b_{1},b_{2},\ldots,b_{k}]</annotation>
+  </semantics>
+</math> of lists, each <math id="-3701198119998990270" display="inline" alttext="b_{i}" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <msub xref="p1.1.m1.1.3.cmml" id="p1.1.m1.1.3">
+      <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1">b</mi>
+      <mi xref="p1.1.m1.1.2.1.cmml" id="p1.1.m1.1.2.1">i</mi>
+    </msub>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <apply xref="p1.1.m1.1.3" id="p1.1.m1.1.3.cmml">
+        <csymbol id="p1.1.m1.1.3.1.cmml" cd="ambiguous">subscript</csymbol>
+        <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">𝑏</ci>
+        <ci xref="p1.1.m1.1.2.1" id="p1.1.m1.1.2.1.cmml">𝑖</ci>
+      </apply>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">b_{i}</annotation>
+  </semantics>
+</math> consisting of integers such that the elements <math id="-8645456467319532217" display="inline" alttext="\sum_{{j\in b_{i}}}" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
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+      <mo xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1" symmetric="true" largeop="true">∑</mo>
+      <mrow xref="p1.1.m1.1.2.1.cmml" id="p1.1.m1.1.2.1">
+        <mi xref="p1.1.m1.1.2.1.1.cmml" id="p1.1.m1.1.2.1.1">j</mi>
+        <mo xref="p1.1.m1.1.2.1.2.cmml" id="p1.1.m1.1.2.1.2">∈</mo>
+        <msub xref="p1.1.m1.1.2.1.5.cmml" id="p1.1.m1.1.2.1.5">
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+        </msub>
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+        <csymbol id="p1.1.m1.1.3.1.cmml" cd="ambiguous">subscript</csymbol>
+        <sum xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml"/>
+        <apply xref="p1.1.m1.1.2.1" id="p1.1.m1.1.2.1.cmml">
+          <in xref="p1.1.m1.1.2.1.2" id="p1.1.m1.1.2.1.2.cmml"/>
+          <ci xref="p1.1.m1.1.2.1.1" id="p1.1.m1.1.2.1.1.cmml">𝑗</ci>
+          <apply xref="p1.1.m1.1.2.1.5" id="p1.1.m1.1.2.1.5.cmml">
+            <csymbol id="p1.1.m1.1.2.1.5.1.cmml" cd="ambiguous">subscript</csymbol>
+            <ci xref="p1.1.m1.1.2.1.3" id="p1.1.m1.1.2.1.3.cmml">𝑏</ci>
+            <ci xref="p1.1.m1.1.2.1.4.1" id="p1.1.m1.1.2.1.4.1.cmml">𝑖</ci>
+          </apply>
+        </apply>
+      </apply>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">\sum_{{j\in b_{i}}}</annotation>
+  </semantics>
+</math><code class="code">E(n)</code><math id="-5417637940190866429" display="inline" alttext="{}^{j}" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <msup xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1">
+      <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1a"/>
+      <mi xref="p1.1.m1.1.1.1.cmml" id="p1.1.m1.1.1.1">j</mi>
+    </msup>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <apply xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">
+        <ci xref="p1.1.m1.1.1.1" id="p1.1.m1.1.1.1.cmml">𝑗</ci>
+      </apply>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">{}^{j}</annotation>
+  </semantics>
+</math> form a basis of the abelian number field <code class="code">NF( <var class="Arg">n</var>, <var class="Arg">stabilizer</var> )</code>, as a vector space over the <var class="Arg">m</var>-th cyclotomic field (see <code class="func">AbelianNumberField</code> (<a shape="rect" href="chap60_mj.html#X80E5AD028143E11E"><span class="RefLink">60.1-2</span></a>)).</p><p xmlns="http://www.w3.org/1999/xhtml">This basis is an integral basis, that is, exactly the integral elements in <code class="code">NF( <var class="Arg">n</var>, <var class="Arg">stabilizer</var> )</code> have integral coefficients. (For details about this basis, see <a shape="rect" href="chapBib_mj.html#biBBre97">[Bre97]</a>.)</p><p xmlns="http://www.w3.org/1999/xhtml">If possible then the result is chosen such that the group described by <var class="Arg">super</var> acts on it, consistently with the action of <var class="Arg">stabilizer</var>, i.e., each orbit of <var class="Arg">super</var> is a union of orbits of <var class="Arg">stabilizer</var>. (A usual case is <var class="Arg">super</var><code class="code"> = </code><var class="Arg">stabilizer</var>, so there is no additional condition.</p><p xmlns="http://www.w3.org/1999/xhtml"><em>Note:</em> The <math id="2032741142945267551" display="inline" alttext="b_{i}" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <msub xref="p1.1.m1.1.3.cmml" id="p1.1.m1.1.3">
+      <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1">b</mi>
+      <mi xref="p1.1.m1.1.2.1.cmml" id="p1.1.m1.1.2.1">i</mi>
+    </msub>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <apply xref="p1.1.m1.1.3" id="p1.1.m1.1.3.cmml">
+        <csymbol id="p1.1.m1.1.3.1.cmml" cd="ambiguous">subscript</csymbol>
+        <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">𝑏</ci>
+        <ci xref="p1.1.m1.1.2.1" id="p1.1.m1.1.2.1.cmml">𝑖</ci>
+      </apply>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">b_{i}</annotation>
+  </semantics>
+</math> are in general not sets, since for <code class="code"><var class="Arg">stabilizer</var> = <var class="Arg">super</var></code>, the first entry is always an element of <code class="code">ZumbroichBase( <var class="Arg">n</var>, <var class="Arg">m</var> )</code>; this property is used by <code class="func">NF</code> (<a shape="rect" href="chap60_mj.html#X80E5AD028143E11E"><span class="RefLink">60.1-2</span></a>) and <code class="func">Coefficients</code> (<a shape="rect" href="chap61_mj.html#X80B32F667BF6AFD8"><span class="RefLink">61.6-3</span></a>) (see <a shape="rect" href="chap60_mj.html#X7D2421AC8491D2BE"><span class="RefLink">60.3</span></a>).</p><p xmlns="http://www.w3.org/1999/xhtml"><var class="Arg">stabilizer</var> must not contain the stabilizer of a proper cyclotomic subfield of the <var class="Arg">n</var>-th cyclotomic field, i.e., the result must describe a basis for a field with conductor <var class="Arg">n</var>.</p><div class="example" xmlns="http://www.w3.org/1999/xhtml"><pre xml:space="preserve">
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">LenstraBase( 24, [ 1, 19 ], [ 1, 19 ], 1 );</span>
+[ [ 1, 19 ], [ 8 ], [ 11, 17 ], [ 16 ] ]
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">LenstraBase( 24, [ 1, 19 ], [ 1, 5, 19, 23 ], 1 );</span>
+[ [ 1, 19 ], [ 5, 23 ], [ 8 ], [ 16 ] ]
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">LenstraBase( 15, [ 1, 4 ], PrimeResidues( 15 ), 1 );</span>
+[ [ 1, 4 ], [ 2, 8 ], [ 7, 13 ], [ 11, 14 ] ]
+</pre></div><p xmlns="http://www.w3.org/1999/xhtml">The first two results describe two bases of the field <math id="-6590770517438568572" display="inline" alttext="?_{3}(\sqrt{{6}})" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mrow xref="p1.1.m1.1.6.cmml" id="p1.1.m1.1.6">
+      <msub xref="p1.1.m1.1.6.2.cmml" id="p1.1.m1.1.6.2">
+        <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1" mathvariant="normal">?</mi>
+        <mn xref="p1.1.m1.1.2.1.cmml" id="p1.1.m1.1.2.1">3</mn>
+      </msub>
+      <mo xref="p1.1.m1.1.6.1.cmml" id="p1.1.m1.1.6.1">⁢</mo>
+      <mrow xref="p1.1.m1.1.4.cmml" id="p1.1.m1.1.6.3">
+        <mo id="p1.1.m1.1.3" stretchy="false">(</mo>
+        <msqrt xref="p1.1.m1.1.4.cmml" id="p1.1.m1.1.4">
+          <mn xref="p1.1.m1.1.4.2.cmml" id="p1.1.m1.1.4.2">6</mn>
+        </msqrt>
+        <mo id="p1.1.m1.1.5" stretchy="false">)</mo>
+      </mrow>
+    </mrow>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <apply xref="p1.1.m1.1.6" id="p1.1.m1.1.6.cmml">
+        <times xref="p1.1.m1.1.6.1" id="p1.1.m1.1.6.1.cmml"/>
+        <apply xref="p1.1.m1.1.6.2" id="p1.1.m1.1.6.2.cmml">
+          <csymbol id="p1.1.m1.1.6.2.1.cmml" cd="ambiguous">subscript</csymbol>
+          <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">?</ci>
+          <cn xref="p1.1.m1.1.2.1" id="p1.1.m1.1.2.1.cmml" type="integer">3</cn>
+        </apply>
+        <apply xref="p1.1.m1.1.6.3" id="p1.1.m1.1.4.cmml">
+          <root id="p1.1.m1.1.4a.cmml"/>
+          <cn xref="p1.1.m1.1.4.2" id="p1.1.m1.1.4.2.cmml" type="integer">6</cn>
+        </apply>
+      </apply>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">?_{3}(\sqrt{{6}})</annotation>
+  </semantics>
+</math>, the third result describes a normal basis of <math id="-6848104539316450458" display="inline" alttext="?_{3}(\sqrt{{5}})" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mrow xref="p1.1.m1.1.6.cmml" id="p1.1.m1.1.6">
+      <msub xref="p1.1.m1.1.6.2.cmml" id="p1.1.m1.1.6.2">
+        <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1" mathvariant="normal">?</mi>
+        <mn xref="p1.1.m1.1.2.1.cmml" id="p1.1.m1.1.2.1">3</mn>
+      </msub>
+      <mo xref="p1.1.m1.1.6.1.cmml" id="p1.1.m1.1.6.1">⁢</mo>
+      <mrow xref="p1.1.m1.1.4.cmml" id="p1.1.m1.1.6.3">
+        <mo id="p1.1.m1.1.3" stretchy="false">(</mo>
+        <msqrt xref="p1.1.m1.1.4.cmml" id="p1.1.m1.1.4">
+          <mn xref="p1.1.m1.1.4.2.cmml" id="p1.1.m1.1.4.2">5</mn>
+        </msqrt>
+        <mo id="p1.1.m1.1.5" stretchy="false">)</mo>
+      </mrow>
+    </mrow>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <apply xref="p1.1.m1.1.6" id="p1.1.m1.1.6.cmml">
+        <times xref="p1.1.m1.1.6.1" id="p1.1.m1.1.6.1.cmml"/>
+        <apply xref="p1.1.m1.1.6.2" id="p1.1.m1.1.6.2.cmml">
+          <csymbol id="p1.1.m1.1.6.2.1.cmml" cd="ambiguous">subscript</csymbol>
+          <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">?</ci>
+          <cn xref="p1.1.m1.1.2.1" id="p1.1.m1.1.2.1.cmml" type="integer">3</cn>
+        </apply>
+        <apply xref="p1.1.m1.1.6.3" id="p1.1.m1.1.4.cmml">
+          <root id="p1.1.m1.1.4a.cmml"/>
+          <cn xref="p1.1.m1.1.4.2" id="p1.1.m1.1.4.2.cmml" type="integer">5</cn>
+        </apply>
+      </apply>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">?_{3}(\sqrt{{5}})</annotation>
+  </semantics>
+</math>.</p> </body>
+    </html>
\ No newline at end of file
--- a/export/mwscrawler/14.html
+++ b/export/mwscrawler/14.html
--- a/export/mwscrawler/15.html
+++ b/export/mwscrawler/15.html
+<html> 
+      <head>
+        <title>60.3 Integral Bases of Abelian Number Fields</title>
+        <meta name="url" content="http://www.gap-system.org/Manuals/doc/ref/TODO#X7D2421AC8491D2BE"></meta>
+      </head>
+      <body> <h4 xmlns="http://www.w3.org/1999/xhtml">60.3 <span class="Heading">Integral Bases of Abelian Number Fields</span></h4><p xmlns="http://www.w3.org/1999/xhtml">Each abelian number field is naturally a vector space over <math id="-4243951106085483006" display="inline" alttext="?" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1" mathvariant="normal">?</mi>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">?</ci>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">?</annotation>
+  </semantics>
+</math>. Moreover, if the abelian number field <math id="-8908099324234125357" display="inline" alttext="F" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1">F</mi>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">𝐹</ci>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">F</annotation>
+  </semantics>
+</math> contains the <math id="3138850455013136997" display="inline" alttext="n" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1">n</mi>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">𝑛</ci>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">n</annotation>
+  </semantics>
+</math>-th cyclotomic field <math id="-4090466234368629443" display="inline" alttext="?_{n}" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <msub xref="p1.1.m1.1.3.cmml" id="p1.1.m1.1.3">
+      <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1" mathvariant="normal">?</mi>
+      <mi xref="p1.1.m1.1.2.1.cmml" id="p1.1.m1.1.2.1">n</mi>
+    </msub>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <apply xref="p1.1.m1.1.3" id="p1.1.m1.1.3.cmml">
+        <csymbol id="p1.1.m1.1.3.1.cmml" cd="ambiguous">subscript</csymbol>
+        <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">?</ci>
+        <ci xref="p1.1.m1.1.2.1" id="p1.1.m1.1.2.1.cmml">𝑛</ci>
+      </apply>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">?_{n}</annotation>
+  </semantics>
+</math> then <math id="-421311888980028774" display="inline" alttext="F" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1">F</mi>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">𝐹</ci>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">F</annotation>
+  </semantics>
+</math> is a vector space over <math id="7414210350085120196" display="inline" alttext="?_{n}" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <msub xref="p1.1.m1.1.3.cmml" id="p1.1.m1.1.3">
+      <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1" mathvariant="normal">?</mi>
+      <mi xref="p1.1.m1.1.2.1.cmml" id="p1.1.m1.1.2.1">n</mi>
+    </msub>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <apply xref="p1.1.m1.1.3" id="p1.1.m1.1.3.cmml">
+        <csymbol id="p1.1.m1.1.3.1.cmml" cd="ambiguous">subscript</csymbol>
+        <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">?</ci>
+        <ci xref="p1.1.m1.1.2.1" id="p1.1.m1.1.2.1.cmml">𝑛</ci>
+      </apply>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">?_{n}</annotation>
+  </semantics>
+</math>. In <strong class="pkg">GAP</strong>, each field object represents a vector space object over a certain subfield <math id="1801983466100099123" display="inline" alttext="S" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1">S</mi>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">𝑆</ci>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">S</annotation>
+  </semantics>
+</math>, which depends on the way <math id="-1517757394707115667" display="inline" alttext="F" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1">F</mi>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">𝐹</ci>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">F</annotation>
+  </semantics>
+</math> was constructed. The subfield <math id="7045353852483731115" display="inline" alttext="S" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1">S</mi>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">𝑆</ci>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">S</annotation>
+  </semantics>
+</math> can be accessed as the value of the attribute <code class="func">LeftActingDomain</code> (<a shape="rect" href="chap57_mj.html#X86F070E0807DC34E"><span class="RefLink">57.1-11</span></a>).</p><p xmlns="http://www.w3.org/1999/xhtml">The return values of <code class="func">NF</code> (<a shape="rect" href="chap60_mj.html#X80E5AD028143E11E"><span class="RefLink">60.1-2</span></a>) and of the one argument versions of <code class="func">CF</code> (<a shape="rect" href="chap60_mj.html#X80D21D80850EFA4B"><span class="RefLink">60.1-1</span></a>) represent vector spaces over <math id="-964803556485730101" display="inline" alttext="?" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1" mathvariant="normal">?</mi>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">?</ci>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">?</annotation>
+  </semantics>
+</math>, and the return values of the two argument version of <code class="func">CF</code> (<a shape="rect" href="chap60_mj.html#X80D21D80850EFA4B"><span class="RefLink">60.1-1</span></a>) represent vector spaces over the field that is given as the first argument. For an abelian number field <var class="Arg">F</var> and a subfield <var class="Arg">S</var> of <var class="Arg">F</var>, a <strong class="pkg">GAP</strong> object representing <var class="Arg">F</var> as a vector space over <var class="Arg">S</var> can be constructed using <code class="func">AsField</code> (<a shape="rect" href="chap58_mj.html#X7C193B7D7AFB29BE"><span class="RefLink">58.1-9</span></a>).</p><p xmlns="http://www.w3.org/1999/xhtml">Let <var class="Arg">F</var> be the cyclotomic field <math id="995609940989272001" display="inline" alttext="?_{n}" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <msub xref="p1.1.m1.1.3.cmml" id="p1.1.m1.1.3">
+      <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1" mathvariant="normal">?</mi>
+      <mi xref="p1.1.m1.1.2.1.cmml" id="p1.1.m1.1.2.1">n</mi>
+    </msub>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <apply xref="p1.1.m1.1.3" id="p1.1.m1.1.3.cmml">
+        <csymbol id="p1.1.m1.1.3.1.cmml" cd="ambiguous">subscript</csymbol>
+        <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">?</ci>
+        <ci xref="p1.1.m1.1.2.1" id="p1.1.m1.1.2.1.cmml">𝑛</ci>
+      </apply>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">?_{n}</annotation>
+  </semantics>
+</math>, represented as a vector space over the subfield <var class="Arg">S</var>. If <var class="Arg">S</var> is the cyclotomic field <math id="2376284400051401582" display="inline" alttext="?_{m}" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <msub xref="p1.1.m1.1.3.cmml" id="p1.1.m1.1.3">
+      <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1" mathvariant="normal">?</mi>
+      <mi xref="p1.1.m1.1.2.1.cmml" id="p1.1.m1.1.2.1">m</mi>
+    </msub>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <apply xref="p1.1.m1.1.3" id="p1.1.m1.1.3.cmml">
+        <csymbol id="p1.1.m1.1.3.1.cmml" cd="ambiguous">subscript</csymbol>
+        <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">?</ci>
+        <ci xref="p1.1.m1.1.2.1" id="p1.1.m1.1.2.1.cmml">𝑚</ci>
+      </apply>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">?_{m}</annotation>
+  </semantics>
+</math>, with <math id="-8433364101409720809" display="inline" alttext="m" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1">m</mi>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">𝑚</ci>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">m</annotation>
+  </semantics>
+</math> a divisor of <math id="627653283343250934" display="inline" alttext="n" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1">n</mi>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">𝑛</ci>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">n</annotation>
+  </semantics>
+</math>, then <code class="code">CanonicalBasis( <var class="Arg">F</var> )</code> returns the Zumbroich basis of <var class="Arg">F</var> relative to <var class="Arg">S</var>, which consists of the roots of unity <code class="code">E(<var class="Arg">n</var>)</code>^<var class="Arg">i</var> where <var class="Arg">i</var> is an element of the list <code class="code">ZumbroichBase( <var class="Arg">n</var>, <var class="Arg">m</var> )</code> (see <code class="func">ZumbroichBase</code> (<a shape="rect" href="chap60_mj.html#X7F52BEA0862E06F2"><span class="RefLink">60.3-1</span></a>)). If <var class="Arg">S</var> is an abelian number field that is not a cyclotomic field then <code class="code">CanonicalBasis( <var class="Arg">F</var> )</code> returns a normal <var class="Arg">S</var>-basis of <var class="Arg">F</var>, i.e., a basis that is closed under the field automorphisms of <var class="Arg">F</var>.</p><p xmlns="http://www.w3.org/1999/xhtml">Let <var class="Arg">F</var> be the abelian number field <code class="code">NF( <var class="Arg">n</var>, <var class="Arg">stab</var> )</code>, with conductor <var class="Arg">n</var>, that is itself not a cyclotomic field, represented as a vector space over the subfield <var class="Arg">S</var>. If <var class="Arg">S</var> is the cyclotomic field <math id="-576215802115201341" display="inline" alttext="?_{m}" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <msub xref="p1.1.m1.1.3.cmml" id="p1.1.m1.1.3">
+      <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1" mathvariant="normal">?</mi>
+      <mi xref="p1.1.m1.1.2.1.cmml" id="p1.1.m1.1.2.1">m</mi>
+    </msub>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <apply xref="p1.1.m1.1.3" id="p1.1.m1.1.3.cmml">
+        <csymbol id="p1.1.m1.1.3.1.cmml" cd="ambiguous">subscript</csymbol>
+        <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">?</ci>
+        <ci xref="p1.1.m1.1.2.1" id="p1.1.m1.1.2.1.cmml">𝑚</ci>
+      </apply>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">?_{m}</annotation>
+  </semantics>
+</math>, with <math id="-8773796078956449250" display="inline" alttext="m" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1">m</mi>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">𝑚</ci>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">m</annotation>
+  </semantics>
+</math> a divisor of <math id="-5692834966176752574" display="inline" alttext="n" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1">n</mi>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">𝑛</ci>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">n</annotation>
+  </semantics>
+</math>, then <code class="code">CanonicalBasis( <var class="Arg">F</var> )</code> returns the Lenstra basis of <var class="Arg">F</var> relative to <var class="Arg">S</var> that consists of the sums of roots of unity described by <code class="code">LenstraBase( <var class="Arg">n</var>, <var class="Arg">stab</var>, <var class="Arg">stab</var>, <var class="Arg">m</var> )</code> (see <code class="func">LenstraBase</code> (<a shape="rect" href="chap60_mj.html#X87DB9C2C858B722A"><span class="RefLink">60.3-2</span></a>)). If <var class="Arg">S</var> is an abelian number field that is not a cyclotomic field then <code class="code">CanonicalBasis( <var class="Arg">F</var> )</code> returns a normal <var class="Arg">S</var>-basis of <var class="Arg">F</var>.</p><div class="example" xmlns="http://www.w3.org/1999/xhtml"><pre xml:space="preserve">
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">f:= CF(8);;   # a cycl. field over the rationals</span>
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">b:= CanonicalBasis( f );;  BasisVectors( b );</span>
+[ 1, E(8), E(4), E(8)^3 ]
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">Coefficients( b, Sqrt(-2) );</span>
+[ 0, 1, 0, 1 ]
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">f:= AsField( CF(4), CF(8) );;  # a cycl. field over a cycl. field</span>
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">b:= CanonicalBasis( f );;  BasisVectors( b );</span>
+[ 1, E(8) ]
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">Coefficients( b, Sqrt(-2) );</span>
+[ 0, 1+E(4) ]
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">f:= AsField( Field( [ Sqrt(-2) ] ), CF(8) );;</span>
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput"># a cycl. field over a non-cycl. field</span>
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">b:= CanonicalBasis( f );;  BasisVectors( b );</span>
+[ 1/2+1/2*E(8)-1/2*E(8)^2-1/2*E(8)^3, 
+  1/2-1/2*E(8)+1/2*E(8)^2+1/2*E(8)^3 ]
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">Coefficients( b, Sqrt(-2) );</span>
+[ E(8)+E(8)^3, E(8)+E(8)^3 ]
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">f:= Field( [ Sqrt(-2) ] );   # a non-cycl. field over the rationals</span>
+NF(8,[ 1, 3 ])
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">b:= CanonicalBasis( f );;  BasisVectors( b );</span>
+[ 1, E(8)+E(8)^3 ]
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">Coefficients( b, Sqrt(-2) );</span>
+[ 0, 1 ]
+</pre></div> </body>
+    </html>
\ No newline at end of file
--- a/export/mwscrawler/16.html
+++ b/export/mwscrawler/16.html
+<html> 
+      <head>
+        <title>60.2-5 GaloisStabilizer</title>
+        <meta name="url" content="http://www.gap-system.org/Manuals/doc/ref/TODO#X87E7313D8070B9CC"></meta>
+      </head>
+      <body> <h5 xmlns="http://www.w3.org/1999/xhtml">60.2-5 GaloisStabilizer</h5><div class="func" xmlns="http://www.w3.org/1999/xhtml"><table width="100%" class="func"><tbody><tr><td colspan="1" rowspan="1" class="tdleft"><code class="func">‣ GaloisStabilizer</code>( <var class="Arg">F</var> )</td><td colspan="1" rowspan="1" class="tdright">( attribute )</td></tr></tbody></table></div><p xmlns="http://www.w3.org/1999/xhtml">Let <var class="Arg">F</var> be an abelian number field (see <code class="func">IsAbelianNumberField</code> (<a shape="rect" href="chap60_mj.html#X7D202D707D5708FA"><span class="RefLink">60.2-3</span></a>)) with conductor <math id="-4737294481319410573" display="inline" alttext="n" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1">n</mi>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">𝑛</ci>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">n</annotation>
+  </semantics>
+</math>, say. (This means that the <math id="-1251700905668443816" display="inline" alttext="n" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1">n</mi>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">𝑛</ci>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">n</annotation>
+  </semantics>
+</math>-th cyclotomic field is the smallest cyclotomic field containing <var class="Arg">F</var>, see <code class="func">Conductor</code> (<a shape="rect" href="chap18_mj.html#X815D6EC57CBA9827"><span class="RefLink">18.1-7</span></a>).) <code class="func">GaloisStabilizer</code> returns the set of all those integers <math id="-7493539776088871027" display="inline" alttext="k" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1">k</mi>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">𝑘</ci>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">k</annotation>
+  </semantics>
+</math> in the range <math id="-2959061408037581052" display="inline" alttext="[1..n]" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mrow id="p1.1.m1.1b">
+      <mo xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1" stretchy="false">[</mo>
+      <mn xref="p1.1.m1.1.2.cmml" id="p1.1.m1.1.2">1</mn>
+      <mo xref="p1.1.m1.1.3.cmml" id="p1.1.m1.1.3">.</mo>
+      <mo xref="p1.1.m1.1.4.cmml" id="p1.1.m1.1.4">.</mo>
+      <mi id="p1.1.m1.1.5">n</mi>
+      <mo xref="p1.1.m1.1.6.cmml" id="p1.1.m1.1.6" stretchy="false">]</mo>
+    </mrow>
+    <annotation-xml id="p1.1.m1.1c" encoding="MathML-Content">
+      <cerror id="p1.1.m1.1d">
+        <csymbol id="p1.1.m1.1e" cd="ambiguous">fragments</csymbol>
+        <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">[</ci>
+        <cn xref="p1.1.m1.1.2" id="p1.1.m1.1.2.cmml" type="integer">1</cn>
+        <ci xref="p1.1.m1.1.3" id="p1.1.m1.1.3.cmml">.</ci>
+        <ci xref="p1.1.m1.1.4" id="p1.1.m1.1.4.cmml">.</ci>
+        <csymbol id="p1.1.m1.1f" cd="unknown">n</csymbol>
+        <ci xref="p1.1.m1.1.6" id="p1.1.m1.1.6.cmml">]</ci>
+      </cerror>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1g" encoding="application/x-tex">[1..n]</annotation>
+  </semantics>
+</math> such that the field automorphism induced by raising <math id="-6979597911055838736" display="inline" alttext="n" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1">n</mi>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">𝑛</ci>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">n</annotation>
+  </semantics>
+</math>-th roots of unity to the <math id="-4443708858965436565" display="inline" alttext="k" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1">k</mi>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">𝑘</ci>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">k</annotation>
+  </semantics>
+</math>-th power acts trivially on <var class="Arg">F</var>.</p><div class="example" xmlns="http://www.w3.org/1999/xhtml"><pre xml:space="preserve">
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">r5:= Sqrt(5);</span>
+E(5)-E(5)^2-E(5)^3+E(5)^4
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">GaloisCyc( r5, 4 ) = r5;  GaloisCyc( r5, 2 ) = r5;</span>
+true
+false
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">GaloisStabilizer( Field( [ r5 ] ) );</span>
+[ 1, 4 ]
+</pre></div> </body>
+    </html>
\ No newline at end of file
--- a/export/mwscrawler/17.html
+++ b/export/mwscrawler/17.html
+<html> 
+      <head>
+        <title>60.2-4 IsCyclotomicField</title>
+        <meta name="url" content="http://www.gap-system.org/Manuals/doc/ref/TODO#X84CAE4627F0CD639"></meta>
+      </head>
+      <body> <h5 xmlns="http://www.w3.org/1999/xhtml">60.2-4 IsCyclotomicField</h5><div class="func" xmlns="http://www.w3.org/1999/xhtml"><table width="100%" class="func"><tbody><tr><td colspan="1" rowspan="1" class="tdleft"><code class="func">‣ IsCyclotomicField</code>( <var class="Arg">F</var> )</td><td colspan="1" rowspan="1" class="tdright">( property )</td></tr></tbody></table></div><p xmlns="http://www.w3.org/1999/xhtml">returns <code class="keyw">true</code> if the field <var class="Arg">F</var> is a <em>cyclotomic field</em>, i.e., an abelian number field (see <code class="func">IsAbelianNumberField</code> (<a shape="rect" href="chap60_mj.html#X7D202D707D5708FA"><span class="RefLink">60.2-3</span></a>)) that can be generated by roots of unity.</p><div class="example" xmlns="http://www.w3.org/1999/xhtml"><pre xml:space="preserve">
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">IsNumberField( CF(9) ); IsAbelianNumberField( Field( [ ER(3) ] ) );</span>
+true
+true
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">IsNumberField( GF(2) );</span>
+false
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">IsCyclotomicField( CF(9) );</span>
+true
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">IsCyclotomicField( Field( [ Sqrt(-3) ] ) );</span>
+true
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">IsCyclotomicField( Field( [ Sqrt(3) ] ) );</span>
+false
+</pre></div> </body>
+    </html>
\ No newline at end of file
--- a/export/mwscrawler/18.html
+++ b/export/mwscrawler/18.html
+<html> 
+      <head>
+        <title>60.2-3 IsAbelianNumberField</title>
+        <meta name="url" content="http://www.gap-system.org/Manuals/doc/ref/TODO#X7D202D707D5708FA"></meta>
+      </head>
+      <body> <h5 xmlns="http://www.w3.org/1999/xhtml">60.2-3 IsAbelianNumberField</h5><div class="func" xmlns="http://www.w3.org/1999/xhtml"><table width="100%" class="func"><tbody><tr><td colspan="1" rowspan="1" class="tdleft"><code class="func">‣ IsAbelianNumberField</code>( <var class="Arg">F</var> )</td><td colspan="1" rowspan="1" class="tdright">( property )</td></tr></tbody></table></div><p xmlns="http://www.w3.org/1999/xhtml">returns <code class="keyw">true</code> if the field <var class="Arg">F</var> is a number field (see <code class="func">IsNumberField</code> (<a shape="rect" href="chap60_mj.html#X87D78F5E875F2E8A"><span class="RefLink">60.2-2</span></a>)) that is a Galois extension of the prime field, with abelian Galois group (see <code class="func">GaloisGroup</code> (<a shape="rect" href="chap58_mj.html#X80CAA5BA82F09ED2"><span class="RefLink">58.3-1</span></a>)).</p> </body>
+    </html>
\ No newline at end of file
--- a/export/mwscrawler/19.html
+++ b/export/mwscrawler/19.html
+<html> 
+      <head>
+        <title>60.2-2 IsNumberField</title>
+        <meta name="url" content="http://www.gap-system.org/Manuals/doc/ref/TODO#X87D78F5E875F2E8A"></meta>
+      </head>
+      <body> <h5 xmlns="http://www.w3.org/1999/xhtml">60.2-2 IsNumberField</h5><div class="func" xmlns="http://www.w3.org/1999/xhtml"><table width="100%" class="func"><tbody><tr><td colspan="1" rowspan="1" class="tdleft"><code class="func">‣ IsNumberField</code>( <var class="Arg">F</var> )</td><td colspan="1" rowspan="1" class="tdright">( property )</td></tr></tbody></table></div><p xmlns="http://www.w3.org/1999/xhtml">returns <code class="keyw">true</code> if the field <var class="Arg">F</var> is a finite dimensional extension of a prime field in characteristic zero, and <code class="keyw">false</code> otherwise.</p> </body>
+    </html>
\ No newline at end of file
--- a/export/mwscrawler/2.html
+++ b/export/mwscrawler/2.html
 <html> 
      <head>
-        <title>TODO</title>
+        <title>2.4 Lists and Tables</title>
-        <meta name="url" content="http://www.gap-system.org/Manuals/doc/ref/TODO#X833C410D85CF96A4"></meta>
+        <meta name="url" content="http://www.gap-system.org/Manuals/doc/ref/TODO#X7F10E951789D6EDF"></meta>
      </head>
-      <body> <h4 xmlns="http://www.w3.org/1999/xhtml">2.3 <span class="Heading">Crossreferencing</span></h4><p xmlns="http://www.w3.org/1999/xhtml">[→ <a shape="rect" href="chapB_mj.html#X7D19CF4782309661"><span class="RefLink">B.8</span></a>]</p><p xmlns="http://www.w3.org/1999/xhtml">In this section we demonstrate various references to parts of this document. Here is a reference to this section: <a shape="rect" href="chap2_mj.html#X833C410D85CF96A4"><span class="RefLink">2.3</span></a>. Here is a reference to chapter <a shape="rect" href="chap1_mj.html#X80E2AD7481DD69D9"><span class="RefLink">1</span></a>, to appendix <a shape="rect" href="chapA_mj.html#X7B53252784137533"><span class="RefLink">A</span></a>, and to subsection <a shape="rect" href="chap1_mj.html#X7E193BD379F58A4C"><span class="RefLink">1.1-1</span></a>.</p><p xmlns="http://www.w3.org/1999/xhtml">We distinguish among others references to functions (see <code class="func">f</code> (<a shape="rect" href="chap1_mj.html#X7FA1D0937FA1D093"><span class="RefLink">1.2-1</span></a>)), to methods with tricky name (see <code class="func">\^\{\}\[\]\&lt;\&amp;</code> (<a shape="rect" href="chap1_mj.html#X822B5C487B29E799"><span class="RefLink">1.2-2</span></a>)), to operations (see <code class="func">MyOperation</code> (<a shape="rect" href="chap1_mj.html#X7D33C2597988F481"><span class="RefLink">1.2-3</span></a>)), to methods (see <code class="func">MyOperation</code> (<a shape="rect" href="chap1_mj.html#X783DCD4E826289D4"><span class="RefLink">1.2-4</span></a>) or <code class="func">MyOperation</code> (<a shape="rect" href="chap1_mj.html#X7A5F4A287D06988C"><span class="RefLink">1.2-5</span></a>)), to filters (see <code class="func">IsBla</code> (<a shape="rect" href="chap1_mj.html#X82954B687D2DF3C2"><span class="RefLink">1.2-6</span></a>)), to properties (see <code class="func">IsBlubb</code> (<a shape="rect" href="chap1_mj.html#X80C364DD7C919CCE"><span class="RefLink">1.2-7</span></a>)), to attributes (see <code class="func">NumberBlobbs</code> (<a shape="rect" href="chap1_mj.html#X8052A45E7F9F054C"><span class="RefLink">1.2-8</span></a>)), to variables (<code class="func">AllBlibbs</code> (<a shape="rect" href="chap1_mj.html#X7C00E05A7DDEF003"><span class="RefLink">1.2-9</span></a>)), to families (see <code class="func">BlibbsFamily</code> (<a shape="rect" href="chap1_mj.html#X7CBC935A8142E374"><span class="RefLink">1.2-10</span></a>)), and to info classes (see <code class="func">InfoBlibbs</code> (<a shape="rect" href="chap1_mj.html#X84D7D77378AD030A"><span class="RefLink">1.2-11</span></a>)).</p><p xmlns="http://www.w3.org/1999/xhtml">There are also references to labels: see <a shape="rect" href="chap2_mj.html#X833C410D85CF96A4"><span class="RefLink">here</span></a>, to other books: see <a shape="rect" href="../../pkg/GAPDoc-1.5.1/doc/chap3_mj.html#X7B76F6F786521F6B"><span class="RefLink">GAPDoc: What is a DTD?</span></a> or <code class="func">IsSubgroup</code> (<a shape="rect" href="../../../doc/ref/chap40_mj.html#X7839D8927E778334"><span class="RefLink">Reference: IsSubgroup</span></a>) in the <strong class="pkg">GAP</strong> reference manual.</p><p xmlns="http://www.w3.org/1999/xhtml">References to sections come in two styles: <a shape="rect" href="chap1_mj.html#X80E2AD7481DD69D9"><span class="RefLink">1</span></a> or <a shape="rect" href="chap1_mj.html#X80E2AD7481DD69D9"><span class="RefLink"><span class="Heading">Sectioning Elements</span></span></a>.</p><p xmlns="http://www.w3.org/1999/xhtml">Another type of cross referencing is bibliography. Here is a citation: <a shape="rect" href="chapBib_mj.html#biBCR1">[CR81, (5.22)]</a> is an interesting lemma.</p><p xmlns="http://www.w3.org/1999/xhtml">There are also URLs:</p><p xmlns="http://www.w3.org/1999/xhtml"><span class="URL"><a shape="rect" href="http://www.math.rwth-aachen.de/">http://www.math.rwth-aachen.de/</a></span></p><p xmlns="http://www.w3.org/1999/xhtml">Email addresses have a special element: <span class="URL"><a shape="rect" href="mailto:Frank.Luebeck@Math.RWTH-Aachen.De">Frank.Luebeck@Math.RWTH-Aachen.De</a></span></p><p xmlns="http://www.w3.org/1999/xhtml">and Homepages another one: <span class="URL"><a shape="rect" href="http://www-groups.mcs.st-and.ac.uk/~neunhoef/">http://www-groups.mcs.st-and.ac.uk/~neunhoef/</a></span></p><p xmlns="http://www.w3.org/1999/xhtml">And here is a link to the <span class="URL"><a shape="rect" href="http://www.math.rwth-aachen.de/~Frank.Luebeck/gap/EDIM/index.html#ARCHS"><strong class="pkg">EDIM</strong> archives</a></span>.</p><p xmlns="http://www.w3.org/1999/xhtml">One can generate index entries as follows (look up the words &quot;TeX-UserGroup&quot;, &quot;RWTH&quot;, &quot;Aachen, Hauptbahnhof&quot;, and &quot;<strong class="pkg">GAP</strong>, <strong class="pkg">GAPDoc</strong>&quot;).</p> </body>
+      <body> <h4 xmlns="http://www.w3.org/1999/xhtml">2.4 <span class="Heading">Lists and Tables</span></h4><p xmlns="http://www.w3.org/1999/xhtml">[→ <a shape="rect" href="chapB_mj.html#X7BB822947F626E1A"><span class="RefLink">B.9</span></a>]</p><p xmlns="http://www.w3.org/1999/xhtml">There are</p><ul xmlns="http://www.w3.org/1999/xhtml"><li><p>lists</p>
+</li><li><p>enumerations, and</p>
+</li><li><p>tables</p>
+</li></ul><p xmlns="http://www.w3.org/1999/xhtml">or:</p><ol xmlns="http://www.w3.org/1999/xhtml"><li><p>lists</p>
+</li><li><p>enumerations, and</p>
+</li><li><p>tables</p>
+</li></ol><p xmlns="http://www.w3.org/1999/xhtml">or with marks:</p><dl xmlns="http://www.w3.org/1999/xhtml"><dt><strong class="Mark">lists:</strong></dt><dd><p>not numbered</p>
+</dd><dt><strong class="Mark">enumerations:</strong></dt><dd><p>numbered</p>
+</dd><dt><strong class="Mark">tables:</strong></dt><dd><p>two-dimensional</p>
+</dd></dl><p xmlns="http://www.w3.org/1999/xhtml">Lists can also be nested:</p><ol xmlns="http://www.w3.org/1999/xhtml"><li><ol><li><p>first item of inner enumeration</p>
+</li><li><p>second item of inner enumeration</p>
+</li></ol>
+</li><li>
+<ul><li><p>first item of inner list</p>
+</li><li><p>second item of inner list</p>
+</li></ul>
+</li></ol><p xmlns="http://www.w3.org/1999/xhtml">Here is a <em>table</em>:</p><div class="pcenter" xmlns="http://www.w3.org/1999/xhtml"><table class="GAPDocTable"><caption class="GAPDocTable"><b>Table: </b>Prices</caption><tbody><tr><td colspan="1" rowspan="1" class="tdright">Object</td><td colspan="1" rowspan="1" class="tdcenter">Price</td><td colspan="1" rowspan="1" class="tdleft">available</td></tr><tr><td colspan="1" rowspan="1" class="tdright">Shoe</td><td colspan="1" rowspan="1" class="tdcenter">$1,00</td><td colspan="1" rowspan="1" class="tdleft">there</td></tr><tr><td colspan="1" rowspan="1" class="tdright">Hat</td><td colspan="1" rowspan="1" class="tdcenter">$2,00</td><td colspan="1" rowspan="1" class="tdleft">not there</td></tr></tbody></table><br/><p> </p><br/>
+</div> </body>
    </html>
\ No newline at end of file
--- a/export/mwscrawler/20.html
+++ b/export/mwscrawler/20.html
+<html> 
+      <head>
+        <title>60.2-1 Factors</title>
+        <meta name="url" content="http://www.gap-system.org/Manuals/doc/ref/TODO#X7B0AB0FB7A4136C4"></meta>
+      </head>
+      <body> <h5 xmlns="http://www.w3.org/1999/xhtml">60.2-1 Factors</h5><div class="func" xmlns="http://www.w3.org/1999/xhtml"><table width="100%" class="func"><tbody><tr><td colspan="1" rowspan="1" class="tdleft"><code class="func">‣ Factors</code>( <var class="Arg">F</var> )</td><td colspan="1" rowspan="1" class="tdright">( method )</td></tr></tbody></table></div><p xmlns="http://www.w3.org/1999/xhtml">Factoring of polynomials over abelian number fields consisting of cyclotomics works in principle but is not very efficient if the degree of the field extension is large.</p><div class="example" xmlns="http://www.w3.org/1999/xhtml"><pre xml:space="preserve">
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">x:= Indeterminate( CF(5) );</span>
+x_1
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">Factors( PolynomialRing( Rationals ), x^5-1 );</span>
+[ x_1-1, x_1^4+x_1^3+x_1^2+x_1+1 ]
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">Factors( PolynomialRing( CF(5) ), x^5-1 );</span>
+[ x_1-1, x_1+(-E(5)), x_1+(-E(5)^2), x_1+(-E(5)^3), x_1+(-E(5)^4) ]
+</pre></div> </body>
+    </html>
\ No newline at end of file
--- a/export/mwscrawler/21.html
+++ b/export/mwscrawler/21.html
+<html> 
+      <head>
+        <title>60.2 Operations for Abelian Number Fields</title>
+        <meta name="url" content="http://www.gap-system.org/Manuals/doc/ref/TODO#X81B5FE06781DB824"></meta>
+      </head>
+      <body> <h4 xmlns="http://www.w3.org/1999/xhtml">60.2 <span class="Heading">Operations for Abelian Number Fields</span></h4><p xmlns="http://www.w3.org/1999/xhtml">For operations for elements of abelian number fields, e.g., <code class="func">Conductor</code> (<a shape="rect" href="chap18_mj.html#X815D6EC57CBA9827"><span class="RefLink">18.1-7</span></a>) or <code class="func">ComplexConjugate</code> (<a shape="rect" href="chap18_mj.html#X7BE001A0811CD599"><span class="RefLink">18.5-2</span></a>), see Chapter <a shape="rect" href="chap18_mj.html#X7DFC03C187DE4841"><span class="RefLink">18</span></a>.</p> </body>
+    </html>
\ No newline at end of file
--- a/export/mwscrawler/22.html
+++ b/export/mwscrawler/22.html
+<html> 
+      <head>
+        <title>60.1-3 GaussianRationals</title>
+        <meta name="url" content="http://www.gap-system.org/Manuals/doc/ref/TODO#X82F53C65802FF551"></meta>
+      </head>
+      <body> <h5 xmlns="http://www.w3.org/1999/xhtml">60.1-3 GaussianRationals</h5><div class="func" xmlns="http://www.w3.org/1999/xhtml"><table width="100%" class="func"><tbody><tr><td colspan="1" rowspan="1" class="tdleft"><code class="func">‣ GaussianRationals</code></td><td colspan="1" rowspan="1" class="tdright">( global variable )</td></tr></tbody></table></div><div class="func" xmlns="http://www.w3.org/1999/xhtml"><table width="100%" class="func"><tbody><tr><td colspan="1" rowspan="1" class="tdleft"><code class="func">‣ IsGaussianRationals</code>( <var class="Arg">obj</var> )</td><td colspan="1" rowspan="1" class="tdright">( category )</td></tr></tbody></table></div><p xmlns="http://www.w3.org/1999/xhtml"><code class="func">GaussianRationals</code> is the field <math id="9015601468690095953" display="inline" alttext="?_{4}=?(\sqrt{{-1}})" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mrow xref="p1.1.m1.1.8.cmml" id="p1.1.m1.1.8">
+      <msub xref="p1.1.m1.1.8.1.cmml" id="p1.1.m1.1.8.1">
+        <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1" mathvariant="normal">?</mi>
+        <mn xref="p1.1.m1.1.2.1.cmml" id="p1.1.m1.1.2.1">4</mn>
+      </msub>
+      <mo xref="p1.1.m1.1.3.cmml" id="p1.1.m1.1.3">=</mo>
+      <mrow xref="p1.1.m1.1.8.2.cmml" id="p1.1.m1.1.8.2">
+        <mi xref="p1.1.m1.1.4.cmml" id="p1.1.m1.1.4" mathvariant="normal">?</mi>
+        <mo xref="p1.1.m1.1.8.2.1.cmml" id="p1.1.m1.1.8.2.1">⁢</mo>
+        <mrow xref="p1.1.m1.1.6.cmml" id="p1.1.m1.1.8.2.2">
+          <mo id="p1.1.m1.1.5" stretchy="false">(</mo>
+          <msqrt xref="p1.1.m1.1.6.cmml" id="p1.1.m1.1.6">
+            <mrow xref="p1.1.m1.1.6.cmml" id="p1.1.m1.1.6.2">
+              <mo xref="p1.1.m1.1.6.2.1.cmml" id="p1.1.m1.1.6.2.1">-</mo>
+              <mn xref="p1.1.m1.1.6.2.2.cmml" id="p1.1.m1.1.6.2.2">1</mn>
+            </mrow>
+          </msqrt>
+          <mo id="p1.1.m1.1.7" stretchy="false">)</mo>
+        </mrow>
+      </mrow>
+    </mrow>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <apply xref="p1.1.m1.1.8" id="p1.1.m1.1.8.cmml">
+        <eq xref="p1.1.m1.1.3" id="p1.1.m1.1.3.cmml"/>
+        <apply xref="p1.1.m1.1.8.1" id="p1.1.m1.1.8.1.cmml">
+          <csymbol id="p1.1.m1.1.8.1.1.cmml" cd="ambiguous">subscript</csymbol>
+          <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">?</ci>
+          <cn xref="p1.1.m1.1.2.1" id="p1.1.m1.1.2.1.cmml" type="integer">4</cn>
+        </apply>
+        <apply xref="p1.1.m1.1.8.2" id="p1.1.m1.1.8.2.cmml">
+          <times xref="p1.1.m1.1.8.2.1" id="p1.1.m1.1.8.2.1.cmml"/>
+          <ci xref="p1.1.m1.1.4" id="p1.1.m1.1.4.cmml">?</ci>
+          <apply xref="p1.1.m1.1.8.2.2" id="p1.1.m1.1.6.cmml">
+            <root id="p1.1.m1.1.6a.cmml"/>
+            <apply xref="p1.1.m1.1.8.2.2" id="p1.1.m1.1.6.2.cmml">
+              <minus xref="p1.1.m1.1.6.2.1" id="p1.1.m1.1.6.2.1.cmml"/>
+              <cn xref="p1.1.m1.1.6.2.2" id="p1.1.m1.1.6.2.2.cmml" type="integer">1</cn>
+            </apply>
+          </apply>
+        </apply>
+      </apply>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">?_{4}=?(\sqrt{{-1}})</annotation>
+  </semantics>
+</math> of Gaussian rationals, as a set of cyclotomic numbers, see Chapter <a shape="rect" href="chap18_mj.html#X7DFC03C187DE4841"><span class="RefLink">18</span></a> for basic operations. This field can also be obtained as <code class="code">CF(4)</code> (see <code class="func">CyclotomicField</code> (<a shape="rect" href="chap60_mj.html#X80D21D80850EFA4B"><span class="RefLink">60.1-1</span></a>)).</p><p xmlns="http://www.w3.org/1999/xhtml">The filter <code class="func">IsGaussianRationals</code> returns <code class="keyw">true</code> for the <strong class="pkg">GAP</strong> object <code class="func">GaussianRationals</code>, and <code class="keyw">false</code> for all other <strong class="pkg">GAP</strong> objects.</p><p xmlns="http://www.w3.org/1999/xhtml">(For details about the field of rationals, see Chapter <code class="func">Rationals</code> (<a shape="rect" href="chap17_mj.html#X7B6029D18570C08A"><span class="RefLink">17.1-1</span></a>).)</p><div class="example" xmlns="http://www.w3.org/1999/xhtml"><pre xml:space="preserve">
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">CF(4) = GaussianRationals;</span>
+true
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">Sqrt(-1) in GaussianRationals;</span>
+true
+</pre></div> </body>
+    </html>
\ No newline at end of file
--- a/export/mwscrawler/23.html
+++ b/export/mwscrawler/23.html
+<html> 
+      <head>
+        <title>60.1-2 AbelianNumberField</title>
+        <meta name="url" content="http://www.gap-system.org/Manuals/doc/ref/TODO#X80E5AD028143E11E"></meta>
+      </head>
+      <body> <h5 xmlns="http://www.w3.org/1999/xhtml">60.1-2 AbelianNumberField</h5><div class="func" xmlns="http://www.w3.org/1999/xhtml"><table width="100%" class="func"><tbody><tr><td colspan="1" rowspan="1" class="tdleft"><code class="func">‣ AbelianNumberField</code>( <var class="Arg">n</var>, <var class="Arg">stab</var> )</td><td colspan="1" rowspan="1" class="tdright">( function )</td></tr></tbody></table></div><div class="func" xmlns="http://www.w3.org/1999/xhtml"><table width="100%" class="func"><tbody><tr><td colspan="1" rowspan="1" class="tdleft"><code class="func">‣ NF</code>( <var class="Arg">n</var>, <var class="Arg">stab</var> )</td><td colspan="1" rowspan="1" class="tdright">( function )</td></tr></tbody></table></div><p xmlns="http://www.w3.org/1999/xhtml">For a positive integer <var class="Arg">n</var> and a list <var class="Arg">stab</var> of prime residues modulo <var class="Arg">n</var>, <code class="func">AbelianNumberField</code> returns the fixed field of the group described by <var class="Arg">stab</var> (cf. <code class="func">GaloisStabilizer</code> (<a shape="rect" href="chap60_mj.html#X87E7313D8070B9CC"><span class="RefLink">60.2-5</span></a>)), in the <var class="Arg">n</var>-th cyclotomic field. <code class="func">AbelianNumberField</code> is mainly thought for internal use and for printing fields in a standard way; <code class="func">Field</code> (<a shape="rect" href="chap58_mj.html#X871AA7D58263E9AC"><span class="RefLink">58.1-3</span></a>) (cf. also <a shape="rect" href="chap60_mj.html#X81B5FE06781DB824"><span class="RefLink">60.2</span></a>) is probably more suitable if one knows generators of the field in question.</p><p xmlns="http://www.w3.org/1999/xhtml"><code class="func">AbelianNumberField</code> can be abbreviated to <code class="func">NF</code>, this form is used also when <strong class="pkg">GAP</strong> prints abelian number fields.</p><p xmlns="http://www.w3.org/1999/xhtml">Fields constructed with <code class="func">NF</code> are stored in the global list <code class="code">ABELIAN_NUMBER_FIELDS</code>, so repeated calls of <code class="func">NF</code> just fetch these field objects after they have been created once.</p><div class="example" xmlns="http://www.w3.org/1999/xhtml"><pre xml:space="preserve">
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">NF( 7, [ 1 ] );</span>
+CF(7)
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">f:= NF( 7, [ 1, 2 ] );  Sqrt(-7); Sqrt(-7) in f;</span>
+NF(7,[ 1, 2, 4 ])
+E(7)+E(7)^2-E(7)^3+E(7)^4-E(7)^5-E(7)^6
+true
+</pre></div> </body>
+    </html>
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--- a/export/mwscrawler/24.html
+++ b/export/mwscrawler/24.html
+<html> 
+      <head>
+        <title>60.1-1 CyclotomicField</title>
+        <meta name="url" content="http://www.gap-system.org/Manuals/doc/ref/TODO#X80D21D80850EFA4B"></meta>
+      </head>
+      <body> <h5 xmlns="http://www.w3.org/1999/xhtml">60.1-1 CyclotomicField</h5><div class="func" xmlns="http://www.w3.org/1999/xhtml"><table width="100%" class="func"><tbody><tr><td colspan="1" rowspan="1" class="tdleft"><code class="func">‣ CyclotomicField</code>( [<var class="Arg">subfield</var>, ]<var class="Arg">n</var> )</td><td colspan="1" rowspan="1" class="tdright">( function )</td></tr></tbody></table></div><div class="func" xmlns="http://www.w3.org/1999/xhtml"><table width="100%" class="func"><tbody><tr><td colspan="1" rowspan="1" class="tdleft"><code class="func">‣ CyclotomicField</code>( [<var class="Arg">subfield</var>, ]<var class="Arg">gens</var> )</td><td colspan="1" rowspan="1" class="tdright">( function )</td></tr></tbody></table></div><div class="func" xmlns="http://www.w3.org/1999/xhtml"><table width="100%" class="func"><tbody><tr><td colspan="1" rowspan="1" class="tdleft"><code class="func">‣ CF</code>( [<var class="Arg">subfield</var>, ]<var class="Arg">n</var> )</td><td colspan="1" rowspan="1" class="tdright">( function )</td></tr></tbody></table></div><div class="func" xmlns="http://www.w3.org/1999/xhtml"><table width="100%" class="func"><tbody><tr><td colspan="1" rowspan="1" class="tdleft"><code class="func">‣ CF</code>( [<var class="Arg">subfield</var>, ]<var class="Arg">gens</var> )</td><td colspan="1" rowspan="1" class="tdright">( function )</td></tr></tbody></table></div><p xmlns="http://www.w3.org/1999/xhtml">The first version creates the <var class="Arg">n</var>-th cyclotomic field <math id="2016962131100400854" display="inline" alttext="?_{n}" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <msub xref="p1.1.m1.1.3.cmml" id="p1.1.m1.1.3">
+      <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1" mathvariant="normal">?</mi>
+      <mi xref="p1.1.m1.1.2.1.cmml" id="p1.1.m1.1.2.1">n</mi>
+    </msub>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <apply xref="p1.1.m1.1.3" id="p1.1.m1.1.3.cmml">
+        <csymbol id="p1.1.m1.1.3.1.cmml" cd="ambiguous">subscript</csymbol>
+        <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">?</ci>
+        <ci xref="p1.1.m1.1.2.1" id="p1.1.m1.1.2.1.cmml">𝑛</ci>
+      </apply>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">?_{n}</annotation>
+  </semantics>
+</math>. The second version creates the smallest cyclotomic field containing the elements in the list <var class="Arg">gens</var>. In both cases the field can be generated as an extension of a designated subfield <var class="Arg">subfield</var> (cf. <a shape="rect" href="chap60_mj.html#X7D2421AC8491D2BE"><span class="RefLink">60.3</span></a>).</p><p xmlns="http://www.w3.org/1999/xhtml"><code class="func">CyclotomicField</code> can be abbreviated to <code class="func">CF</code>, this form is used also when <strong class="pkg">GAP</strong> prints cyclotomic fields.</p><p xmlns="http://www.w3.org/1999/xhtml">Fields constructed with the one argument version of <code class="func">CF</code> are stored in the global list <code class="code">CYCLOTOMIC_FIELDS</code>, so repeated calls of <code class="func">CF</code> just fetch these field objects after they have been created once.</p><div class="example" xmlns="http://www.w3.org/1999/xhtml"><pre xml:space="preserve">
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">CyclotomicField( 5 );  CyclotomicField( [ Sqrt(3) ] );</span>
+CF(5)
+CF(12)
+<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">CF( CF(3), 12 );  CF( CF(4), [ Sqrt(7) ] );</span>
+AsField( CF(3), CF(12) )
+AsField( GaussianRationals, CF(28) )
+</pre></div> </body>
+    </html>
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--- a/export/mwscrawler/25.html
+++ b/export/mwscrawler/25.html
+<html> 
+      <head>
+        <title>60.1 Construction of Abelian Number Fields</title>
+        <meta name="url" content="http://www.gap-system.org/Manuals/doc/ref/TODO#X7D4E43E5799753B5"></meta>
+      </head>
+      <body> <h4 xmlns="http://www.w3.org/1999/xhtml">60.1 <span class="Heading">Construction of Abelian Number Fields</span></h4><p xmlns="http://www.w3.org/1999/xhtml">Besides the usual construction using <code class="func">Field</code> (<a shape="rect" href="chap58_mj.html#X871AA7D58263E9AC"><span class="RefLink">58.1-3</span></a>) or <code class="func">DefaultField</code> (<a shape="rect" href="chap18_mj.html#X7FE3D5637B5485D0"><span class="RefLink">18.1-16</span></a>) (see <code class="func">DefaultField</code> (<a shape="rect" href="chap18_mj.html#X7FE3D5637B5485D0"><span class="RefLink">18.1-16</span></a>)), abelian number fields consisting of cyclotomics can be created with <code class="func">CyclotomicField</code> (<a shape="rect" href="chap60_mj.html#X80D21D80850EFA4B"><span class="RefLink">60.1-1</span></a>) and <code class="func">AbelianNumberField</code> (<a shape="rect" href="chap60_mj.html#X80E5AD028143E11E"><span class="RefLink">60.1-2</span></a>).</p> </body>
+    </html>
\ No newline at end of file
--- a/export/mwscrawler/26.html
+++ b/export/mwscrawler/26.html
+<html> 
+      <head>
+        <title>TODO</title>
+        <meta name="url" content="http://www.gap-system.org/Manuals/doc/ref/TODO#X80510B5880521FDC"></meta>
+      </head>
+      <body> <div class="ChapSects" xmlns="http://www.w3.org/1999/xhtml"><a shape="rect" href="chap60_mj.html#X80510B5880521FDC">60 <span class="Heading">Abelian Number Fields</span></a>
+<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a shape="rect" href="chap60_mj.html#X7D4E43E5799753B5">60.1 <span class="Heading">Construction of Abelian Number Fields</span></a>
+</span>
+<div class="ContSSBlock">
+<span class="ContSS"><br/><span class="nocss">  </span><a shape="rect" href="chap60_mj.html#X80D21D80850EFA4B">60.1-1 CyclotomicField</a></span>
+<span class="ContSS"><br/><span class="nocss">  </span><a shape="rect" href="chap60_mj.html#X80E5AD028143E11E">60.1-2 AbelianNumberField</a></span>
+<span class="ContSS"><br/><span class="nocss">  </span><a shape="rect" href="chap60_mj.html#X82F53C65802FF551">60.1-3 GaussianRationals</a></span>
+</div></div>
+<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a shape="rect" href="chap60_mj.html#X81B5FE06781DB824">60.2 <span class="Heading">Operations for Abelian Number Fields</span></a>
+</span>
+<div class="ContSSBlock">
+<span class="ContSS"><br/><span class="nocss">  </span><a shape="rect" href="chap60_mj.html#X7B0AB0FB7A4136C4">60.2-1 Factors</a></span>
+<span class="ContSS"><br/><span class="nocss">  </span><a shape="rect" href="chap60_mj.html#X87D78F5E875F2E8A">60.2-2 IsNumberField</a></span>
+<span class="ContSS"><br/><span class="nocss">  </span><a shape="rect" href="chap60_mj.html#X7D202D707D5708FA">60.2-3 IsAbelianNumberField</a></span>
+<span class="ContSS"><br/><span class="nocss">  </span><a shape="rect" href="chap60_mj.html#X84CAE4627F0CD639">60.2-4 IsCyclotomicField</a></span>
+<span class="ContSS"><br/><span class="nocss">  </span><a shape="rect" href="chap60_mj.html#X87E7313D8070B9CC">60.2-5 GaloisStabilizer</a></span>
+</div></div>
+<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a shape="rect" href="chap60_mj.html#X7D2421AC8491D2BE">60.3 <span class="Heading">Integral Bases of Abelian Number Fields</span></a>
+</span>
+<div class="ContSSBlock">
+<span class="ContSS"><br/><span class="nocss">  </span><a shape="rect" href="chap60_mj.html#X7F52BEA0862E06F2">60.3-1 ZumbroichBase</a></span>
+<span class="ContSS"><br/><span class="nocss">  </span><a shape="rect" href="chap60_mj.html#X87DB9C2C858B722A">60.3-2 LenstraBase</a></span>
+</div></div>
+<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a shape="rect" href="chap60_mj.html#X7E4AB4B17C7BA10C">60.4 <span class="Heading">Galois Groups of Abelian Number Fields</span></a>
+</span>
+<div class="ContSSBlock">
+<span class="ContSS"><br/><span class="nocss">  </span><a shape="rect" href="chap60_mj.html#X7B55A90582E818F3">60.4-1 GaloisGroup</a></span>
+<span class="ContSS"><br/><span class="nocss">  </span><a shape="rect" href="chap60_mj.html#X8643D4B47A827D9D">60.4-2 ANFAutomorphism</a></span>
+</div></div>
+<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a shape="rect" href="chap60_mj.html#X85E9E90D7FE877CC">60.5 <span class="Heading">Gaussians</span></a>
+</span>
+<div class="ContSSBlock">
+<span class="ContSS"><br/><span class="nocss">  </span><a shape="rect" href="chap60_mj.html#X80BD5EAB879F096E">60.5-1 GaussianIntegers</a></span>
+<span class="ContSS"><br/><span class="nocss">  </span><a shape="rect" href="chap60_mj.html#X7BFD33D27BFB7C5A">60.5-2 IsGaussianIntegers</a></span>
+</div></div>
+</div><h3 xmlns="http://www.w3.org/1999/xhtml">60 <span class="Heading">Abelian Number Fields</span></h3><p xmlns="http://www.w3.org/1999/xhtml">An <em>abelian number field</em> is a field in characteristic zero that is a finite dimensional normal extension of its prime field such that the Galois group is abelian. In <strong class="pkg">GAP</strong>, one implementation of abelian number fields is given by fields of cyclotomic numbers (see Chapter <a shape="rect" href="chap18_mj.html#X7DFC03C187DE4841"><span class="RefLink">18</span></a>). Note that abelian number fields can also be constructed with the more general <code class="func">AlgebraicExtension</code> (<a shape="rect" href="chap67_mj.html#X7CDA90537D2BAC8A"><span class="RefLink">67.1-1</span></a>), a discussion of advantages and disadvantages can be found in <a shape="rect" href="chap18_mj.html#X8557FC2D7ACD6105"><span class="RefLink">18.6</span></a>. The functions described in this chapter have been developed for fields whose elements are in the filter <code class="func">IsCyclotomic</code> (<a shape="rect" href="chap18_mj.html#X841C425281A6F775"><span class="RefLink">18.1-3</span></a>), they may or may not work well for abelian number fields consisting of other kinds of elements.</p><p xmlns="http://www.w3.org/1999/xhtml">Throughout this chapter, <math id="8586465557677769213" display="inline" alttext="?_{n}" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <msub xref="p1.1.m1.1.3.cmml" id="p1.1.m1.1.3">
+      <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1" mathvariant="normal">?</mi>
+      <mi xref="p1.1.m1.1.2.1.cmml" id="p1.1.m1.1.2.1">n</mi>
+    </msub>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <apply xref="p1.1.m1.1.3" id="p1.1.m1.1.3.cmml">
+        <csymbol id="p1.1.m1.1.3.1.cmml" cd="ambiguous">subscript</csymbol>
+        <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">?</ci>
+        <ci xref="p1.1.m1.1.2.1" id="p1.1.m1.1.2.1.cmml">𝑛</ci>
+      </apply>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">?_{n}</annotation>
+  </semantics>
+</math> will denote the cyclotomic field generated by the field <math id="8103627879763627883" display="inline" alttext="?" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1" mathvariant="normal">?</mi>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">?</ci>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">?</annotation>
+  </semantics>
+</math> of rationals together with <math id="-4895042398210646987" display="inline" alttext="n" class="ltx_Math" xmlns="http://www.w3.org/1998/Math/MathML">
+  <semantics id="p1.1.m1.1a">
+    <mi xref="p1.1.m1.1.1.cmml" id="p1.1.m1.1.1">n</mi>
+    <annotation-xml id="p1.1.m1.1b" encoding="MathML-Content">
+      <ci xref="p1.1.m1.1.1" id="p1.1.m1.1.1.cmml">𝑛</ci>
+    </annotation-xml>
+    <annotation id="p1.1.m1.1c" encoding="application/x-tex">n</annotation>
+  </semantics>
+</math>-th roots of unity.</p><p xmlns="http://www.w3.org/1999/xhtml">In <a shape="rect" href="chap60_mj.html#X7D4E43E5799753B5"><span class="RefLink">60.1</span></a>, constructors for abelian number fields are described, <a shape="rect" href="chap60_mj.html#X81B5FE06781DB824"><span class="RefLink">60.2</span></a> introduces operations for abelian number fields, <a shape="rect" href="chap60_mj.html#X7D2421AC8491D2BE"><span class="RefLink">60.3</span></a> deals with the vector space structure of abelian number fields, and <a shape="rect" href="chap60_mj.html#X7E4AB4B17C7BA10C"><span class="RefLink">60.4</span></a> describes field automorphisms of abelian number fields,</p> </body>
+    </html>
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--- a/export/mwscrawler/3.html
+++ b/export/mwscrawler/3.html