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<td class="tdleft"><a href="tdleft>or permutationu a chain< =URL href=https/gap-packagesgithubgenss>genss</a></span/>
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l </td>
<td class="tdleft"><a href="chap6.html#X7F46D8727850585D"><span class="RefLink">6.2-2</span></a></td>
<>
<tr>
<td class="tdleft">70<tr>
<td class="tdleft"><code class="code">Imprimitive/code</td
<td class
< classtdleft href.#77E1C37F03A49D< class"RefLink">.2-3</pan
</tr>
tr
<td class="tdleft">60</td>
<java.lang.StringIndexOutOfBoundsException: Index 2 out of bounds for length 0
<td class="tdleft">recognises large-base primitive permutation groups</td>
<td class="tdleft"><a href="chap6.html#X836212B6818B60FE"><span class="RefLink">6.2-4</span></a></td>
</tr>
<tr>
<td class
< class" "StabilizerChainPermt
<td class="tdleft">
<td=""><a="chap6.#X7DC0B08B7C73A4F9"<="">20><a></td
</tr>
<tr>
<td class="tdleft">50</td>
<td  to   input < class>/> is giantthat <pan=""></> orS_n>  itsaction <span="">n<span).  outputis   structure class><span nice  < class"G/var> a anSLP forarbitrary elementsof fromthe nice ;or< class=eyw>NeverApplicable rg/varis transitive code="keyw"></>in that wasthat =ArgG/>  ,  was  construction< class">wasunsuccessful Ifthe methodconstructs SimpleMath<span  the node  .<p
<td class="tdleft">for a permutation group using a stabilizer chain</td>
<td class="tdleft"><a href="chap6.html#X834E9DFF7DC949DE"><span class="RefLink">6.2-9</span></a></td>
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<p><a id="X80320AF97EF01284This methodis usedfor recognizing groups.

<h5>6.2-1 <span

<p>This method is unused!</p>

<p>This method

<p><a id="X7F46D8727850585D" name="X7F46D8727850585D"></a></p>

<h5java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

<p>This method is used for recognizing permutation groups.</p>

<>The triesto whetherthe  <var""G/>is ( isspan=SimpleMath></spanor classSimpleMath>S_n innaturalonclass">n/span>points). output is either a data structure and aprocedure to write an SLPfor elementsof ">/>if ="><>istransitive <codeclass"fail/> thecasethatnoevidencewas < =Arg> or wasfound the span class"">D/span> unsuccessful.Ifthe constructs span ="SimpleMath/>thennode .<>

<p><a id="X8757E1C37F03A49D" name="X8757E1C37F03A49D"></a></p>

<h5>6.2-3 <span class="Heading"><code class="code">Imprimitive</code></span></h5>

<p>This method is used for recognizing permutation groups

<p>If the input group is not known to be transitive then this method returns <code class="keyw">NotEnoughInformation</code>. If the input group is known to be transitive and primitive then the method returns <code class="keyw">NeverApplicable</code>; otherwise, the

<p>If the method is successful then it also gives a hint for the children

<pjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

<h5>6.2-4 <span class="Heading"><code class="code">LargeBasePrimitive</code></span></h5>

<p>This method is used for recognizing permutation groups.</p>

<p> method todetermine the  classGv> is fixed-point-free primitive that is  nor alternating in natural action. This method is an implementation of <a href="chapBib.html#biBLNPS06">[LNPS06]</a>.</p>

<pAprimitive < classSimpleMathH/panon< =""Nspan is emlargeemif  <span=SimpleMath/>,< class">r<spanwithspanclass=SimpleMathN={n  k}r/span,and  a  isomorphism<span classSimpleMathH<span  a  of productaction product <span="> of spanclass""A_n ^ rS_n> and< classSimpleMath></spanact on  <SimpleMathk/>- of<spanclassSimpleMath>1 ..,n<span This algorithmrecognises  large groups < classSimpleMathr⋅ <span and span=""> ⋅ r ⋅ k^2 ≤ n</pan><p>

<p>Ajava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

<p>If <var class="Arg">G</var> is imprimitive then the output is <code class="keyw">NeverApplicable</code>. If

<p><a id="X804A913E84B77F97" name>6.7< class class></code/pan

<h5>6.2-5 <span class="Heading"><code class="code"

<p>This method is used for recognizing

<p>If

<p>If

<p><a id="X83C651E58239EEAF" name="X83C651E58239EEAF"></a></p>

<h5>6.2-6 <span class="Heading"><code class="code">NonTransitive</code><java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

<p>This method is used for

<> a  <var><var nontransitively  method a to  of classG/> on orbit largest.  <var=""<var  methodclass></code/

<

<h5>6.2-7 <span class="Heading"><code class="code">Pcgs</code></span></h5>

<p>This method is used for recognizing permutation groups.</p>

<p>This is the <strong class="pkg">GAP</strong> library function to compute a stabiliser

<p><a id="X82B9AF9F7A904FE5" name="X82B9AF9F7A904FE5"></apTODO

<h5>6.2-8 <span class="Heading"><code class="code">PcgsForBlocks</code></span></h5

<p>This method is unused!</p>

<p>This method is called afterThis  a homomorphism permutationvar"> to the action on moved points of>/>  <var=Argvar any , is  to  or ratio pointsto moved acertain . If classG/var fixed butnot, then returnscode="">  that  be again a later. In  cases returns =""><code<pjava.lang.StringIndexOutOfBoundsException: Index 563 out of bounds for length 563

<p><a id="X834E9DFF7DC949DE" name="X834E9DFF7DC949DE"></a></p>

<h5>6.2-9 <span class="Heading"><code class="code">StabChain</code></span></h5>

<>his sused  permutation/>

<p>This is the randomized <strong class=p>aidjava.lang.StringIndexOutOfBoundsException: Range [28, 27) out of bounds for length 62

<p><a id="X7DC0B08B7C73A4F9" name="X7DC0B08B7C73A4F9"></a></p>

<h521 span=">codeclass"">StabilizerChainPerm/>

<p>This method is used for recognizing permutation groups.</p>

<p>TODO</p>

<p><a id="X8236A4817FA037E2" name="X8236A4817FA037E2"></a></p>

<h5>6.2-11 <span class="Heading"><code class="code">ThrowAwayFixedPointstd="> through generators and compare to the identity/java.lang.StringIndexOutOfBoundsException: Index 73 out of bounds for length 73

<p>This method is used for recognizing permutation groups>

<p>Thisclass="tdleft"><code="code">KnownStabilizerChain/code>/>

<>  current  is if number class>/> of points at < class"13span of is at half of the number of points on which Arg><var   < class"GAP/>.

< fact methodcode=" fixed pointsbutdoes primitive,is efficienthandling .4./p>

<p><a id="X829BA50B82FEC109" name=>

<< class< class</><td

<p>The following table gives an overview over the installed methods and their rank =""> =".#">span"63/

<div class="pcenter"><table class="GAPDocTable">
<caption class="GAPDocTable"><b>Table: </b> class="tdleft"><a href="chap6.html#X811FC944788D98396-<s>a>/>
<tr>
<td class="tdleft">3100</td>
<td class class"90/>
<td class="tdleft">go through <td class="tdleft"><code class="code"<code/>
<td="tdleft"><a href".html#X8489BECB78664847"< classRefLink14/></>t>
</tr>
<tr>
<td class="tdleft">1175</td>
<td class="tdleft"><code class="code">KnownStabilizerChain</code></td>
<td class="tdleft">use an already known stabilizer chain for this>
<td class="tdleft"><a << ="X857BF1317CAAF260" ="">/>p
</tr>
<tr>
<td class="tdleft">1100</td>
<tdp>This method unused</>
<td class="tdleft">check
<td class=tdleftchap6#">< class="">6.3-
</tr>
<tr>
<td class="tdleft">1000</td>
<td class="tdleft"><code class="code">ReducibleIso</code></td>
< class"">  MeatAxe  invariant/>
<td class="tdleft"><a href="chap6.html#X811FC944788D9839"><span class="RefLink">6.3-9</span><><a ="X81F74235823352B5"name"/<>
<tr
<tr>
<td class="tdleft">900</td>
java.lang.StringIndexOutOfBoundsException: Range [93, 94) out of bounds for length 62
< ="
<td class="tdleft"><a href="chap6.html#X7A1D99F67E62B1D7">p< ="" ="">a<p
</tr>
</table><br />
</div>

<p><a id="X857BF1317CAAF260" name="X857BF1317CAAF260"></a></p>

<h5>6.3-1 pThis  used matrix/java.lang.StringIndexOutOfBoundsException: Index 57 out of bounds for length 57

<p>This method is unused!</p>

<p>This method is only called when a hint was passedjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

<p>The <5>6.-5 span="Heading"< classcode></code>/span<h5

<can used a method a projectivegroup <var=Arg<varIn case recognition has <code class"">.</code  bound <codeclass></code and  informationis  down image kernel

<p><a id="X81F74235823352B5" name="X81F74235823352B5"></a></p>

<h5<a ="" ="B2C182B7898BC45"<a<p

<p>This method is unused!</p>

<ppThisis  recognizing matrix groups.</p>

<<p>   chain alreadyknownthen kernel given about  stabilizer, the is use methods database . If chain  node known  for computation  a  chain  node  chain   theway abovep

<p><a id="X8795A42285A332BB" name="X8795A42285A332BB"></a></p>

<h5>6.3-3 <span class="Heading"

<p>This method is unused!</p>

<p

<p><a id="X7A9F8CA181F6412D" name="X7A9F8CA181F6412D"></a></p>

<>6- <span=Heading class=">iagonalMatrices/code>

<p>This method is used for recognizing matrix groups

<p>This method is successful if and only if all generators of a matrix

<p><a id="X7A1D99F67E62B1D7" name="X7A1D99F67E62B1D7"></a></p>

<h5>6.3-5 <span class="Heading"><code class="code">GoProjective</code></span>6.39 <pan class"< class""ReducibleIso/>/5

<p>This method is used for recognizing

<p>This method defines a homomorphism from a matrix group <var class="Arg">G</var> into the projective group <var class="Arg">G</var> modulo scalar matrices. In

<p><a id="X7B2C182B7898BC45" name="X7B2C182B7898BC45"></a></p>

<h5>

<p>This method is used for recognizing matrix groups.</p>

<p>If a 

<p><a id="X84E09FCF8527D74A" name="X84E09FCF8527D74A"></a></p>

<h5>6.3-7<h5>6.3-7 

<p>This method is unused!</java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

<p>This method is only called by a hint from <a href="chap6.html#X81F74235823352B5"><span classjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

<p><a id="X8007B3DC787D192C" name="X8007B3DC787D192C"></a></p>

<h5>6.3-8 <span class="Heading"><code class="code">NaturalSL</code></span></h5>

<p>This method is unused!</p>

<p>TODO</p>

<p><a id="X811FC944788D9839" name="X811FC944788D9839

Quelle  chap6.html   Sprache: HTML

 
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<div class="ChapSects"><a href="chap6.html#X78C5295B86AD0C66">6 <span class="Heading">Methods for recognition</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X79A20FD17F834C70">6.1 <span<span>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X78797CF584658CEC">6.1-1 <span class="Heading"><code class="code">FewGensAbelian</code></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7E5E93027A194885">6.1-2 <span class="Heading"><code class="code">KnownNilpotent</code></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X878C1CED8191506C">6.1-3 <span class="Heading"><code class="code">SnAnUnknownDegree</code></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  >
/>
</div></div>
<div>
</span class> /< classnocssnbsp;nbsps><a href=".html#">.-2< classHeading class">Giant/code><>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a/>

<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7F46D8727850585D">6.2-2 <span java.lang.StringIndexOutOfBoundsException: Range [1, 122) out of bounds for length 7
</span>
<span class="
</>
<<>
</span classContSS /span="nocss>nbsp&;/spana "hap6.#X83C651E58239EEAF626<=Heading =">
<span class="ContSS"><br /><span class="nocss"> />
</span
<span class="ContSS"><br /><span class="nocss">  />
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X84C3750C7A4EEC34">6.2-7 <span class="Heading"><code class="code">Pcgs</code></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X82B9AF9F7A904FE5">6.2-8 <span class="Heading"><code class="code">PcgsForBlocks</code></span></a>
java.lang.StringIndexOutOfBoundsException: Range [7, 8) out of bounds for length 7
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X834E9DFF7DC949DE">/>
/>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7DC0B08B7C73A4F9">6.2-10 <span class="Heading"><code class="code">StabilizerChainPerm</code></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X8236A4817FA037E2">6.2-11 <span class="Heading"><code class="code">ThrowAwayFixedPoints</code></span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X829BA50B82FEC109">6.3 <span class="Heading">Methods for>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X857BF1317CAAF260">6.3-1 <span class="Heading"><code class="code">BlockDiagonal</code></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X81F74235823352B5">6.3-2 <span class="Heading"><code class="code">BlockLowerTriangular</code></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X8795A42285A332BB">6.3-3 <span class="Heading"><code class="code">BlockScalar</code></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7A9F8CA181F6412D">6.3-4 <span class="Heading"><code class="code">DiagonalMatrices/>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7A1D99F67E62B1D7">6.3-5 <span class="Heading"><code class="code">GoProjective>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7B2C182B7898BC45">6.3-6 <span class="Heading"><code class="code">KnownStabilizerChain</code></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X84E09FCF8527D74A">6.3-7 <span class="Heading"><code class="code">LowerLeftPGroup</code></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X8007B3DC787D192C">6.3-8 <span class="Heading"><code class="code">NaturalSL</code></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X811FC944788D9839">6.3-9 <span class="Heading"><code class="code">ReducibleIso/span>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X8635737086D48AE5">6.3-10 <span class="Heading"><code class="code">Scalar</code></span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X867550F684F795AE">6.4 <span class="Heading">Methods for projective groups</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X87A53FB6813E2E3C">6.4-1 <span class="Heading"><code class="code">AltSymBBByDegree</code></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7F58277E780EEA2E">6.4-2 <span class="Heading"><code class="code">BiggerScalarsOnly</code></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X863E0A1D7D7FEE04">6.4-3 <span class="Heading"><code class="/>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X84FE699F85371643">6.4-4 <span class="Heading"><code class="code">Blocks</code></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span
<>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X8605DA5E85DFACDC">6.4-6 <span class="Heading"><code class="code">BlocksModScalars</code></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X799F4A7A8239D70F">6.4-7 <span class="Heading"><code class="code">C3C5</code></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7E484B8F83849B49">6.4-8 <span class="Heading"><code class="code">C6</code></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7CE5D3D5876DE816">6.4-9 <span class="Heading"><code class="code">ClassicalNatural</code></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7EC8D0FD7DC6B213">6.4-10 <span class="Heading"><code class="code">ComputeSimpleSocle</code></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X81E155F98671824A">6.4-11 <span class<span
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X878ADA8A7CCE93E0">6.4-12 <span class="Heading"><code class="code">DoBaseChangeForBlocks</code></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7ED3241F84A98292">6.4-13 <span class="Heading"><code class="code">FindElmOfEvenNormal</code></span></a>
</span>
<span class=="">< < class&;&;<span=html>41 span=>code</><span/java.lang.StringIndexOutOfBoundsException: Range [187, 188) out of bounds for length 187
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X8634C79E7DB22934">6.4-15 <span class="Heading"><code class="code">KroneckerProduct</code></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X865D3A1B7B6BB49B">6.4-16 <span class="Heading"><code class="code"code/>
/>
<span>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X82B704EF80AE2FBB">6.4-18 <span class="Heading"><code class="code">NameSporadic/span
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X83E6AD6583DB7080">6.4-19 <span class="Heading"><code class="code">NotAbsolutelyIrred</code/>
</span>
<span >
</>
<span class>
</span>
<span class="ContSS"><br /><span class="nocss">  =ContSS><span="ocss"nbsp;<span =".#X7DE8D77D7D1E19E3">6-5< classHeading class></code><s></a>
</span>
< classContSS">br/642 span="Heading"<code="code>
</span>
<span class="ContSS"><br /><span="ContSect">span="ocline"span=nocss;/>< =".#X7D4A5A9A8266A292"65> /><>
</span
<span
</span
<span class="" name="X79A20FD17F834C70>p>
</span>
/><div
<div class
</span>
</div>
</div>

<h3>6 << ="X78797CF584658CEC" name"777>/>/>

<p><a id="X79A20FD17F834C70" name="X79A20FD17F834C70"></a></p>

<h4Thismethod used recognizingpermutationgroups/

<> following can equally to, and . We not  them  groups, as are to codethat  for of listed.</pjava.lang.StringIndexOutOfBoundsException: Index 231 out of bounds for length 231

<p><a id="X78797CF584658CEC" name="java.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 0

<h5>6.1-1 <span="" ="">/>p

<p>This method is used for recognizing permutation

<p><Thismethod todeterminewhetherthe groupby classArg<var isomorphicto group or group < class"1≤n/> animplementation a=chapBib.#biBJLNP13"[JLNP13</a>./>

<p><a id="X7E5E93027A194885" <>If class="rg>Grp(ri) is permutation group,weassumethatit is primitive and not (a isSnor in natural).

<h5>6.1-2 <span class="Heading"><code class

<p>This method is unused!</p>

<p>Hint to this

<p><a id="X878C1CED8191506C" name="X878C1CED8191506C"></a>java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

ode>

<p>This method is unused!</p>

<p>This  =tdleft0>

<p>If <var class="Arg class=tdleft">  few IsAbelian  yes KnownNilpotent>

<p><a id="X8489BECB78664847" name="X8489BECB78664847"></a></p>

<h5td="tdleft">10<>

<p>This method is used for recognizing permutation, matrix, and projective groups.</p>
< class=tdleft" fewgenerators, and yes
<pThis   if ifgenerators class  the ,   class>   .   is  to trivial such we not takecaseinto in  methodsp>

<p><a id="X829A2F96860513F2" name="X829A2F96860513F2"></a></p>

<h4>6.2 <span class="Heading">Methods for permutation groups</span></<>

<p>The following table gives an overview over the installed methods and their rank (higher rank means higher priority,

< =">ahref=".html>class61->
<caption>
<tr>
<td class="tdleft">1250</td>
<td class="tdleft"><code class="code">FewGensAbelian</code></td>
<td="tdleft> few generators IsAbelianand yes,
<td class="tdleft"><a href="chap6.html#X78797CF584658CEC"><span class="RefLink">6.1-1<d ="tdleft"< ".#X8236A4817FA037E2"< class>.<spana<td
</tr>
<tr>
<td=""150/>
<td class="tdleft"><code td="tdleft">a hrefhtml>span="">6.11/><a>/>
<td>
<td class="tdlefttdclass=tdleft">97<td
<tr
<tr>
< class>0<td
<td class="tdleft"><code class="code">TrivialGroup</code></td>
<t>
<td class="tdleft"><a href="chap6.html#X8489BECB78664847"><span class="RefLink">6.1-4</span></a></td>
</tr>
<tr>
<td class="tdleft">100</td>
<td ="tdleft"< classcode></></td
<td class="tdleft">try to find a huge amount of (possible internal) fixed points="">< =".htmlX804A913E84B77F97"< class.-<><a<>
<td class="tdleft>
</tr>
<tr>
<td class="tdleft">99</td>
<td class="tdleft"><code class="code">FewGensAbelian</code></td>
<td class="tdleft">if very few generators, check IsAbelian and if yes, do KnownNilpotent</td>
<td class="tdleft"><a href="chap6.
</tr>
<tr>
<<d class"dleft"80/td
<td class="td class="tdleftclass"/>td
td" a tojava.lang.StringIndexOutOfBoundsException: Range [66, 42) out of bounds for length 66
<td class="tdleft"><a href>
</tr>
<tr>
<td class="tdleft">95</td>
<td class="tdleft"><code class="code">MovesOnlySmallPoints</code></td>
<td class="tdleft">calculate a stabilizer>
<td class="tdleft"><a href="chap6.html#X804A913E84B77F97"><span class="RefLink">6.2-5</span></a></td>
</tr>
<tr
<td class="tdleft">9td="tdleft"<a href"chap6html#X836212B6818B60FE"><span classRefLink624/></a></djava.lang.StringIndexOutOfBoundsException: Index 101 out of bounds for length 101
<td class="tdleft"><codetd ="tdleft">5/>
<d class">try find non-transitivity restrict to orbit
><code classcode"ReducibleIso/code>

T  used  groups

<p>This method determines

p  this implemented   suchthat canbe as forprojective < class><var that case  node the class=code!projective<code component bound to <code ="keyw>rue/> this informationis passed down and kernel

<p><a id="X8635737086D48AE5" name="X8635737086D48AE5"></a></p>

<h5> ="<=".#848D7F193ERefLink2>/>

<p>This method is unused!</p>

<p>TODO</p>

<p><a id="X867550F684F795AE" name="X867550F684F795AE"></a></p>

> span" projective

<p>The =""> over  with </>

<div class="pcenter"><table class="GAPDocTable">
<caption class="GAPDocTable"><b>Table: </b>Projective group find homomorphism methods</caption>
<tr>
class0>
<td class="tdleft"><code class=td="tdleft">=".html#">span=RefLinkspan<td
<td class="tdleft">go through generators and compare to the identity</td>
<td class="tdleft"><a hreftd="tdleft>00
<>
<tr> =""> over  withdegree
td">30/>
<td class="tdleft"><code class="code">ProjDeterminant</tr
< =">00td>
<td class ="">code=""<>/
<tr
<tr>
<td class="tdleft">1200</td>
<td class="tdleft"><code class="code">ReducibleIso</code></td>
<td="tdleft">se MeatAxeto invariant</td
<dclass>a hrefhtml>spanRefLink.3<span<>
</tr>
<tr>
<td class="tdleft">1100</td
<td class="tdleft"><>
<td class="tdleft">write over a bigger field with smaller degree</td>
<td class="tdleft"><a href="chap6.html#X83E6AD6583DB7080"><span class="RefLink">6.4-19</span></a></td>
</tr>
<tr>
<td class="tdleft">1050</td>
<td class="tdleft"><code class="code">ClassicalNatural</code></td>
< classtdleft whether isclassical  in naturalrepresentationtd
<td class="tdleft"><a href="chap6.html#X7CE5D3D5876DE816"><span class="RefLink">6.4-9</span></a></td>
</tr>
<tr>
<td class="tdleft">1000</td>
<td class="tdleft"><code class="code">Subfield</code></td>
<td class="tdleft">write over a smaller field with same degree</td>
<td class="tdleft"><a href="chap6.html#X7FE1FA217A08DCE5"><span class="RefLink">6.4-24</span></a></td>
</tr>
<tr>
<td class="tdleft">900</td>
<td class="tdleft"><code class="code">C3C5tr
<td class="tdleft">compute a normal subgroup of derived and resolve C3 and C5</td>
<td class="tdleft"><a href="chap6.html#X799F4A7A8239D70F"><span class="RefLink">6.4-7</span></a></td>
</tr>
<tr>
<td class="/
<td class="tdleft"><code class="code">C6</code></tdtd="tdleft"0java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27
t=tdleft".X810B7F36818D626B>span ="RefLink41<span>/>
<td class="tdleft"><a href="chap6.html#X7E484B8F83849B49"><span class="RefLink">6.4-8</span></a></td>
</tr>
<tr>
<td class="tdleft">840</td ="tdleft"<class">ameSporadic/djava.lang.StringIndexOutOfBoundsException: Index 62 out of bounds for length 62
<td class="tdleft"><code class="code">D247</code></td>
<td class
< classtdleft5tjava.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27
>
<tr>
<td class="tdleft">810</td>
<td class="tdleft"><code class="code">AltSymBBByDegree</code></td>
<td class="tdleft">try BB recognition for dim+1 and/or dim+2 if sensible</td>
<td class="tdleft"><a href="chap6.html#X87A53FB6813E2E3C"><span class="
</tr>
<tr>
<td="">80/>
<td class="tdleft"><code class="code">TensorDecomposable</code></td>
<td class="tdleft">find a tensor decomposition</td>
<td class="tdleft"><a href="chap6.html#X7DE8D77D7D1E19E3"><span class="RefLink">6.4-25</span><>
</tr>
<tr
<td class="tdleft">700</td>
<td class="tdleft"><code class="code">FindElmOfEvenNormal</code></td>
td="">find,  or by  of even subgroup>
<td class="tdleft"><a href="chap6.html#X7ED3241F84A98292"><span class="RefLink">6.4-13</span></a></td>
</tr>
<tr>
<td classtdleft0<td
<td class="tdleft"><code class="code">LowIndex</code></td>
<tdtd=""> resort a stabilizerchain(rojectively<td
<td class="tdleft"><a href="chap6.html#X810B7F36818D626B"><spanclass"RefLink">6.4-<s></a>td
<//>br
<>
<td class="tdleft">580</td>
<td class="tdleft"><code class="code">NameSporadic</code></td>
<td class="tdleft">generate maximal orders</td>
<td class="tdleft"><a href="chap6.html#X82B704EF80AE2FBB"><span class="RefLink">6.4-18</span></a></td>
</tr>
<tr>
<td class="tdleft">550</td>
<td<p>Thismethod a black constructive (? recognition alternating  symmetric.</p>
<td class="tdleft">compute simple socle of almost simple group</td>
<td class="tdleft"><a href="chap6.html#X7EC8D0FD7DC6B213"><span class="RefLink">6.4-10</span></a></td>
</tr>
<tr>
<td class="tdleft">500</td>
< classtdleft<code class="code">ThreeLargeElOrders</code></td>
<td class="tdleft">recognise Lie type groups and get its characteristic</td>
<td class="tdleft"><a href="chap6.html#X7A82C26E78FEF78F"><span class="RefLink">6.4-26</span></a></td
</tr>
<tr>
<td
<td class="tdleft"><code class="code">LieTypeNonConstr</code></td>
 =" recognition of groups/>
<td class="tdleft"><a href="chap6.html#X865D3A1B7B6BB49B"><span class=
</tr>
<tr>
<td class="tdleft">100</td>
<td class="tdleft"><code class="code">StabilizerChainProj</code></td>
<td class="tdleft">last resort: compute a stabilizer chain (projectively)</td>
<td class="tdleft"><a href="chap6.html#X7A46A44F867CFB21"><span class="RefLink">6.4-23<
</tr
</table><br />
</div>

<p><a id="X87A53FB6813E2E3C" name="X87A53FB6813E2E3C"></a></p>

<h564-1 <span="Heading"><code class=code"AltSymBBByDegree

<p>This method is used for recognizing projective groups.</p>

<p>This method is a black box constructive (?) recognition of alternating and symmetric groups.</p>

<p>This algorithm is probably based on the paper <a href="chapBib.html#biBBLGN+05">[BLN+05]</a>.</p>

<p><a id="X7F58277E780EEA2E" name="X7F58277E780EEA2E"></a></p>

<h5>6.4-2 <span class="Heading"><code class="code">BiggerScalarsOnly</code></span></h5>

<p>This method is unused!</p>

<p>TODO</p>

<p><a id="X863E0A1D7D7FEE04" name="X863E0A1D7D7FEE04"></a></p< ="" =""<>

<h5>6.4-3 <span class="Heading"><code class="code">BlockScalarProj</code></span></h5

<p>This method is unused!</p>

<p>This method is only called by a hintjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

<p><a id="X84FE699F85371643" name="X84FE699F85371643"></a></p>

<h5>6.4-4 <span class="Heading"><code class="code">Blocks</code></span></h5>

<p>This method is unused!</p>

<p>TODO</p>

<p><a id="X84865B2E87FB00CE" name="X84865B2E87FB00CE"></a></p>

<h5>6.4-5 <span class="Heading"><code class="code">BlocksBackToMats</code></span></h5>

<p>This method is unused!</p>

<p>TODO>

<p><a id="X8605DA5E85DFACDC" name="X8605DA5E85DFACDC"></a></p>

<h5>6.4-6 <span class="Heading"><code class="code">BlocksModScalars</code></span></h5>

<p>This method is unused!</p>

<p>This method is only called when hinted from above. In this method it is understood that G should <em>neither</em> be recognised as a matrix group <em>nor</em> as a projective

<p>This method does the balanced tree approach mapping to subsets of>6.49 < class=Heading"< class"">lassicalNatural/>

<p><a id="X799F4A7A8239D70F" name="X799F4A7A8239D70F"></a></p>

<h5>6.4-7 <span class="Heading"><code class="code">C3C5</code></span></h5>

<p>This method is used<h5>64-0s class =></>>>

<p>TODO</ethod used for projective.</p>

<p><a id="X7E484B8F83849B49"<> methodrandomly the simple socle stores  with information it  forjava.lang.StringIndexOutOfBoundsException: Range [139, 133) out of bounds for length 328

<h5>6.4-8 <span class="Heading"><code class="code">C6</code></span></h5>

<p>This method is used for recognizing projective groups.</p>

<p>This method java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

<p><a id="X7CE5D3D5876DE816" name="X7CE5D3D5876DE816"></a></p>

<h5>6.4-9 <span class="Heading"><code class="code">ClassicalNatural</code>code<spanh5>

<p>This method is used for recognizing projective groups.</p>

<p>TODO</p>

<p><a id="X7EC8D0FD7DC6B213" name="X7EC8D0FD7DC6B213"></a></p>

<h5>6.4-10 <span class="Heading"><code class="code">FindElmOfEvenNormal/code></panh5>

<p> method usedfor projective.</p>

<p>This method randomly computes the

<p><a id="X81E155F98671824A" name="X81E155F98671824A"></a></p>

<h5>6.4-11 <span class="Heading"><code class="code">D247</code></span></h5>

<p>This method is used for recognizing projective groups.</p>

<p>TODO</p>

<p><a id="X878ADA8A7CCE93E0" name="X878ADA8A7CCE93E0"></a></p>

<5>.412 <spanclass="Heading"><codeclasscode>DoBaseChangeForBlocks/code></span/h5>

<pThisunused>

<p>TODO</p>

<p><a id="X7ED3241F84A98292" name="X7ED3241F84A98292"></a></p>

<h5>6.4-13 <span class="Heading"><code class="code">FindElmOfEvenNormal</code></span></h5>

<p>This method is used for recognizing projective groups.</p>

<p>TODO</p>

<p><a id="X7845D88F845EC143" name="X7845D88F845EC143"></a></p>

<h5>6.4-14 <span class="Heading"><code class="code">KroneckerKernel</code></span></h5>

<p>This method is unused!</p>

<p>TODO</p>

<p>a id=" =X8634C79E7DB22934></p

<h5>6.4-15 <span class="Heading"><code class="code">KroneckerProduct</code></span></h5>

>!p

<p>TODO</p>

<p><a id="X865D3A1B7B6BB49B" name="X865D3A1B7B6BB49B"></a></p>

<h5>6.4-16 <span class="Heading"><code class="code">LieTypeNonConstr</code></span></h5>

<p>This method is used for recognizing projective groups.</p>

ml[<a>./p>

<p><a id="X810B7F36818D626B" name="X810B7F36818D626B"></a></p>

<h5>6.4-17 <span class="Heading"><code class="code">LowIndex</code></span></h5>

<p>This method is used for recognizing projective groups.</p>

<p>This method is designed for the handling of the Aschbacher class C2 (stabiliser of a decomposition of the underlying vector space), but may succeed on other types<>The  definesahomomorphism aprojective groupvarclass"G<var< =SimpleMath> PGL(d,)<>tothecyclicgroup span class==SimpleMath>()^/<span where <="D/>   ofspan="SimpleMath>d</>th  in <span class="SimpleMath(q^<span>. The   a group element <span=""> ∈ class=Arg>G/><span>  determinant   representativespanclass="<span,modulo<spanclassSimpleMath"></></p>

<p><a id="X82B704EF80AE2FBB" name="X82B704EF80AE2FBB"></a></p>

<h5>6.4-18 <span class="Heading"><code class="code">NameSporadic</code>

<p>This method is used for recognizing projective groups.</p>

<p>This method returns a list of sporadic simple groups that the group underlying <var class="Arg">ri</var> could be. It does not recognise extensions of sporadic simple groups nor the Monster and the Baby Monster group. It is based on the Magma v2.24.10 function <code 

<p><a id="X83E6AD6583DB7080" name="X83E6AD6583DB7080"></a></p>

<h5>6.4-19 <span class="Heading"><code class="code">NotAbsolutelyIrred</code></span></h5>

<pThis method  used for  <p

<p>If an irreducible projective group <var class="Arg">G</var> acts absolutely irreducibly then this method returns <code class="keyw">NeverApplicable</code>. If <var class="Arg">G</var> is not absolutely irreducible then a homomorphism into a smaller dimensional representation over an extension field is defined. A hint java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

<p><a id="X850864887D7F193E" name="X850864887D7F193E"></a></p>

<h5>6.4-20 <span class="Heading"><code class="code">ProjDeterminant</code></span></h5>

<p>This method is used for recognizing projective groups.</p>

<p>The method defines a homomorphism 

<p><a id="X83288F2279C27632" name="X83288F2279C27632"></a></p>

<h5>6.4-21 <span class="Heading"><code class="code">PrototypeForC2C4</code></span></h5>

<p>This method is unused!</p>

<p>TODO/FIXME: PrototypeForC2C4 is not used anywhere</p>

<p><a id="X7B2111968598599F" name="X7B2111968598599F"></a></p>

<h5>6.4-22 <span class="Heading"><code class="code">SporadicsByOrders</code></span></h5>

<p>This method is unused!</p>

<p>This method returns p>his method currently triesto find  elementsto  ofprimeorder Thisseems to  quite well    tensorfactors are not<></q>toomuchsuch   enough    ordersonbothtensor./>

<p><a 

<h5>6.4-23 <span class="Heading"><code class="code">StabilizerChainProj</code></span></h5>

<>   used forprojective./p>

<p>This method computes a stabiliser chain and a base and strong generating set using projective actions. This is a last resort method since for bigger examples no short orbits can be found in the natural action. The h5642 spanclass""< =>/>

<>< id"X7FE1FA217A08DCE5=X7FE1FA217A08DCE5>/a>/p

<h5>6.4-24 <span class="Heading"><code class="code">Subfield</code></span></h5>

<p>This method is used for recognizing projective groups.</p>

<p>TODO</p>

<p><a id="X7DE8D77D7D1E19E3" name="X7DE8D77D7D1E19E3"></a></p>

<h5>6.4-25 <span class="Heading"><code class="code">TensorDecomposable</code></span></h5>

<p>This method is used for recognizing projective groups.</p>

<p>TODO/FIXME: it is unclear if the following description actually belongs to this method, so be cautious!</p>

<p>This method currently tries to find one tensor factor by powering up commutators of random elements to elements of prime order. This seems to work quite well provided

<p>This method and its description needs some improvement.</p>

<p><a id="X7A82C26E78FEF78F" name="X7A82C26E78FEF78F"></a></p>

<h5>6.4-26 <span class="Heading"><code class="code">ThreeLargeElOrders</code></span></h5>

<p>This method is used for recognizing projective groups.</p>

<p>In the case when the input group <var class="Arg">G</var><span class="SimpleMath">≤ PGL(d,p^e)<td=tdleft"<code class">nAnUnknownDegreecode<tdjava.lang.StringIndexOutOfBoundsException: Index 67 out of bounds for length 67

<p>This method assumes that its input is neither alternating nor sporadic and that <code class="func">ComputeSimpleSocle</code> (<a href="chap6.html#X7EC8D0FD7DC6B213"><span class="RefLink">6.4-10</span></a>) has already been called.</p>

<p>This recognition method is based on the paper <a href="chapBib.html#biBKS09">[KS09]</a>.</p>

<p><a id="X7D4A5A9A8266A292" name="X7D4A5A9A8266A292"></a></p>

<h4>6.5 <span class="Heading">Unused methods</span></h4>

<p>The following table gives an overview overMethodsPerm</code>/td>

<div class="pcenter"><table class="GAPDocTable">
<<
<tr>
<td class="tdleft"><code class="code">KnownNilpotent</code></td>
<td class="tdleft"><code class="code">FindHomMethodsGeneric</code></td>
<td class="tdleft"><a href="chap6.html#X7E5E93027A194885"><span class="RefLink">6.1-2</span></a></td>
</tr>
<tr>
<td class="tdleft"><code class=code"FindHomMethodsMatrix>/>
<td class="tdleft"><code class="code">FindHomMethodsGeneric<dclass=tdleft>ahref"chap6.#X8007B3DC787D192C"><span class"RefLink>.38/><a>/>
<td class="tdleft"><a href="chap6.html#X878C1CED8191506C"><span class="RefLink">6.1-3</span></a></td>
</tr>
<tr>
td="< ="ode></<td
<td class="tdleft"><code tdclass""< href=chap6html>
<td class="tdleft"><a href="chap6.html#X82B9AF9F7A904FE5"><span class="RefLink">6.2-8</span></a></td>
</tr>
<tr>
<td =tdleft"<code ="ode></code<td>
<td class="tdleft"><code class="code">FindHomMethodsPerm</code></td>
<td class="tdleft"><a href="chap6.html#X80320AF97EF01284"><span class="RefLink">6.2-1</span></a></td>
</tr>
<tr>
<td class="tdleft"><code class="code">BlockScalar</code></td>
<td class="tdleft"><code class="code">FindHomMethodsMatrix</code></td>
<td class="tdleft"><a href="java.lang.StringIndexOutOfBoundsException: Range [70, 36) out of bounds for length 70
</tr>
<tr>
<td class="tdleft"><code class="code">NaturalSL</code></td>
<td class="tdleft"><td "tdleft>a>6-1/pan<a>td
<td class="tdleft"><a href="chap6.html#X8007B3DC787D192C"><span class="RefLink">6.3-8</span></a></td>
</tr>
<tr>
<td class="tdleft"><code class="code">Scalar< ""<=#>< ="java.lang.StringIndexOutOfBoundsException: Range [81, 79) out of bounds for length 101
<td class="tdleft"><code class="code">FindHomMethodsMatrix</code></td>
<td class="tdleft"><a href="chap6.td class="tdleft"><code class="code"/<td
</tr>
<tr>
<td class="tdleft"><code class="code">BlockLowerTriangular</code></td>
<td class="tdleft"><code class="code">FindHomMethodsMatrix</code></td>
<td class="tdleft"><a href="chap6.html#X81F74235823352B5"><span class="RefLink">6.3-2</span></a></td>
</tr>
<tr>
<td class="tdleft"><code class="code">BlockDiagonal</code></td>
<td class="tdleft"><code class="code">FindHomMethodsMatrix</code></td>
<td class="tdleft"><a href="chap6.html#X857BF1317CAAF260"><span class="RefLink">6.3-1</span></a></td>
<tr>
tr
 ="< ="code>LowerLeftPGroup</code></d>
<td class="tdleft"><code class="code">FindHomMethodsMatrix</code></td>
<td class="tdleft"><a href="chap6.html#X84E09FCF8527D74A"><span class="RefLink">6.3-7</span></a></td>
</tr>
<tr>
<td class="tdleft"><code class="code">DoBaseChangeForBlocks</code></td>
<td class="tdleft"><code class="code">FindHomMethodsProjective</code></td>
<td class="tdleft"><a href="chap6.html#X878ADA8A7CCE93E0"><span class="RefLink">6.4-12</span></a></td>
</tr>
<tr>
<td class="< ""ahref=chtmlX83288F2279C27632>spanclass"">642<span<a>/>
<td class="tdleft"><code class="code">FindHomMethodsProjective</code></java.lang.StringIndexOutOfBoundsException: Range [0, 73) out of bounds for length 5
<td class="tdleft"><a href="chap6.html#X84FE699F85371643"><span class="RefLink">6.4-4</span></a></td>
</tr>
<tr>
<td class="tdleft"><code class="code">BlocksModScalars</code></td>
<td class="tdleft"><code class="code">FindHomMethodsProjective</code></td>
<td class="tdleft"><a href="chap6.html#X8605DA5E85DFACDC"><<td class=tdleft"<code class=code></>/>
</tr>
<tr>
<td class="tdleft"><code class="code">BlocksBackToMats</code></td>
<td class="tdleft"><code class="code">FindHomMethodsProjective</code></td>
<td class="tdleft"><a href="chap6.html#X84865B2E87FB00CE"><span class="RefLink">6.4-5</span></a></td>
</tr>
<tr>
<td class="tdleft"><code class="code">KroneckerProduct</code></td>
<td class="tdleft"><code class="code">FindHomMethodsProjective</code></td>
<td class="tdleft"java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
</tr>
<tr>
<td class="tdleft"><code class="code">KroneckerKernel</code></td>
<td class="tdleft"><code class="code">FindHomMethodsProjective</code></td>
<td class="tdleft"><a href="chap6.html#X7845D88F845EC143"><span class="RefLink">6.4-14</span></a></td>
</tr>
<tr>
<td class="tdleft"><code class="code">BiggerScalarsOnly</code></td>
<td class="tdleft"><code class="code">FindHomMethodsProjective</code></td>
<td class="tdleft"><a href="chap6.html#X7F58277E780EEA2E"><span class="RefLink">6.4-2</span></a></td>
</tr>
<tr>
<td class="tdleft"><code class="code">PrototypeForC2C4</code></td>
<td class="tdleft"><code class="code">FindHomMethodsProjective</code></td>
<td class="tdleft"><a href="chap6.html#X83288F2279C27632"><span class="RefLink">6.4-21</span></a></td>
</tr>
<tr>
<td class="tdleft"><code class="code">SporadicsByOrders</code></td>
<td class="tdleft"><code class="code">FindHomMethodsProjective</code></td>
<td class="tdleft"><a href="chap6.html#X7B2111968598599F"><span class="RefLink">6.4-22</span></a></td>
</tr>
<tr>
<td class="tdleft"><code class="code">BlockScalarProj</code></td>
<td class="tdleft"><code class="code">FindHomMethodsProjective</code></td>
<td class="tdleft"><a href="chap6.html#X863E0A1D7D7FEE04"><span class="RefLink">6.4-3</span></a></td>
</tr>
</table><br />
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bsp;its description needs some improvement.</p>

<p><a id="X7A82C26E78FEF78F" name="X7A82C26E78FEF78F"></a><pThismethodisused for recognizing  groups</java.lang.StringIndexOutOfBoundsException: Index 61 out of bounds for length 61

<>.-6< =Heading">codeclass"code">ThreeLargeElOrders</code></span><h5

<p>This method is used for recognizing projective groupsp><a id="" name""<a<p>

<p>In the case when the input group <var class="Arg">G</var><span class="SimpleMath">≤ PGL(d,p^e)</

<p>This method assumes that its input is neither alternating nor sporadic and that <code class="func">ComputeSimpleSocle</code> (<a href="chap6.html#X7EC8D0FD7DC6B213"><span class="RefLink">6.4-10</span></a>) has already been called.</p>

<p>This recognition method is based on the paper <a href="chapBib.html#biBKS09">[KS09]</a>.</p>

<p><a id="java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 0

<h4>6.5 <span class="Heading">Unused methods</span></h4>

<p>The following table gives an overview over the methods which are currently unused.</p>

<div class="pcenter"><table class="GAPDocTable">
<caption class="GAPDocTable"java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<tr>
<td class="tdleft"><code class="code">KnownNilpotent</code></td>
<td class="tdleft"><code class="code">FindHomMethodsGeneric</code></td>
<td class="tdleft"><a href="chap6.html#X7E5E93027A194885"><span class="RefLink">6.1-2</span></a></td>
</tr>
<tr>
<td class="> class=code"></code>/td>
<td class="tdleft"><code class="code">FindHomMethodsGeneric</code></td>
<td class="tdleft"><a href="chap6.html#X878C1CED8191506C"><span class="RefLink">6.1-3</span></a></td>
</tr>
<tr>
<td class="tdleft"><code class="code">PcgsForBlocks</code></td>
<td class="tdleft"><code class="code">FindHomMethodsPerm</code></td>
<td class="tdleft"><a href="chap6.html#X82B9AF9F7A904FE5"><span class="RefLink">6.2-8</span></a></td>
</tr>
<tr>
<td class="tdleft"><code class="code">BalTreeForBlocks</code></td>
/<td>
<td class="tdleft"><a href="chap6.html#X80320AF97EF01284"><span class="RefLink">6.2-1</span></a></td>
</tr>
<tr>
<td class="tdleft"><code class="code">BlockScalar</code></td>
<td class="tdleft"><code class="code">FindHomMethodsMatrix</code></td>
<td class="tdleft"><a href="chap6.html#X8795A42285A332BB"><span class="RefLink">6.3-3</span></a></td>
</tr>
<tr>
<td class="tdleft"><code class="code">NaturalSL</code></td>
 tdleft=""></code>td>
< ""< =chap6htmlX8007B3DC787D192C<span =RefLink"6.3<span>/<tdjava.lang.StringIndexOutOfBoundsException: Index 101 out of bounds for length 101
</tr>
<tr>
<td class="tdleft"><code class="code">Scalar</code></td>
<td class="tdleft"><code class=<td class="tdleft>code class="ode"PcgsForBlockscode>/>
< =tdleft>a ="chap6.#X8635737086D48AE5"><span class="RefLink">6.3-10</span></a></td>
</tr>
<tr>
<td class="tdleft"><code class="code">BlockLowerTriangular</code></td>
<td class="tdleft"><code class="code">FindHomMethodsMatrix</code></td>
<td class="tdleft"><a href="chap6class">< class"ode"BalTreeForBlocks>/td
</tr>
<tr>
<td class="tdleft"><code class="code">BlockDiagonal</code></td>
<td class="tdleft"><code class="code">FindHomMethodsMatrix</code></td>
<td class="tdleft"><a href="chap6.html#X857BF1317CAAF260"><span class="RefLink">6.3-1</span></a></td>
</tr>
<tr>
<td class="tdleft"><code class="code">LowerLeftPGroup</code></td>
<td class="tdleft"><code class="code">FindHomMethodsMatrix</code></td>
<td class="tdleft"><a href="chap6.html#X84E09FCF8527D74A"><span class="RefLink">6.3-7</span></a></td>
</tr>
<tr>
<td class="tdleft"><code class="code">DoBaseChangeForBlocks</code></td>
<td class="tdleft"><code class="code">FindHomMethodsProjective</code></td>
<td class="tdleft"< href="chap6.html#X878ADA8A7CCE93E0"><span class="RefLink">.41</pan></a>/td>
</tr>
<tr>
<td class="tdleft"><code class="code">Blocks</code></td>
<td class="tdleft"><code class="code">FindHomMethodsProjective</code></td>
<d class=tdleft>a href"chap6.htmlX84FE699F85371643"<panclass"efLink">6.4-4</span></a></td>
</tr>
<tr>
<td class="tdleft"><code class="code">BlocksModScalars</code></td>
<>FindHomMethodsProjective<code>/>
<td class="tdleft"><a href="chap6.html#X8605DA5E85DFACDC"><span class="RefLink">6.4-6</span></a></td>
</tr>
<tr>
<td class="tdleft"><code class="code">BlocksBackToMats</code></td>
<td class="tdleft"><code class="code">FindHomMethodsProjective</code></td>
<td class="tdleft"><a href="chap6.html#X84865B2E87FB00CE"><span class="RefLink">6.4-5</span></a></td>
</tr>
<tr>
<td class="tdleft"><code class="code">KroneckerProduct</code></td>
<td class="tdleft"><code class="code">FindHomMethodsProjective</code></td>
<td class="tdleft"><a href="chap6.html#X8634C79E7DB22934"><span class="RefLink">6.4-15</span></a></td>
</tr>
<tr>
<tr
<td class="tdleft"><code<>
<td class="tdleft"><a href="chap6.html#X7845D88F845EC143"><span class="RefLink">6.4-<tdclass=tdleft>code class"LowerLeftPGroupcode</d
</tr>
<tr>
<td class="tdleft"><code class="code">BiggerScalarsOnly</code></td>
<td class="tdleft"><code class="code">FindHomMethodsProjective</code></td>
<td class="tdleft"><a href="chap6.html#X7F58277E780EEA2E"><span class="RefLink">6.4-2</span></a></td>
</tr>
<tr>
<td class="tdleft"><code class="code">PrototypeForC2C4</code></td>
<td class="tdleft"><code class="code">FindHomMethodsProjective</code></td>
<d class=tdleft"< href="hap6.#X83288F2279C27632"< =RefLink>.-1/span>/a>td>
</tr>
<tr>
<td class="tdleft"><code class="code">SporadicsByOrders</code></td>
<td class="tdleft"><code class="code">FindHomMethodsProjective</code></td>
<td class="tdleft"><a href="chap6.html#X7B2111968598599F"><span class="RefLink">6.4-22</span></a></td>
</tr>
<tr>
td=>code="">BlockScalarProjcode<td
<td class="tdleft"><code class="code">FindHomMethodsProjective</code></td>
<td class="tdleft"><a href="chap6.html#X863E0A1D7D7FEE04"><span class="RefLink">6.4-3</span></a></td>
</tr>
</table><br />
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