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<h1>recog</h1>
<h2>A package for constructive recognition of permutation and matrix groups</h2>
<p>
1 .4 .4 </p>
<p>
22 January 2025
</p>
</div>
<p><b>
Max Neunhöffer
</b>
<br />Email: <span class="URL"><a href="mailto:max@9 hoeffer.de">max@9 hoeffer.de</a></span>
</p><p><b>
Ákos Seress
</b>
</p>
<p><a id="X81488B807F2A1CF1" name="X81488B807F2A1CF1"></a></p>
<h3>Copyright</h3>
<p>© 2005 -2014 by Max Neunhöffer and Ákos Seress</p>
<p>© 2005 -2022 by its authors, see file <code class="file">COPYRIGHT</code> for details.</p>
<p>This package may be distributed under the terms and conditions of the GNU Public License Version 3 or (at your option) any later version.</p>
<p><a id="X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8"></a></p>
<div class="contents">
<h3>Contents<a id="contents" name="contents"></a></h3>
<div class="ContChap"><a href="chap1_mj.html#X7DFB63A97E67C0A1">1 <span class="Heading">Introduction</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X873C99678745ABAF">1 .1 <span class="Heading">Philosophy</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X786BACDB82918A65">1 .2 <span class="Heading">Overview over this manual</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X828241117D993F36">1 .3 <span class="Heading">Feedback and support</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X804FB63186BEBD38">1 .4 <span class="Heading">Literature (temporary)</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap2_mj.html#X7AA0519A7CFE18C2">2 <span class="Heading">Installation of the <strong class="pkg">recog</strong> package</span></a>
</div>
<div class="ContChap"><a href="chap3_mj.html#X7F73983582251807">3 <span class="Heading">Group recognition</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X81E31E377B16CF39">3 .1 <span class="Heading">The recursive procedure</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X7BFEB34483548A89">3 .1 -1 RecogniseGeneric</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X84338F037B91CDD0">3 .1 -2 RecognisePermGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X788DCF6A7D9E80BD">3 .1 -3 RecogniseMatrixGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X841176DD7BA1CAA0">3 .1 -4 RecogniseProjectiveGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X853B4EE27AF57CD3">3 .1 -5 RecogniseGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X7AD4A7168016DF8F">3 .1 -6 TryFindHomMethod</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X83A18ADB8207154F">3 .2 <span class="Heading">Recognition nodes</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X7D2B419B83CD3BF8">3 .2 -1 RecogNodeFamily</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X801C44668004C0A0">3 .2 -2 IsRecogNode</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X8408B8B286312375
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X8469BB658377FD92">3 .2 -4 IsLeaf</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X7D6CEF0178ED73A7">3 .2 -5 IsReady</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X7972380780D99B04">3 .2 -6 Grp</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X8273C2FC79FB6543">3 .2 -7 Homom</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X864194958685AAD7">3 .2 -8 NiceGens</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X808A01AA869115EC">3 .2 -9 pregensfac</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X78DE5A1782456494">3 .2 -10 ImageRecogNode</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X7DE53FAA782440B2">3 .2 -11 KernelRecogNode</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X83BA3AE582319312">3 .2 -12 ParentRecogNode</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X7ACD6B4C7982B1E3">3 .2 -13 fhmethsel</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X83167779869A3BF5">3 .2 -14 slpforelement</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X83167779869A3BF5">3 .2 -15 SLPforElement</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X7FBE4706828964EB">3 .2 -16 StdPresentation</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X82F234BC853D1323">3 .2 -17 methodsforimage</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X7FEEE37F858F614B">3 .2 -18 validatehomominput</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X7FEEE37F858F614B">3 .2 -19 ValidateHomomInput</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X7EFA298E7E4760A0">3 .2 -20 calcnicegens</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X78B05A1E78564BBF">3 .2 -21 CalcNiceGensGeneric</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X80444E4E8501D0B0">3 .2 -22 CalcNiceGensHomNode</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X7EFA298E7E4760A0">3 .2 -23 CalcNiceGens</a></span>
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X80C2451F805CA06D" >3 .2 -24 slptonice</a ></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7B7E9EAC7AACF8D8" >3 .2 -25 gensN</a ></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X81644C3A8064063F" >3 .2 -26 findgensNmeth</a ></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7DC1D16F807D6895" >3 .2 -27 FindKernelRandom</a ></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X8244F0DE86C23ECA" >3 .2 -28 FindKernelDoNothing</a ></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X87E8AB1B78F60112" >3 .2 -29 FindKernelFastNormalClosure</a ></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X82154EA88011654F" >3 .2 -30 gensNslp</a ></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X86A101E17F87F01F" >3 .2 -31 immediateverification</a ></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X868D75F87B0F33C5" >3 .2 -32 InitialDataForKernelRecogNode</a ></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X86F6DB9482B4D8AC" >3 .2 -33 InitialDataForImageRecogNode</a ></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X814D78347858EC13" >3 .2 -34 isone</a ></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7D0F06047B88E5CD" >3 .2 -35 isequal</a ></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X860CF50D80A4215A" >3 .2 -36 OrderFunc</a ></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7EBE1C5D7C99FA2F" >3 .2 -37 <span class="Heading" >Other components of recognition nodes</span ></a >
</span >
</div ></div >
<div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X8577717D85D631C2" >3 .3 <span class="Heading" >Methods to find homomorphisms</span ></a >
</span >
<div class="ContSSBlock" >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7FCBB7C686D0B1DF" >3 .3 -1 FindHomomorphism</a ></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7F299344834AAB6E" >3 .3 -2 SLPforElementGeneric</a ></span >
</div ></div >
</div >
<div class="ContChap" ><a href="chap4_mj.html#X8058CC8187162644" >4 <span class="Heading" >Method selection</span ></a >
<div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4_mj.html#X7F89FF55818F1139" >4 .1 <span class="Heading" >What are methods?</span ></a >
</span >
<div class="ContSSBlock" >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X80EC4782856AAD35" >4 .1 -1 IsRecogMethod</a ></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7E18720E87B4B2DE" >4 .1 -2 RecogMethod</a ></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X87AA2A587E4E00C2" >4 .1 -3 BindRecogMethod</a ></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7EF3EAEF78786349" >4 .1 -4 Stamp</a ></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7A2F979E86F77A6F" >4 .1 -5 Comment</a ></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X79650A3E79D0E4A3" >4 .1 -6 CallRecogMethod</a ></span >
</div ></div >
<div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4_mj.html#X854385507D03A016" >4 .2 <span class="Heading" >Method Databases</span ></a >
</span >
<div class="ContSSBlock" >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X845DB71C806CADDC" >4 .2 -1 AddMethod</a ></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X836B50947A46B1A5" >4 .2 -2 FindHomDbPerm</a ></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7CA5F5FA7E850885" >4 .2 -3 FindHomDbMatrix</a ></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7A4F8342854507E3" >4 .2 -4 FindHomDbProjective</a ></span >
</div ></div >
<div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4_mj.html#X83FCCBCA78F608E1" >4 .3 <span class="Heading" >How methods are called</span ></a >
</span >
<div class="ContSSBlock" >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7BC2692183B6C4E6" >4 .3 -1 CallMethods</a ></span >
</div ></div >
<div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4_mj.html#X852A8E538590BCF3" >4 .4 <span class="Heading" >Global records storing functions</span ></a >
</span >
<div class="ContSSBlock" >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7A94720080D344DA" >4 .4 -1 FindHomMethodsPerm</a ></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X79B60CEF8292F142" >4 .4 -2 FindHomMethodsMatrix</a ></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7D796A2179E9026A" >4 .4 -3 FindHomMethodsProjective</a ></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X78B948847D596167" >4 .4 -4 FindHomMethodsGeneric</a ></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7B5561D187242287" >4 .4 -5 SLPforElementFuncsPerm</a ></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7A2E7DF67F4949C8" >4 .4 -6 SLPforElementFuncsMatrix</a ></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7F6FCC4F81ACF20F" >4 .4 -7 SLPforElementFuncsProjective</a ></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X795ACFD386A106B8" >4 .4 -8 SLPforElementFuncsGeneric</a ></span >
</div ></div >
</div >
<div class="ContChap" ><a href="chap5_mj.html#X851A3F04786123D5" >5 <span class="Heading" >After successful recognition</span ></a >
<div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5_mj.html#X80EB3C7481C63B7F" >5 .1 <span class="Heading" >Functions and methods for recognition nodes</span ></a >
</span >
<div class="ContSSBlock" >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X82F5B37186B949BF" >5 .1 -1 SLPforNiceGens</a ></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X87BDB89B7AAFE8AD" ><code >5 .1 -2 \in</code ></a ></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X858ADA3B7A684421" >5 .1 -3 Size</a ></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X80FFBDCD816690E3" >5 .1 -4 DisplayCompositionFactors</a ></span >
</div ></div >
</div >
<div class="ContChap" ><a href="chap6_mj.html#X78C5295B86AD0C66" >6 <span class="Heading" >Methods for recognition</span ></a >
<div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap6_mj.html#X79A20FD17F834C70" >6 .1 <span class="Heading" >Methods for generic groups</span ></a >
</span >
<div class="ContSSBlock" >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.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_mj.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_mj.html#X878C1CED8191506C" >6 .1 -3 <span class="Heading" ><code class="code" >SnAnUnknownDegree</code ></span ></a >
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X8489BECB78664847" >6 .1 -4 <span class="Heading" ><code class="code" >TrivialGroup</code ></span ></a >
</span >
</div ></div >
<div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap6_mj.html#X829A2F96860513F2" >6 .2 <span class="Heading" >Methods for permutation groups</span ></a >
</span >
<div class="ContSSBlock" >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X80320AF97EF01284" >6 .2 -1 <span class="Heading" ><code class="code" >BalTreeForBlocks</code ></span ></a >
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7F46D8727850585D" >6 .2 -2 <span class="Heading" ><code class="code" >Giant</code ></span ></a >
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X8757E1C37F03A49D" >6 .2 -3 <span class="Heading" ><code class="code" >Imprimitive</code ></span ></a >
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X836212B6818B60FE" >6 .2 -4 <span class="Heading" ><code class="code" >LargeBasePrimitive</code ></span ></a >
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X804A913E84B77F97" >6 .2 -5 <span class="Heading" ><code class="code" >MovesOnlySmallPoints</code ></span ></a >
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X83C651E58239EEAF" >6 .2 -6 <span class="Heading" ><code class="code" >NonTransitive</code ></span ></a >
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.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_mj.html#X82B9AF9F7A904FE5" >6 .2 -8 <span class="Heading" ><code class="code" >PcgsForBlocks</code ></span ></a >
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X834E9DFF7DC949DE" >6 .2 -9 <span class="Heading" ><code class="code" >StabChain</code ></span ></a >
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.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_mj.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_mj.html#X829BA50B82FEC109" >6 .3 <span class="Heading" >Methods for matrix groups</span ></a >
</span >
<div class="ContSSBlock" >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.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_mj.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_mj.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_mj.html#X7A9F8CA181F6412D" >6 .3 -4 <span class="Heading" ><code class="code" >DiagonalMatrices</code ></span ></a >
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7A1D99F67E62B1D7" >6 .3 -5 <span class="Heading" ><code class="code" >GoProjective</code ></span ></a >
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.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_mj.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_mj.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_mj.html#X811FC944788D9839" >6 .3 -9 <span class="Heading" ><code class="code" >ReducibleIso</code ></span ></a >
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.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_mj.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_mj.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_mj.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_mj.html#X863E0A1D7D7FEE04" >6 .4 -3 <span class="Heading" ><code class="code" >BlockScalarProj</code ></span ></a >
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X84FE699F85371643" >6 .4 -4 <span class="Heading" ><code class="code" >Blocks</code ></span ></a >
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X84865B2E87FB00CE" >6 .4 -5 <span class="Heading" ><code class="code" >BlocksBackToMats</code ></span ></a >
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.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_mj.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_mj.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_mj.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_mj.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_mj.html#X81E155F98671824A" >6 .4 -11 <span class="Heading" ><code class="code" >D247</code ></span ></a >
</span >
<java.lang.StringIndexOutOfBoundsException: Range [19, 5) out of bounds for length 195
</span >
<span class"java.lang.StringIndexOutOfBoundsException: Range [20, 19) out of bounds for length 193
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7845D88F845EC143" >6 .4 -14 <span class="Heading" ><code class="code" >KroneckerKernel</code ></span ></a >
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.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_mj.html#X865D3A1B7B6BB49B" >6 .4 -16 <span class="Heading" ><code class="code" >LieTypeNonConstr</code ></span ></a >
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X810B7F36818D626B" >6 .4 -17 <span class="Heading" ><code class="code" >LowIndex</code ></span ></a >
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X82B704EF80AE2FBB" >6 .4 -18 <span class="Heading" ><code class="code" >NameSporadic</code ></span ></a >
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#java.lang.StringIndexOutOfBoundsException: Index 100 out of bounds for length 7
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X850864887D7F193E" >6 .4 -20 <span class="Heading" ><code class="code" >java.lang.StringIndexOutOfBoundsException: Index 162 out of bounds for length 7
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<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X83288F2279C27632" >6 .4 -21 <span class="Heading" ><code class="code" >PrototypeForC2C4</code /span
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7B2111968598599F" >6 .4 -22 <span class="Heading" ><code class
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7A46A44F867CFB21" >6 .4 -23 <span class="Heading" ><code class>
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7FE1FA217A08DCE5" >6 .4 -24 <span class="Heading" ><code class="code" >Subfield</code ></span ></a >
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7DE8D77D7D1E19E3" >6 .4 -25 <span class="Heading" ><code class="code</span>
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7A82C26E78FEF78F" >6 .4 -26 <span class="Heading" ><code class="code" >ThreeLargeElOrders</java.lang.StringIndexOutOfBoundsException: Range [1, 180) out of bounds for length 7
</span >
</div ></div >
<div class="ContSect" ><span <div class="ContSect"><span class"" >&bsp<spana =c.htmlX7FE1FA217A08DCE5>6 .-4 <span class="<code class" "Subfield/code<span</java.lang.StringIndexOutOfBoundsException: Index 182 out of bounds for length 182
</span >
</div >
</div >
<div class="ContChap" ><a href="chap7_mj.html#X7A489A5D79DA9E5C" >7 <span class="Heading" >Examples<span >
java.lang.StringIndexOutOfBoundsException: Range [53, 54) out of bounds for length 6
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