<Chapter Label="MIP">
<Heading>The Modular Isomorphism Problem</Heading>

<Section Label="MIPTheory">
<Heading>Known results on MIP</Heading>

???????????????????????????????????<P/>

</Section>

<!-- ######################################################### -->

<Section Label="MIPInvariants">
<Heading>Invariants determined by group algebras</Heading>

<ManSection>
   <Attr Name="SandlingFactorGroup" 
         Arg="G" />  
   <Returns>
         factorgroup
   </Returns>
   <Description>
         ???????????????????????????????????
   </Description>
</ManSection>

<Example>
<![CDATA[
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</Example>

<ManSection>
   <Attr Name="JenningsFactors" 
         Arg="G" />  
   <Returns>
         list of lists of IdGroup
   </Returns>
   <Description>
         ???????????????????????????????????
   </Description>
</ManSection>

<Example>
<![CDATA[
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</Example>


<ManSection>
   <Attr Name="NumberOfConjugacyClassesPPowers" 
         Arg="G" />  
   <Returns>
         list of integers
   </Returns>
   <Description>
         ???????????????????????????????????
   </Description>
</ManSection>

<Example>
<![CDATA[
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</Example>


<ManSection>
   <Attr Name="ClassSumNumbers" 
         Arg="G" />  
   <Returns>
         list of integers
   </Returns>
   <Description>
         ???????????????????????????????????
   </Description>
</ManSection>

<Example>
<![CDATA[
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</Example>


<ManSection>
   <Attr Name="QuillenSeries" 
         Arg="G" />  
   <Returns>
         list of integers
   </Returns>
   <Description>
         ???????????????????????????????????
   </Description>
</ManSection>

<Example>
<![CDATA[
]]>
</Example>


<ManSection>
   <Attr Name="RoggenkampParameter" 
         Arg="G" />  
   <Returns>
         integer 
   </Returns>
   <Description>
         ???????????????????????????????????
   </Description>
</ManSection>

<Example>
<![CDATA[
]]>
</Example>


<ManSection>
   <Func Name="RoggenkampParameterForNormalSubset" 
         Arg="G S" />  
   <Returns>
         integer 
   </Returns>
   <Description>
         ???????????????????????????????????
   </Description>
</ManSection>

<Example>
<![CDATA[
]]>
</Example>


<ManSection>
   <Attr Name="KernelSize" 
         Arg="FG [n,m,k]" />  
   <Returns>
         integer or fail
   </Returns>
   <Description>
         ???????????????????????????????????
   </Description>
</ManSection>

<Example>
<![CDATA[
]]>
</Example>

</Section>

<!-- ######################################################### -->

<Section Label="MIPTools">
<Heading>MIP testing tools</Heading>

<ManSection>
   <Func Name="PrintMIPInvariants" 
         Arg="G" />  
   <Description>
         ???????????????????????????????????
   </Description>
</ManSection>

<Example>
<![CDATA[
]]>
</Example>


<ManSection>
   <Func Name="PrintMIPInvariantsTable" 
         Arg="list filename" />  
   <Returns>
         text file generated in the current directory
   </Returns>
   <Description>
         ???????????????????????????????????
   </Description>
</ManSection>

<Example>
<![CDATA[
]]>
</Example>


<ManSection>
   <Func Name="MIPInvariantsRecord" 
         Arg="G" />  
   <Returns>
         record
   </Returns>
   <Description>
         ???????????????????????????????????
   </Description>
</ManSection>

<Example>
<![CDATA[
]]>
</Example>


<ManSection>
   <Func Name="MIPInvariantsLibrary" 
         Arg="n" />  
   <Returns>
         text file generated in the current directory
   </Returns>
   <Description>
         ???????????????????????????????????
   </Description>
</ManSection>

<Example>
<![CDATA[
]]>
</Example>


<ManSection>
   <Func Name="MIPInvariantsLibraryClassification" 
         Arg="invlib mode" />  
   <Returns>
         list of lists and (optionally) a text file 
         generated in the current directory
   </Returns>
   <Description>
         ???????????????????????????????????
   </Description>
</ManSection>

<Example>
<![CDATA[
]]>
</Example>


<ManSection>
   <Func Name="KernelSizeTest" 
         Arg="FG FH" />  
   <Returns>
         a list of parameters and kernel sizes or fail
   </Returns>
   <Description>
         ???????????????????????????????????
   </Description>
</ManSection>

<Example>
<![CDATA[
]]>
</Example>


<ManSection>
   <Func Name="JenningsLieAlgebraTest" 
         Arg="FG FH" />  
   <Returns>
         true or false
   </Returns>
   <Description>
         ???????????????????????????????????
   </Description>
</ManSection>

<Example>
<![CDATA[
]]>
</Example>


<ManSection>
   <Func Name="MIPSplittingByKernelSize" 
         Arg="list no mode" />  
   <Returns>
         text file generated in the current directory
   </Returns>
   <Description>

         ???????????????????????????????????
   </Description>
</ManSection>

<Example>
<![CDATA[
]]>
</Example>


<ManSection>
   <Func Name="MIPSplittingByJenningsLieAlgebra" 
         Arg="list no mode" />  
   <Returns>
         text file generated in the current directory
   </Returns>
   <Description>

         ???????????????????????????????????
   </Description>
</ManSection>

<Example>
<![CDATA[
]]>
</Example>

<ManSection>
   <Func Name="MIPSplittingReport" 
         Arg="list" />  
   <Description>
         ???????????????????????????????????
   </Description>
</ManSection>

<Example>
<![CDATA[
]]>
</Example>

</Section>

</Chapter>
