<!-- $Id: mip.xml,v 1.4 2006/07/11 10:35:48 alexk Exp $ --> <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[ ]]> </Example> <ManSection> <Attr Name="JenningsFactors" Arg="G" /> <Returns> list of lists of IdGroup </Returns> <Description> ??????????????????????????????????? </Description> </ManSection> <Example> <![CDATA[ ]]> </Example> <ManSection> <Attr Name="NumberOfConjugacyClassesPPowers" Arg="G" /> <Returns> list of integers </Returns> <Description> ??????????????????????????????????? </Description> </ManSection> <Example> <![CDATA[ ]]> </Example> <ManSection> <Attr Name="ClassSumNumbers" Arg="G" /> <Returns> list of integers </Returns> <Description> ??????????????????????????????????? </Description> </ManSection> <Example> <![CDATA[ ]]> </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>