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<html><head><title>IRREDSOL : a GAP 4 package - Index </title></head>
<body text="#000000" bgcolor="#ffffff">
<h1><font face="Gill Sans,Helvetica,Arial">IRREDSOL</font> : a <font face="Gill Sans,Helvetica,Arial">GAP</font> 4 package - Index </h1>
<p>
<a href="#idxA">A</A>
<a href="#idxB">B</A>
<a href="#idxC">C</A>
<a href="#idxD">D</A>
<a href="#idxF">F</A>
<a href="#idxG">G</A>
<a href="#idxI">I</A>
<a href="#idxL">L</A>
<a href="#idxM">M</A>
<a href="#idxO">O</A>
<a href="#idxP">P</A>
<a href="#idxR">R</A>
<a href="#idxS">S</A>
<a href="#idxT">T</A>
<a href="#idxU">U</A>
<a href="#idxV">V</A>
<a href="#idxW">W</A>
<H2><A NAME="idxA">A</A></H2>
<dl>
<dt>AbsolutelyIrreducibleSolubleMatrixGroup <a href="CHAP002.htm#SSEC002.6">2.2.6</a> 
<dt>Accessing the data library <a href="CHAP002.htm">2.0</a> 
<dt>Additional functionality for matrix groups <a href="CHAP004.htm">4.0</a> 
<dt>AllIrredSolMatGroups <a href="CHAP002.htm#SSEC003.1">2.3.1</a> 
<dt>AllIrreducibleSolubleMatrixGroups <a href="CHAP002.htm#SSEC003.1">2.3.1</a> 
<dt>AllIrreducibleSolvableMatrixGroups <a href="CHAP002.htm#SSEC003.1">2.3.1</a> 
<dt>AllPrimitivePcGroups <a href="CHAP005.htm#SSEC002.1">5.2.1</a> 
<dt>AllPrimitiveSolublePermGroups <a href="CHAP005.htm#SSEC003.1">5.3.1</a> 
<dt>AllPrimitiveSolublePermutationGroups <a href="CHAP005.htm#SSEC005.1">5.5.1</a> 
<dt>AllPrimitiveSolvablePermGroups <a href="CHAP005.htm#SSEC003.1">5.3.1</a> 
<dt>AllPrimitiveSolvablePermutationGroups <a href="CHAP005.htm#SSEC005.1">5.5.1</a> 
<dt>attributes, basic, for matrix groups <a href="CHAP004.htm#I0">4.1</a> 
</dl><p>
<H2><A NAME="idxB">B</A></H2>
<dl>
<dt>Basic attributes for matrix groups <a href="CHAP004.htm#SECT001">4.1</a> 
</dl><p>
<H2><A NAME="idxC">C</A></H2>
<dl>
<dt>Characteristic, for matrix groups <a href="CHAP004.htm#SSEC001.5">4.1.5</a> 
<dt>CharacteristicOfField <a href="CHAP004.htm#SSEC001.5">4.1.5</a> 
<dt>Compatibility with other data libraries <a href="CHAP003.htm#SECT002">3.2</a> 
<dt>compatibility, with other data libraries <a href="CHAP003.htm#I2">3.2</a> 
<dt>Conjugating matrix groups into smaller fields <a href="CHAP004.htm#SECT004">4.4</a> 
<dt>ConjugatingMatTraceField <a href="CHAP004.htm#SSEC004.2">4.4.2</a> 
<dt>Converting between irreducible soluble matrix groups and primitive soluble groups <a href="CHAP005.htm#SECT001">5.1</a> 
</dl><p>
<H2><A NAME="idxD">D</A></H2>
<dl>
<dt>DefaultFieldOfMatrixGroup <a href="CHAP004.htm#SSEC001.3">4.1.3</a> 
<dt>Degree, for matrix groups <a href="CHAP004.htm#SSEC001.1">4.1.1</a> 
<dt>DegreeOfMatrixGroup <a href="CHAP004.htm#SSEC001.1">4.1.1</a> 
<dt>Design of the group library <a href="CHAP002.htm#SECT001">2.1</a> 
<dt>Dimension, for matrix groups <a href="CHAP004.htm#SSEC001.1">4.1.1</a> 
<dt>DimensionOfMatrixGroup <a href="CHAP004.htm#SSEC001.1">4.1.1</a> 
</dl><p>
<H2><A NAME="idxF">F</A></H2>
<dl>
<dt>FieldOfMatrixGroup <a href="CHAP004.htm#SSEC001.2">4.1.2</a> 
<dt>find, matrix group <a href="CHAP002.htm#I2">2.3</a> 
<dt>find, primitive pc group <a href="CHAP005.htm#I4">5.2</a> 
<dt>find, primitive permutation group <a href="CHAP005.htm#I6">5.3</a> 
<dt>Finding matrix groups with given properties <a href="CHAP002.htm#SECT003">2.3</a> 
<dt>Finding primitive pc groups with given properties <a href="CHAP005.htm#SECT002">5.2</a> 
<dt>Finding primitive soluble permutation groups with given properties <a href="CHAP005.htm#SECT003">5.3</a> 
</dl><p>
<H2><A NAME="idxG">G</A></H2>
<dl>
<dt>group, primitive soluble <a href="CHAP005.htm#I2">5.0</a> 
</dl><p>
<H2><A NAME="idxI">I</A></H2>
<dl>
<dt>IdAbsolutelyIrreducibleSolubleMatrixGroup <a href="CHAP003.htm#SSEC001.5">3.1.5</a> 
<dt>IdAbsolutelyIrreducibleSolvableMatrixGroup <a href="CHAP003.htm#SSEC001.5">3.1.5</a> 
<dt>Identification of irreducible groups <a href="CHAP003.htm#SECT001">3.1</a> 
<dt>identification, of matrix groups <a href="CHAP003.htm#I1">3.0</a> 
<dt>identification, of primitive pc group <a href="CHAP005.htm#I8">5.4</a> 
<dt>identification, of primitive permutation group <a href="CHAP005.htm#I9">5.4</a> 
<dt>IdIrreducibleSolubleMatrixGroup <a href="CHAP003.htm#SSEC001.3">3.1.3</a> 
<dt>IdIrreducibleSolubleMatrixGroupIndexMS <a href="CHAP003.htm#SSEC002.1">3.2.1</a> 
<dt>IdIrreducibleSolvableMatrixGroup <a href="CHAP003.htm#SSEC001.3">3.1.3</a> 
<dt>IdPrimitiveSolubleGroup <a href="CHAP005.htm#SSEC004.1">5.4.1</a> 
<dt>IdPrimitiveSolubleGroupNC <a href="CHAP005.htm#SSEC004.1">5.4.1</a> 
<dt>IdPrimitiveSolvableGroup <a href="CHAP005.htm#SSEC004.1">5.4.1</a> 
<dt>IdPrimitiveSolvableGroupNC <a href="CHAP005.htm#SSEC004.1">5.4.1</a> 
<dt>ImprimitivitySystems <a href="CHAP004.htm#SSEC003.3">4.3.3</a> 
<dt>IndexMSIdIrreducibleSolubleMatrixGroup <a href="CHAP003.htm#SSEC002.2">3.2.2</a> 
<dt>IndicesAbsolutelyIrreducibleSolubleMatrixGroups <a href="CHAP002.htm#SSEC002.6">2.2.6</a> 
<dt>IndicesIrreducibleSolubleMatrixGroups <a href="CHAP002.htm#SSEC002.2">2.2.2</a> 
<dt>IndicesIrreducibleSolvableMatrixGroups <a href="CHAP002.htm#SSEC002.2">2.2.2</a> 
<dt>IndicesMaximalAbsolutelyIrreducibleSolubleMatrixGroups <a href="CHAP002.htm#SSEC002.5">2.2.5</a> 
<dt>IndicesMaximalAbsolutelyIrreducibleSolvableMatrixGroups <a href="CHAP002.htm#SSEC002.5">2.2.5</a> 
<dt>IRREDSOL <a href="CHAP001.htm#I0">1.0</a> 
<dt>IRREDSOL, accessing low level data <a href="CHAP002.htm#I1">2.2</a> 
<dt>IRREDSOL, database design <a href="CHAP002.htm#I0">2.1</a> 
<dt>Irreducibility and maximality of matrix groups <a href="CHAP004.htm#SECT002">4.2</a> 
<dt>irreducibility, of matrix group <a href="CHAP004.htm#I4">4.2</a> 
<dt>IrreducibleMatrixGroupPrimitiveSolubleGroup <a href="CHAP005.htm#SSEC001.4">5.1.4</a> 
<dt>IrreducibleMatrixGroupPrimitiveSolvableGroupNC <a href="CHAP005.htm#SSEC001.4">5.1.4</a> 
<dt>IrreducibleSolubleMatrixGroup <a href="CHAP002.htm#SSEC002.3">2.2.3</a> 
<dt>IrreducibleSolvableMatrixGroup <a href="CHAP002.htm#SSEC002.3">2.2.3</a> 
<dt>IsAbsolutelyIrreducible <a href="CHAP004.htm#SSEC002.2">4.2.2</a> 
<dt>IsAbsolutelyIrreducibleMatrixGroup <a href="CHAP004.htm#SSEC002.2">4.2.2</a> 
<dt>IsAvailableAbsolutelyIrreducibleSolubleGroupData <a href="CHAP002.htm#SSEC002.4">2.2.4</a> 
<dt>IsAvailableAbsolutelyIrreducibleSolvableGroupData <a href="CHAP002.htm#SSEC002.4">2.2.4</a> 
<dt>IsAvailableIdAbsolutelyIrreducibleSolubleMatrixGroup <a href="CHAP003.htm#SSEC001.2">3.1.2</a> 
<dt>IsAvailableIdAbsolutelyIrreducibleSolvableMatrixGroup <a href="CHAP003.htm#SSEC001.2">3.1.2</a> 
<dt>IsAvailableIdIrreducibleSolubleMatrixGroup <a href="CHAP003.htm#SSEC001.1">3.1.1</a> 
<dt>IsAvailableIdIrreducibleSolvableMatrixGroup <a href="CHAP003.htm#SSEC001.1">3.1.1</a> 
<dt>IsAvailableIrreducibleSolubleGroupData <a href="CHAP002.htm#SSEC002.1">2.2.1</a> 
<dt>IsAvailableIrreducibleSolvableGroupData <a href="CHAP002.htm#SSEC002.1">2.2.1</a> 
<dt>IsIrreducible, for matrix groups <a href="CHAP004.htm#SSEC002.1">4.2.1</a> 
<dt>IsIrreducibleMatrixGroup <a href="CHAP004.htm#SSEC002.1">4.2.1</a> 
<dt>IsLinearlyPrimitive <a href="CHAP004.htm#SSEC003.2">4.3.2</a> 
<dt>IsMaximalAbsolutelyIrreducibleSolubleMatrixGroup <a href="CHAP004.htm#SSEC002.3">4.2.3</a> 
<dt>IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup <a href="CHAP004.htm#SSEC002.3">4.2.3</a> 
<dt>IsPrimitive, for matrix groups <a href="CHAP004.htm#SSEC003.2">4.3.2</a> 
<dt>IsPrimitiveMatrixGroup <a href="CHAP004.htm#SSEC003.2">4.3.2</a> 
<dt>IteratorIrredSolMatGroups <a href="CHAP002.htm#SSEC003.3">2.3.3</a> 
<dt>IteratorIrreducibleSolubleMatrixGroups <a href="CHAP002.htm#SSEC003.3">2.3.3</a> 
<dt>IteratorIrreducibleSolvableMatrixGroups <a href="CHAP002.htm#SSEC003.3">2.3.3</a> 
<dt>IteratorPrimitivePcGroups <a href="CHAP005.htm#SSEC002.3">5.2.3</a> 
<dt>IteratorPrimitivePermGroups <a href="CHAP005.htm#SSEC003.3">5.3.3</a> 
<dt>IteratorPrimitivePermutationGroups <a href="CHAP005.htm#SSEC005.1">5.5.1</a> 
</dl><p>
<H2><A NAME="idxL">L</A></H2>
<dl>
<dt>LoadAbsoIrredSolGroupData <a href="CHAP002.htm#SSEC004.1">2.4.1</a> 
<dt>LoadAbsolutelyIrreducibleSolubleGroupData <a href="CHAP002.htm#SSEC004.1">2.4.1</a> 
<dt>LoadAbsolutelyIrreducibleSolubleGroupFingerprints <a href="CHAP003.htm#SSEC003.1">3.3.1</a> 
<dt>LoadAbsolutelyIrreducibleSolvableGroupData <a href="CHAP002.htm#SSEC004.1">2.4.1</a> 
<dt>LoadedAbsoIrredSolGroupData <a href="CHAP002.htm#SSEC004.2">2.4.2</a> 
<dt>LoadedAbsolutelyIrreducibleSolubleGroupData <a href="CHAP002.htm#SSEC004.2">2.4.2</a> 
<dt>LoadedAbsolutelyIrreducibleSolubleGroupFingerprints <a href="CHAP003.htm#SSEC003.2">3.3.2</a> 
<dt>LoadedAbsolutelyIrreducibleSolvableGroupData <a href="CHAP002.htm#SSEC004.2">2.4.2</a> 
<dt>Loading and unloading group data manually <a href="CHAP002.htm#SECT004">2.4</a> 
<dt>Loading and unloading recognition data manually <a href="CHAP003.htm#SECT003">3.3</a> 
<dt>loading, of group data <a href="CHAP002.htm#I4">2.4</a> 
<dt>loading, of recognition data <a href="CHAP003.htm#I3">3.3</a> 
<dt>Low level access functions <a href="CHAP002.htm#SECT002">2.2</a> 
</dl><p>
<H2><A NAME="idxM">M</A></H2>
<dl>
<dt>matrix group, basic attributes <a href="CHAP004.htm#I1">4.1</a> 
<dt>matrix group, conjugating into smaller fieldss <a href="CHAP004.htm#I8">4.4</a> 
<dt>matrix group, irreducibility <a href="CHAP004.htm#I2">4.2</a> 
<dt>matrix group, maximality <a href="CHAP004.htm#I3">4.2</a> 
<dt>matrix group, primitivity <a href="CHAP004.htm#I6">4.3</a> 
<dt>matrix group, with given properties <a href="CHAP002.htm#I3">2.3</a> 
<dt>maximality, of matrix group <a href="CHAP004.htm#I5">4.2</a> 
<dt>MinimalBlockDimension, for matrix groups <a href="CHAP004.htm#SSEC003.1">4.3.1</a> 
<dt>MinimalBlockDimensionOfMatrixGroup <a href="CHAP004.htm#SSEC003.1">4.3.1</a> 
</dl><p>
<H2><A NAME="idxO">O</A></H2>
<dl>
<dt>Obsolete functions <a href="CHAP005.htm#SECT005">5.5</a> 
<dt>obsolete functions, for primitive soluble permutation groups <a href="CHAP005.htm#I16">5.5</a> 
<dt>OneIrredSolMatGroup <a href="CHAP002.htm#SSEC003.2">2.3.2</a> 
<dt>OneIrreducibleSolubleMatrixGroup <a href="CHAP002.htm#SSEC003.2">2.3.2</a> 
<dt>OneIrreducibleSolvableMatrixGroup <a href="CHAP002.htm#SSEC003.2">2.3.2</a> 
<dt>OnePrimitivePcGroup <a href="CHAP005.htm#SSEC002.2">5.2.2</a> 
<dt>OnePrimitiveSolublePermGroup <a href="CHAP005.htm#SSEC003.2">5.3.2</a> 
<dt>OnePrimitiveSolublePermutationGroup <a href="CHAP005.htm#SSEC005.1">5.5.1</a> 
<dt>OnePrimitiveSolvablePermGroup <a href="CHAP005.htm#SSEC003.2">5.3.2</a> 
<dt>OnePrimitiveSolvablePermutationGroup <a href="CHAP005.htm#SSEC005.1">5.5.1</a> 
<dt>Overview <a href="CHAP001.htm">1.0</a> 
</dl><p>
<H2><A NAME="idxP">P</A></H2>
<dl>
<dt>permutation group, primitive soluble <a href="CHAP005.htm#I3">5.0</a> 
<dt>primitive pc group, identification <a href="CHAP005.htm#I12">5.4</a> 
<dt>primitive pc group, recognition <a href="CHAP005.htm#I14">5.4</a> 
<dt>primitive pc group, with given properties <a href="CHAP005.htm#I5">5.2</a> 
<dt>primitive permutation group, identification <a href="CHAP005.htm#I13">5.4</a> 
<dt>primitive permutation group, recognition <a href="CHAP005.htm#I15">5.4</a> 
<dt>primitive permutation group, with given properties <a href="CHAP005.htm#I7">5.3</a> 
<dt>Primitive soluble groups <a href="CHAP005.htm">5.0</a> 
<dt>primitive soluble groups <a href="CHAP005.htm#I0">5.0</a> 
<dt>PrimitivePcGroup <a href="CHAP005.htm#SSEC001.1">5.1.1</a> 
<dt>PrimitivePcGroupIrreducibleMatrixGroup <a href="CHAP005.htm#SSEC001.2">5.1.2</a> 
<dt>PrimitivePcGroupIrreducibleMatrixGroupNC <a href="CHAP005.htm#SSEC001.2">5.1.2</a> 
<dt>PrimitivePermGroupIrreducibleMatrixGroup <a href="CHAP005.htm#SSEC001.3">5.1.3</a> 
<dt>PrimitivePermGroupIrreducibleMatrixGroupNC <a href="CHAP005.htm#SSEC001.3">5.1.3</a> 
<dt>PrimitivePermutationGroupIrreducibleMatrixGroup <a href="CHAP005.htm#SSEC005.1">5.5.1</a> 
<dt>PrimitivePermutationGroupIrreducibleMatrixGroupNC <a href="CHAP005.htm#SSEC005.1">5.5.1</a> 
<dt>PrimitiveSolublePermGroup <a href="CHAP005.htm#SSEC001.1">5.1.1</a> 
<dt>PrimitiveSolublePermutationGroup <a href="CHAP005.htm#SSEC005.1">5.5.1</a> 
<dt>PrimitiveSolvablePermGroup <a href="CHAP005.htm#SSEC001.1">5.1.1</a> 
<dt>PrimitiveSolvablePermutationGroup <a href="CHAP005.htm#SSEC005.1">5.5.1</a> 
<dt>Primitivity of matrix groups <a href="CHAP004.htm#SECT003">4.3</a> 
<dt>primitivity, of matrix group <a href="CHAP004.htm#I7">4.3</a> 
</dl><p>
<H2><A NAME="idxR">R</A></H2>
<dl>
<dt>Recognising primitive soluble groups <a href="CHAP005.htm#SECT004">5.4</a> 
<dt>Recognition of matrix groups <a href="CHAP003.htm">3.0</a> 
<dt>recognition, of matrix groups <a href="CHAP003.htm#I0">3.0</a> 
<dt>recognition, of primitive pc group <a href="CHAP005.htm#I10">5.4</a> 
<dt>recognition, of primitive permutation group <a href="CHAP005.htm#I11">5.4</a> 
<dt>RecognitionAbsolutelyIrreducibleSolubleMatrixGroup <a href="CHAP003.htm#SSEC001.5">3.1.5</a> 
<dt>RecognitionAbsolutelyIrreducibleSolubleMatrixGroupNC <a href="CHAP003.htm#SSEC001.5">3.1.5</a> 
<dt>RecognitionAbsolutelyIrreducibleSoluvaleMatrixGroupNC <a href="CHAP003.htm#SSEC001.5">3.1.5</a> 
<dt>RecognitionAbsolutelyIrreducibleSolvableMatrixGroup <a href="CHAP003.htm#SSEC001.5">3.1.5</a> 
<dt>RecognitionIrreducibleSolubleMatrixGroup <a href="CHAP003.htm#SSEC001.4">3.1.4</a> 
<dt>RecognitionIrreducibleSolubleMatrixGroupNC <a href="CHAP003.htm#SSEC001.4">3.1.4</a> 
<dt>RecognitionIrreducibleSolvableMatrixGroup <a href="CHAP003.htm#SSEC001.4">3.1.4</a> 
<dt>RecognitionIrreducibleSolvableMatrixGroupNC <a href="CHAP003.htm#SSEC001.4">3.1.4</a> 
<dt>RecognitionPrimitiveSolubleGroup <a href="CHAP005.htm#SSEC004.2">5.4.2</a> 
<dt>RecognitionPrimitiveSolvableGroup <a href="CHAP005.htm#SSEC004.2">5.4.2</a> 
<dt>RepresentationIsomorphism <a href="CHAP004.htm#SSEC001.6">4.1.6</a> 
</dl><p>
<H2><A NAME="idxS">S</A></H2>
<dl>
<dt>soluble primitive groups <a href="CHAP005.htm#I1">5.0</a> 
<dt>SplittingField <a href="CHAP004.htm#SSEC001.4">4.1.4</a> 
<dt>structure of IRREDSOL <a href="CHAP001.htm#I1">1.0</a> 
</dl><p>
<H2><A NAME="idxT">T</A></H2>
<dl>
<dt>TraceField <a href="CHAP004.htm#SSEC004.1">4.4.1</a> 
</dl><p>
<H2><A NAME="idxU">U</A></H2>
<dl>
<dt>UnloadAbsoIrredSolGroupData <a href="CHAP002.htm#SSEC004.3">2.4.3</a> 
<dt>UnloadAbsolutelyIrreducibleSolubleGroupData <a href="CHAP002.htm#SSEC004.3">2.4.3</a> 
<dt>UnloadAbsolutelyIrreducibleSolubleGroupFingerprints <a href="CHAP003.htm#SSEC003.3">3.3.3</a> 
<dt>UnloadAbsolutelyIrreducibleSolvableGroupData <a href="CHAP002.htm#SSEC004.3">2.4.3</a> 
<dt>unloading, of group data <a href="CHAP002.htm#I5">2.4</a> 
<dt>unloading, of recognition data <a href="CHAP003.htm#I4">3.3</a> 
</dl><p>
<H2><A NAME="idxV">V</A></H2>
<dl>
<dt>Version History <a href="CHAP00A.htm">A.0</a> 
</dl><p>
<H2><A NAME="idxW">W</A></H2>
<dl>
<dt>workspace, running out of <a href="CHAP002.htm#I6">2.4</a> <a href="CHAP003.htm#I5">3.3</a> 
</dl><p>
[<a href="chapters.htm">Up</a>]<p>
<P>
<address>IRREDSOL manual<br>November 2022
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