GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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<!-- %W  interfac.xml    GAP 4 package AtlasRep             Thomas Breuer -->
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<!-- %Y  Copyright 2001, Lehrstuhl D f�r Mathematik, RWTH Aachen, Germany -->
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<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
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<Chapter Label="chap:The User Interface of the AtlasRep Package">
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<Heading>The User Interface of the <Package>AtlasRep</Package> Package
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</Heading>
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The <E>user interface</E> is the part of the &GAP; interface that allows one
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to display information about the current contents of the database and to
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access individual data (perhaps from a remote server,
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see Section&nbsp;<Ref Sect="subsect:Local or remote access"/>).
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The corresponding functions are described in this chapter.
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See Section&nbsp;<Ref Sect="sect:Examples of Using the AtlasRep Package"/>
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for some small examples how to use the functions of the interface.
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<P/>
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Extensions of the <Package>AtlasRep</Package> package are regarded as another
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part of the &GAP; interface,
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they are described in Chapter&nbsp;<Ref Chap="chap:Private Extensions"/>.
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Finally, the low level part of the interface are described in
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Chapter&nbsp;<Ref Chap="chap:Technicalities of the AtlasRep Package"/>.
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<P/>
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For some of the examples in this chapter,
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the &GAP; packages <Package>CTblLib</Package> and <Package>TomLib</Package>
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are needed, so we load them.
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<P/>
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<Example><![CDATA[
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gap> LoadPackage( "ctbllib" );
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true
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gap> LoadPackage( "tomlib" );
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true
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]]></Example>
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<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
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<Section Label="sect:Accessing vs. Constructing Representations">
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<Heading>Accessing vs. Constructing Representations</Heading>
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Note that <E>accessing</E> the data means in particular
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that it is <E>not</E> the aim of this package to <E>construct</E>
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representations from known ones.
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For example, if at least one permutation representation for a group <M>G</M>
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is stored but no matrix representation in a positive characteristic <M>p</M>,
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say, then <Ref Func="OneAtlasGeneratingSetInfo"/>
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returns <K>fail</K> when it is asked for a description of an available set of
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matrix generators for <M>G</M> in characteristic <M>p</M>,
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although such a representation can be obtained by reduction modulo <M>p</M>
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of an integral matrix representation,
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which in turn can be constructed from any permutation representation.
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</Section>
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<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
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<Section Label="sect:Group Names Used in the AtlasRep Package">
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<Heading>Group Names Used in the <Package>AtlasRep</Package> Package</Heading>
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<!-- The section title is referenced in htm/data/overview.htm. -->
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<Alt Only="HTML"><![CDATA[<a id="sect:groupnames"/>]]></Alt>
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When you access data via the <Package>AtlasRep</Package> package,
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you specify the group in question by an admissible <E>name</E>.
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Thus it is essential to know these names,
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which are called <E>the &GAP; names</E> of the group in the following.
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<P/>
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For a group <M>G</M>, say, whose character table is available in
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&GAP;'s Character Table Library,
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the admissible names of <M>G</M> are the admissible names
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of this character table.
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If <M>G</M> is almost simple, one such name is the 
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<Ref Attr="Identifier" Label="for character tables" BookName="ref"/> value
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of the character table,
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see&nbsp;<Ref Func="Accessing a Character Table from the Library" BookName="ctbllib"/>.
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This name is usually very similar to the name used in the
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&ATLAS; of Finite Groups <Cite Key="CCN85"/>.
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For example,
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<C>"M22"</C> is a &GAP; name of the Mathieu group <M>M_{22}</M>,
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<C>"12_1.U4(3).2_1"</C> is a &GAP; name of <M>12_1.U_4(3).2_1</M>,
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the two names <C>"S5"</C> and <C>"A5.2"</C> are &GAP; names of
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the symmetric group <M>S_5</M>,
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and the two names <C>"F3+"</C> and <C>"Fi24'"</C> are &GAP; names of
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the simple Fischer group <M>Fi_{24}^\prime</M>.
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<P/>
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When a &GAP; name is required as an input of a package function,
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this input is case insensitive.
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For example, both <C>"A5"</C> and <C>"a5"</C> are valid arguments of
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<Ref Func="DisplayAtlasInfo"/>.
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<P/>
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Internally, for example as part of filenames
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(see Section&nbsp;<Ref Sect="sect:Filenames Used in the AGR"/>),
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the package uses names that may differ from the &GAP; names;
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these names are called <E>&ATLAS;-file names</E>.
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For example, <C>"A5"</C>, <C>"TE62"</C>, and <C>"F24"</C> are
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&ATLAS;-file names.
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Of these, only <C>"A5"</C> is also a &GAP; name, but the other two are not;
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corresponding &GAP; names are <C>"2E6(2)"</C> and <C>"Fi24'"</C>,
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respectively.
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</Section>
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<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
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<Section Label="sect:Standard Generators Used in AtlasRep">
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<Heading>Standard Generators Used in the <Package>AtlasRep</Package> Package
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</Heading>
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For the general definition of <E>standard generators</E> of a group,
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see <Cite Key="Wil96"/>.
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<!-- or
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Section&nbsp;<Ref Sect="Standard Generators of Groups" BookName="tomlib"/>. -->
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<P/>
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Several <E>different</E> standard generators may be defined for a group,
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the definitions can be found at
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<P/>
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&ATLASSERVER;
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<P/>
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When one specifies the standardization,
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the <M>i</M>-th set of standard generators is denoted by the number <M>i</M>.
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Note that when more than one set of standard generators is defined for
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a group, one must be careful to use <E>compatible standardization</E>.
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For example, the straight line programs, straight line decisions and
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black box programs in the database refer to a specific standardization
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of their inputs.
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That is, a straight line program for computing generators of a certain
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subgroup of a group <M>G</M> is defined only for a specific set of standard
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generators of <M>G</M>, and applying the program to matrix or permutation
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generators of <M>G</M> but w.r.t.&nbsp;a different standardization may yield
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unpredictable results.
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Therefore the results returned by the functions described in this chapter
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contain information about the standardizations they refer to.
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</Section>
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<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
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<Section Label="sect:Class Names Used in the AtlasRep Package">
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<Heading>Class Names Used in the <Package>AtlasRep</Package> Package</Heading>
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For each straight line program (see&nbsp;<Ref Func="AtlasProgram"/>)
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that is used to compute lists of class representatives,
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it is essential to describe the classes in which these elements lie.
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Therefore, in these cases the records returned by the function
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<Ref Func="AtlasProgram"/> contain a component <C>outputs</C>
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with value a list of <E>class names</E>.
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<P/>
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Currently we define these class names only for simple groups and
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certain extensions of simple groups,
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see Section&nbsp;<Ref Subsect="subsect:Definition of ATLAS Class Names"/>.
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The function <Ref Func="AtlasClassNames"/> can be used to compute the list
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of class names from the character table in the &GAP; Library.
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<#Include Label="classnames">
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<#Include Label="AtlasClassNames">
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<#Include Label="AtlasCharacterNames">
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</Section>
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<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
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<Section Label="sect:Accessing Data of the AtlasRep Package">
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<Heading>Accessing Data of the <Package>AtlasRep</Package> Package</Heading>
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Note that the output of the examples in this section refers to a perhaps
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outdated table of contents;
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the current version of the database may contain more information
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than is shown here.
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<P/>
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<#Include Label="DisplayAtlasInfo">
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<#Include Label="AtlasGenerators">
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<#Include Label="AtlasProgram">
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<#Include Label="AtlasProgramInfo">
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<#Include Label="OneAtlasGeneratingSetInfo">
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<#Include Label="AllAtlasGeneratingSetInfos">
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<#Include Label="AtlasGroup">
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<#Include Label="AtlasSubgroup">
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<#Include Label="AtlasRepInfoRecord">
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</Section>
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<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
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<Section Label="sect:Browse and AtlasRep">
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<Heading><Package>Browse</Package> Applications Provided by
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<Package>AtlasRep</Package></Heading>
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The functions <Ref Func="BrowseMinimalDegrees"/>,
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<Ref Func="BrowseBibliographySporadicSimple"/>,
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and <Ref Func="BrowseAtlasInfo" BookName="Browse"/> 
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(an alternative to <Ref Func="DisplayAtlasInfo"/>)
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are available only if
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the &GAP; package <Package>Browse</Package> (see <Cite Key="Browse"/>)
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is loaded.
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<#Include Label="BrowseMinimalDegrees">
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<#Include Label="BrowseBibliographySporadicSimple">
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</Section>
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<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
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</Chapter>
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