The User Interface of the `AtlasRep` Package

The user interface is the part of the &GAP; interface that allows one to display information about the current contents of the database and to access individual data (perhaps from a remote server, see Section ). The corresponding functions are described in this chapter. See Section for some small examples how to use the functions of the interface.

Extensions of the `AtlasRep` package are regarded as another part of the &GAP; interface, they are described in Chapter . Finally, the low level part of the interface are described in Chapter .

For some of the examples in this chapter, the &GAP; packages `CTblLib` and `TomLib` are needed, so we load them.

gap> LoadPackage( "ctbllib" ); true gap> LoadPackage( "tomlib" ); true
Accessing vs. Constructing Representations

Note that accessing the data means in particular that it is not the aim of this package to construct representations from known ones. For example, if at least one permutation representation for a group G is stored but no matrix representation in a positive characteristic p, say, then returns fail when it is asked for a description of an available set of matrix generators for G in characteristic p, although such a representation can be obtained by reduction modulo p of an integral matrix representation, which in turn can be constructed from any permutation representation.

Group Names Used in the `AtlasRep` Package
<a id="sect:groupnames"/>

When you access data via the `AtlasRep` package, you specify the group in question by an admissible name. Thus it is essential to know these names, which are called the &GAP; names of the group in the following.

For a group G, say, whose character table is available in &GAP;'s Character Table Library, the admissible names of G are the admissible names of this character table. If G is almost simple, one such name is the value of the character table, see . This name is usually very similar to the name used in the &ATLAS; of Finite Groups . For example, "M22" is a &GAP; name of the Mathieu group M_{22}, "12_1.U4(3).2_1" is a &GAP; name of 12_1.U_4(3).2_1, the two names "S5" and "A5.2" are &GAP; names of the symmetric group S_5, and the two names "F3+" and "Fi24'" are &GAP; names of the simple Fischer group Fi_{24}^\prime.

When a &GAP; name is required as an input of a package function, this input is case insensitive. For example, both "A5" and "a5" are valid arguments of .

Internally, for example as part of filenames (see Section ), the package uses names that may differ from the &GAP; names; these names are called &ATLAS;-file names. For example, "A5", "TE62", and "F24" are &ATLAS;-file names. Of these, only "A5" is also a &GAP; name, but the other two are not; corresponding &GAP; names are "2E6(2)" and "Fi24'", respectively.

Standard Generators Used in the `AtlasRep` Package

For the general definition of standard generators of a group, see .

Several different standard generators may be defined for a group, the definitions can be found at

&ATLASSERVER;

When one specifies the standardization, the i-th set of standard generators is denoted by the number i. Note that when more than one set of standard generators is defined for a group, one must be careful to use compatible standardization. For example, the straight line programs, straight line decisions and black box programs in the database refer to a specific standardization of their inputs. That is, a straight line program for computing generators of a certain subgroup of a group G is defined only for a specific set of standard generators of G, and applying the program to matrix or permutation generators of G but w.r.t. a different standardization may yield unpredictable results. Therefore the results returned by the functions described in this chapter contain information about the standardizations they refer to.

Class Names Used in the `AtlasRep` Package

For each straight line program (see ) that is used to compute lists of class representatives, it is essential to describe the classes in which these elements lie. Therefore, in these cases the records returned by the function contain a component outputs with value a list of class names.

Currently we define these class names only for simple groups and certain extensions of simple groups, see Section . The function can be used to compute the list of class names from the character table in the &GAP; Library.

<#Include Label="classnames"> <#Include Label="AtlasClassNames"> <#Include Label="AtlasCharacterNames">

Accessing Data of the `AtlasRep` Package

Note that the output of the examples in this section refers to a perhaps outdated table of contents; the current version of the database may contain more information than is shown here.

<#Include Label="DisplayAtlasInfo"> <#Include Label="AtlasGenerators"> <#Include Label="AtlasProgram"> <#Include Label="AtlasProgramInfo"> <#Include Label="OneAtlasGeneratingSetInfo"> <#Include Label="AllAtlasGeneratingSetInfos"> <#Include Label="AtlasGroup"> <#Include Label="AtlasSubgroup"> <#Include Label="AtlasRepInfoRecord">

Browse
Applications Provided by `AtlasRep`

The functions , , and (an alternative to ) are available only if the &GAP; package `Browse` (see ) is loaded.

<#Include Label="BrowseMinimalDegrees"> <#Include Label="BrowseBibliographySporadicSimple">