4 Technicalities of the AtlasRep Package

If the info level of InfoAtlasRep is at least 1 then information about fail results of functions in the AtlasRep package is printed. If the info level is at least 2 then information about calls to external programs is printed. The default level is 0, no information is printed on this level.

If the info level of InfoCMeatAxe is at least 1 then information about fail results of C-MeatAxe functions is printed. The default level is 0, no information is printed on this level.

Information about files that are read can be obtained by setting the value of the global variable InfoRead1 to Print.

The info level of an info class can be changed using SetInfoLevel (see SetInfoLevel in the GAP Reference Manual). For example, the info level of InfoAtlasRep can be set to the nonnegative integer n using SetInfoLevel( InfoAtlasRep, n ).

AtlasOfGroupRepresentationsInfo is a record with the following components.

remote

a boolean that controls what files are available; if the value is true then GAP is allowed to try remotely accessing any ATLAS file from the servers (see below) and thus all files listed in the global table of contents are available, if the value is false then GAP may access only those files that are stored in the database directories of the local GAP installation,

compress

a boolean that controls whether MeatAxe format files are stored in compressed form; if the value is true then these files are compressed with gzip after they have been fetched from a server.

servers

a list of quadrupels [ server, path, login, password ], where server is a string denoting the ftp address of a server where files can be fetched that are not stored in the local database, path is a string describing the path where the data directories on the server reside (relative to the directory entered via ftp login), login is the login name for the server access, and password is the corresponding password; only this list must be adjusted if new servers are added or if the addresses of servers change,

dirnames

a list of the names of the directories on the servers that contain subdirectories corresponding to the individual groups,

GAPnames

a list of pairs, each containing the GAP name and the ATLAS-file name of a group (see Group Names Used in the AtlasRep Package),

groupnames

a list of triples, each containing at the first position the name of the directory on each server that contains data about the group G in question, at the second position the name of the (usually simple) group for which a subdirectory exists that contains the data about G, and at the third position the ATLAS-file name used for G (see Filenames used in the Atlas of Group Representations),

fieldinfo

a list of triples, each containing at the first position the name of the file with the matrices of a characteristic zero representation, at the second position a string describing the field generated by the matrix entries, and at the third position this field itself; DisplayAtlasInfo (see DisplayAtlasInfo) displays this information for representations over proper extensions of the rational number field only if the representation is mentioned in the fieldinfo list,

private

a list of pairs of strings used for administrating private data (see Chapter Private Extensions of the AtlasRep Package),

markprivate

a string used to mark private data (see The Effect of Private Extensions on the User Interface), and

TableOfContents

a record with at most the components local, remote, types, data, and the names of private data directories; the values of the components local and remote can be computed automatically by AtlasTableOfContents, and the values of the components for local data directories are created by AtlasOfGroupRepresentationsNotifyPrivateDirectory.

The record components, except TableOfContents, are not computed automatically. If new groups or new field information for characteristic zero representations become available then the file atlasprm.g must be updated.

4.2 Reading and Writing MeatAxe Format Files

Let filename be the name of a GAP readable file (see Filename in the GAP Reference Manual) that contains a matrix or a permutation or a list of permutations in MeatAxe text format (see the section about the program zcv in the MeatAxe manual Rin98), and let q be a prime power. ScanMeatAxeFile returns the corresponding GAP matrix or list of permutations, respectively.

The file is read line by line, and the matrix is constructed line by line, in a compressed representation (see Row Vectors over Finite Fields and Matrices over Finite Fields in the GAP Reference Manual), which makes it possible to read large matrices in a reasonable amount of space. If the parameter q is given and the result is a matrix then this matrix is represented over the field with q elements.

In the second form, the first argument string must be a string as obtained by reading a file in MeatAxe text format as a text stream (see InputTextFile in the GAP Reference Manual), and the third argument the string "string". Also in this case, ScanMeatAxeFile returns the corresponding GAP matrix or list of permutations, respectively.

In the first form, for a matrix mat whose entries lie in the finite field with q elements, MeatAxeString returns a string that encodes mat as a matrix over GF(q), in MeatAxe text format.

In the second form, for a nonempty list perms of permutations that move only points up to the positive integer degree, MeatAxeString returns a string that encodes perms as permutations of degree degree, in MeatAxe text format.

In the third form, for a permutation perm with largest moved point n, say, a prime power q, and a list dims of length 2 containing two positive integers larger than or equal to n, MeatAxeString returns a string that encodes perm as a matrix over GF(q), of dimensions dims, whose first n rows and columns describe the permutation matrix corresponding to perm, and the remaining rows and columns are zero.

gap> mat:= [ [ 1, -1 ], [ 0, 1 ] ] * Z(3)^0;;
gap> str:= MeatAxeString( mat, 3 );
"1 3 2 2\n12\n01\n"
gap> mat = ScanMeatAxeFile( str, "string" );
true
gap> str:= MeatAxeString( mat, 9 );
"1 9 2 2\n12\n01\n"
gap> mat = ScanMeatAxeFile( str, "string" );
true
gap> perms:= [ (1,2,3)(5,6) ];;
gap> str:= MeatAxeString( perms, 6 );
"12 1 6 1\n2\n3\n1\n4\n6\n5\n"
gap> perms = ScanMeatAxeFile( str, "string" );
true
gap> str:= MeatAxeString( perms, 8 );
"12 1 8 1\n2\n3\n1\n4\n6\n5\n7\n8\n"
gap> perms = ScanMeatAxeFile( str, "string" );
true
gap> perm:= (1,2,4);;
gap> str:= MeatAxeString( perm, 3, [ 5, 6 ] );
"2 3 5 6\n2\n4\n3\n1\n5\n"
gap> mat:= ScanMeatAxeFile( str, "string" );;  Print( mat, "\n" );
[ [ 0*Z(3), Z(3)^0, 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ], 
  [ 0*Z(3), 0*Z(3), 0*Z(3), Z(3)^0, 0*Z(3), 0*Z(3) ], 
  [ 0*Z(3), 0*Z(3), Z(3)^0, 0*Z(3), 0*Z(3), 0*Z(3) ], 
  [ Z(3)^0, 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ], 
  [ 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), Z(3)^0, 0*Z(3) ] ]
gap> MeatAxeString( mat, 3 ) = str;
true

FFList is a utility program for the conversion of vectors and matrices from MeatAxe format to GAP format and vice versa. It is used by ScanMeatAxeFile (see ScanMeatAxeFile) and MeatAxeString (see MeatAxeString).

For a finite field F, FFList returns a list l giving the correspondence between the MeatAxe numbering and the GAP numbering of the elements in F.

The element of F corresponding to MeatAxe number n is l[ n+1 ], and the MeatAxe number of the field element z is Position( l, z ) - 1.

The global variable FFLists is used to store the information about F once it has been computed.

gap> FFList( GF(4) );
[ 0*Z(2), Z(2)^0, Z(2^2), Z(2^2)^2 ]
gap> IsBound( FFLists[4] );
true

4.3 Reading and Writing Atlas Straight Line Programs

Let filename be the name of a file that contains a straight line program in the sense that it consists only of lines in the following form.

# anything

lines starting with a hash sign # are ignored,

echo anything

lines starting with echo are ignored for the program component of the result record (see below), they are used to set up the bijection between the labels used in the program and conjugacy class names in the case that the program computes dedicated class representatives,

inp n

means that there are n inputs, referred to via the labels 1, 2, ¼, n,

inp k a1 a2 ... ak

means that the next k inputs are referred to via the labels a1, a2, ..., ak,

cjr a b

means that a is replaced by b^(-1) a b,

cj a b c

means that c is defined as b^(-1) a b,

com a b c

means that c is defined as a^(-1) b^(-1) a b,

iv a b

means that b is defined as a^(-1),

mu a b c

means that c is defined as a*b,

pwr a b c

means that c is defined to be b^a, and

cp a b

means that b is defined as a copy of a,

oup l

means that there are l outputs, stored in the labels 1, 2, ¼, l,

oup l b1 b2 ... bl

means that the next l outputs are stored in the labels b1, b2, ... bl.

Each of the labels a, b, c can be any nonempty sequence of digits and alphabet characters, except that the first argument of pwr must denote an integer.

If the inp or oup statements are missing then the input or output, respectively, is assumed to be given by the labels 1 and 2. There can be multiple inp lines at the beginning of the program and multiple oup lines at the end of the program. Only the first inp or oup line may omit the names of the elements. No command except cjr may overwrite its own input.

ScanStraightLineProgram returns a record containing as the value of its component program the corresponding GAP straight line program (see IsStraightLineProgram in the GAP Reference Manual) if the input string satisfies the syntax rules stated above, and returns fail otherwise. In the latter case, information about the first corrupted line of the program is printed if the info level of InfoCMeatAxe is at least 1 (see InfoCMeatAxe).

In the second form, the first argument string must be a string as obtained by reading a file in MeatAxe text format as a text stream (see InputTextFile in the GAP Reference Manual), and the second argument the string "string". Also in this case, ScanStraightLineProgram returns either a record with the corresponding GAP straight line program or fail.

If the input describes a straight line program that computes certain class representatives of the group in question then the result record also contains the component outputs. Its value is a list of strings, the entry at position i denoting the name of the class in which the i output of the straight line program lies; see Class Names Used in the AtlasRep Package for the definition of the class names that occur.

Such straight line programs must end with a sequence of output specifications of the following form.

echo "Classes 1A 2A 3A 5A 5B"
oup 5 3 1 2 4 5

This example means that the list of outputs of the program contains elements of the classes 1A, 2A, 3A, 5A, and 5B (in this order), and that inside the program, these elements are referred to by the names 3, 1, 2, 4, and 5.

For a straight line program prog (see IsStraightLineProgram in the GAP Reference Manual), AtlasStringOfStraightLineProgram returns a string describing the format of an equivalent straight line program as used in the ATLAS of Group Representations, that is, the lines are of the form described in ScanStraightLineProgram.

A list of strings that is given as the optional second argument outputnames is interpreted as the class names corresponding to the outputs; this argument has the effect that appropriate echo statements appear in the result string.

gap> str:= "inp 2\nmu 1 2 3\nmu 3 1 2\niv 2 1\noup 2 1 2";;
gap> prg:= ScanStraightLineProgram( str, "string" );
rec( program := <straight line program> )
gap> prg:= prg.program;;
gap> Display( prg );
# input:
r:= [ g1, g2 ];
# program:
r[3]:= r[1]*r[2];
r[2]:= r[3]*r[1];
r[1]:= r[2]^-1;
# return values:
[ r[1], r[2] ]
gap> StringOfResultOfStraightLineProgram( prg, [ "a", "b" ] );
"[ (aba)^-1, aba ]"
gap> AtlasStringOfStraightLineProgram( prg );
"inp 2\nmu 1 2 3\nmu 3 1 2\niv 2 1\noup 2\n"
gap> prg:= StraightLineProgram( "(a^2b^3)^-1", [ "a", "b" ] );
<straight line program>
gap> Print( AtlasStringOfStraightLineProgram( prg ) );
inp 2
pwr 2 1 4
pwr 3 2 5
mu 4 5 3
iv 3 4
oup 1 4
gap> prg:= StraightLineProgram( [ [2,3], [ [3,1,1,4], [1,2,3,1] ] ], 2 );
<straight line program>
gap> Print( AtlasStringOfStraightLineProgram( prg ) );
inp 2
pwr 3 2 3
pwr 4 1 5
mu 3 5 4
pwr 2 1 6
mu 6 3 5
oup 2 4 5

4.4 Data Types Used in the Atlas of Group Representations

Let kind be one of the strings "rep" or "slp", and record be a record. AGRDeclareDataType declares a new data type of representations (if kind is "rep") or of straight line programs (if kind is "slp"). For each group used in the AtlasRep package, the data that belongs to the new type is stored (as a list) in the component name of the records for this group. Examples of name are "perm", "matff", and "classes".

Compulsory components of record are

FilenameFormat

This defines the format of the filenames containing data of the type in question. The value must be a list that can be used as the second argument of AGRParseFilenameFormat (see AGRParseFilenameFormat), such that exactly filenames of the type in question are matched.

AddFileInfo

This defines the information stored in the table of contents for the data of the type. The value must be a function that takes three arguments (the current list of data for the type and the given group, a data list returned by AGRParseFilenameFormat, see AGRParseFilenameFormat, and a filename). This function adds the necessary parts of the data entry to the list, and returns true if the data belongs to the type, otherwise false is returned.

DisplayGroup (for rep only)

This defines the format of the lines printed by DisplayAtlasInfo (see DisplayAtlasInfo) for a given group. The value must be a function that takes a list as returned by the function given in the component AddFileInfo, and returns the string to be printed for the representation in question.

Optional components of record are

DisplayOverviewInfo

This is used to introduce a new column in the output of DisplayAtlasInfo (see DisplayAtlasInfo) when this is called without arguments or with a list of group names as its only argument. The value must be a list of length three, containing at its first position a string used as the header of the column, at its second position one of the strings "r" or "l", denoting right or left aligned column entries, and at its third position a function that takes two arguments (a list of tables of contents of the AtlasRep package and a group name), and returns a list of length two, containing the string to be printed as the column value and true or false, depending on whether private data is involved or not. (The default is to print no column for the data type.)

DisplaySLP (for slp only)

This is used in DisplayAtlasInfoStraightLineProgram. The value must be a function that takes four arguments (a list of tables of contents to examine, the name of the given group, a list of integers or true for the required standardization, and a list of all available standardizations), and prints the information about the available straight line programs of the current type and for the given group. (The default value is Ignore.)

AccessGroupCondition (for rep only)

This is used in DisplayAtlasInfoGroup and OneAtlasGeneratingSet. The value must be a function that takes two arguments (a list as returned by AGRParseFilenameFormat, see AGRParseFilenameFormat, and a list of conditions --see below), and returns true or false, depending on whether the first argument satisfies the conditions. (The default value is ReturnFalse.)

AccessSLP (for slp only)

This is used in AtlasStraightLineProgram (see AtlasStraightLineProgram). The value must be a function that takes three arguments (the record with the information about the given group in the current table of contents, an integer or a list of integers or true for the required standardization, and a list of conditions --see below), and returns either fail or a list that together with the group name forms the identifier of a straight line program that matches the conditions. (The default value is ReturnFail.)

TOCEntryString

This is used in StringOfAtlasTableOfContents, so it is needed only for those data types for which data is stored in the official part. The value must be a function that takes two arguments (the name name of the type and a list as returned by AGRParseFilenameFormat, see AGRParseFilenameFormat) and returns a string that describes the appropriate call to AGRTOC. (The default value is TOCEntryStringDefault.)

PostprocessFileInfo

This is used in the construction of a table of contents via AtlasTableOfContents, for testing or rearranging the data of the current table of contents after executing all AGRTOC statements. The value must be a function that takes two arguments, the table of contents record and the record in it that belongs to one fixed group. (The default value is Ignore.)

SortTOCEntries

This is used in the construction of a table of contents via AtlasTableOfContents, for sorting the entries after they have been added with ARGTOC and after PostprocessFileInfo has been called. The value must be a function that takes a list as returned by AGRParseFilenameFormat (see AGRParseFilenameFormat), and returns the sorting key. (There is no default value, which means that no sorting is needed.)

TestFileHeaders (for rep only)

This is used in the function AtlasOfGroupRepresentationsTestFileHeaders. The value must be a function that takes the same three arguments as FilenameAtlas (see FilenameAtlas), except that the first argument "datagens" can be replaced by "local" and that the third argument is a list as returned by AGRParseFilenameFormat (see AGRParseFilenameFormat). (The default value is ReturnTrue.)

TestFiles (for rep only)

This is used in the function AtlasOfGroupRepresentationsTestFiles. The format of the value and the default are the same as for TestFileHeaders.

TestWords (for slp only)

This is used in the function AtlasOfGroupRepresentationsTestWords. The value must be a function that takes the same three arguments as FilenameAtlas (see FilenameAtlas), except that the first argument "dataword" can be replaced by "local". (The default is to call AGRTestWordsDefault with fourth argument false.)

The lists of conditions used as arguments of AccessGroupCondition and AccessSLP usually contain functions such as IsPermGroup, which are just checked for presence, and functions such as NrMovedPoints followed by a prescribed value or a list of prescribed values. Examples of such conditions are [ IsPermGroup ] and [ NrMovedPoints, [ 5, 6 ] ].

Note that it cannot be checked whether the ``detection function'' in the component FilenameFormat matches exactly one type, so one must be very careful when declaring a new type.

4.5 Filenames Used in the Atlas of Group Representations

The data of each local GAP version of the ATLAS of Group Representations is either private (see Chapter Private Extensions of the AtlasRep Package) or is stored in the two directories datagens and dataword. In the following, we describe the format of filenames in the latter two directories, as a reference of the ``official'' part of the ATLAS.

In the directory datagens, the generators for the representations available are stored, the directory dataword contains the straight line programs to compute conjugacy class representatives, generators of maximal subgroups, or images of generators under automorphisms of a given group G from standard generators of G (see Standard Generators Used in the AtlasRep Package).

The name of each data file in the ATLAS of Group Representations describes the contents of the file. This section lists the definitions of the filenames used.

Each filename consists of two parts, separated by a minus sign -. The first part is always of the form groupnameGi, where the integer i denotes the i-th set of standard generators for the group with ATLAS-file name groupname (see Group Names Used in the AtlasRep Package). The translations of the name groupname to the name(s) used within GAP is given by the list AtlasOfGroupRepresentationsInfo.GAPnames (see AtlasOfGroupRepresentationsInfo).

The filenames in the directory dataword have one of the following forms. In each of these cases, the suffix Wn means that n is the version number of the straight line program.

groupnameGi-cycWn

In this case, the file contains a straight line program that returns a list of representatives of generators of maximally cyclic subgroups of G. An example is Co1G1-cycW1.

groupnameGi-cclsWn

In this case, the file contains a straight line program that returns a list of conjugacy class representatives of G. An example is RuG1-cclsW1.

groupnameGicycWn-cclsWm

In this case, the file contains a straight line program that takes the return value of the program in the file groupnameGi-cycWn (see above), and returns a list of conjugacy class representatives of G. An example is M11G1cycW1-cclsW1.

groupnameGi-maxkWn

In this case, the file contains the straight line program that takes generators of G w.r.t. the i-th set of standard generators, and returns a list of generators (in general not standard generators) for a subgroup U in the k-th class of maximal subgroups of G. An example is J1G1-max7W1.

groupnameGimaxkWn-subgroupnameGjWm

In this case, the file contains a straight line program that takes the return value of the program in the file groupnameGi-maxkWn (see above), which are generators for a group U, say; subgroupname is a name for U, and the return value are standard generators for U, w.r.t. the j-th set of standard generators. (Of course this implies that the groups in the k-th class of maximal subgroups of G are isomorphic to the group with name subgroupname.) An example is J1G1max1W1-L211G1W1. The first class of maximal subgroups of the Janko group J₁ consists of groups isomorphic to the linear group L₂(11), for which standard generators are defined.

groupnameGi-aoutnameWn

In this case, the file contains the straight line program that takes generators of G w.r.t. the i-th set of standard generators, and returns the list of their images under the outer automorphism a of G given by the name outname; if this name is empty then a is the unique nontrivial outer automorphism of G; if it is a positive integer k then a is a generator of the unique cyclic order k subgroup of the outer automorphism group of G; if it is of the form 2₁, 4₂, 3₃ ¼ then a generates the cyclic group of automorphisms induced on G by G.2₁, G.4₂, G.3₃ ¼; finally, if it is of the form kpd, with k one of the above forms and d an integer then d denotes the number of dashes appended to the automorphism described by k; if d = 1 then d can be omitted. Examples are A5G1-aW1, L34G1-a2_1W1, U43G1-a2_3pW1, and O8p3G1-a2_2p5W1; these file names describe the outer order 2 automorphism of A₅ (induced by the action of S₅) and the order 2 automorphisms of L₃(4), U₄(3), and O₈⁺(3) induced by the actions of L₃(4).2₁, U₄(3).2₂^¢, and O₈⁺(3).2₂^¢¢¢¢¢, respectively.

groupnameGi-XdescrWn

In this case, the file contains the straight line program that takes generators of G w.r.t. the i-th set of standard generators, the return value corresponds to descr. This format is used only in private extensions (see Chapter Private Extensions of the AtlasRep Package), such a script can be accessed with descr as the third argument of AtlasStraightLineProgram (see AtlasStraightLineProgram).

The filenames in the directory datagens have one of the following forms. In each of these cases, id is a (possibly empty) string that starts with a non-digit character, and m is a nonnegative integer, meaning that the generators are written w.r.t. the m-th basis (in a list defined by the ATLAS developers).

groupnameGi-ArdimidBm.g

a GAP readable file containing all generators of a matrix representation of dimension dim over an algebraic number field not specified further. An example is A5G1-Ar3aB0.g.

groupnameGi-ZrdimidBm.g

a GAP readable file containing all generators of a matrix representation over the integers, of dimension dim. An example is A5G1-Zr4B0.g.

groupnameGi-HrdimidBm.g

a GAP readable file containing all generators of a matrix representation over a quaternion algebra over an algebraic number field, of dimension dim. An example is 2A6G1-Hr2aB0.g.

groupnameGi-ZnrdimidBm.g

a GAP readable file containing all generators of a matrix representation of dimension dim over the ring of integers mod n. An example is 2A8G1-Z4r4aB0.g.

groupnameGi-fqrdimidBm.mnr

a file in MeatAxe textfile format containing the nr-th generator of a matrix representation over the field with q elements, of dimension dim. An example is S5G1-f2r4aB0.m1.

groupnameGi-pnidBm.mnr

a file in MeatAxe textfile format containing the nr-th generator of a permutation representation on n points. An example is M11G1-p11B0.m1.

Let string be a filename, and format a list [ c₁, c₂, ¼, c_n ] such that each entry c_i is a list of strings and of functions that take a character as their argument and return true or false.

AGRParseFilenameFormat returns a list of strings whose concatenation yields string if string matches format, and fail otherwise. Matching is defined as follows. Splitting string at each - character yields m parts s₁, s₂, ¼, s_m. The string string matches format if s_i matches the conditions in c_i, for 1 £ i £ n, in the sense that scanning s_i backwards yields the strings in c_i, separated by substrings for which each character matches the corresponding functions in c_i.

Let dirname, groupname, and filename be strings, where dirname is one of "datagens", "dataword". If groupname is the ATLAS-file name of a group G (see Group Names Used in the AtlasRep Package), and filename is the name of an accessible file in the dirname directory of the ATLAS, with data concerning G, then FilenameAtlas returns the corresponding filename (see Filename in the GAP Reference Manual), otherwise fail is returned.

A file is regarded as accessible either if it is already stored in the dirname directory of the local installation or if the remote component of the record AtlasOfGroupRepresentationsInfo has value true (see AtlasOfGroupRepresentationsInfo) and the required file is found on one of the relevant servers; in the latter case, the file is transferred to the local directory before FilenameAtlas returns the filename, such that afterwards the file can be read into GAP using Read (see Read in the GAP Reference Manual).

Note that FilenameAtlas does not check whether the table of contents of the ATLAS of Group Representations actually contains filename.

4.6 The Tables Of Contents of the Atlas of Group Representations

The list of data currently available is stored in two tables of contents, one for the local GAP installation, one for the remote servers. They are created and accessed automatically when ReloadAtlasTableOfContents (see ReloadAtlasTableOfContents) is called.

The low level functions used by ReloadAtlasTableOfContents are AtlasTableOfContents, which actually fetches and composes the necessary information, and StringOfAtlasTableOfContents, which translates the filenames into calls of AGRGRP and AGRTOC and creates a string that can be printed to a file. These functions and the utilities for them can be found in the files access.gd and access.gi in the gap directory of the package.

Note that it is assumed that the local data directories contain only files that are also available on servers. Private extensions to the database (cf. Extending the Atlas Database and Chapter Private Extensions of the AtlasRep Package) cannot be handled by putting the data files into the local directories.

The following two administrational functions may be useful for private extensions of the package (see Chapter Private Extensions of the AtlasRep Package).

Let gapname be a string denoting a GAP group name, and atlasname be a string denoting the corresponding ATLAS-file name used in filenames of the ATLAS of Group Representations. AGRGNAN adds the pair [ gapname, atlasname ] to the list AtlasOfGroupRepresentationsInfo.GAPnames (see AtlasOfGroupRepresentationsInfo), making the ATLAS data involving atlasname accessible for the group with name gapname.

Let filename be a string denoting the name of a file containing the generators of a representation written over a proper extension of the rational number field, descr a string describing the field generated by the matrix entries, and F this field itself. AGRFLD adds the triple [ filename, descr, F ] to the list AtlasOfGroupRepresentationsInfo.fieldinfo (see AtlasOfGroupRepresentationsInfo).

4.7 Sanity Checks for the Atlas of Group Representations

The fact that the ATLAS of Group Representations is designed as an open database (see Local or Remote Installation of the AtlasRep Package) makes it especially desirable to have consistency checks available which can be run automatically whenever new data are entered by the developers of the ATLAS. These checks can also be used for the private extensions of the package (see Chapter Private Extensions of the AtlasRep PAckage).

The file atlasrep.tst in the tst directory of the package contains a collection of such sanity checks; one can run them by starting GAP in the tst directory, and then calling ReadTest( "atlasrep.tst" ), see ReadTest in the GAP Reference Manual.

The functions available to perform these tests and detailed information about them can be found in the files test.gd and test.gi in the gap directory of the package.

All these tests apply only to the local table of contents (see The Tables Of Contents of the Atlas of Group Representations), that is, only those data files are checked that are actually available in the local GAP installation.

The examples in this manual are collected in the file docxpl.tst in the tst directory of the package; analogously to the tests mentioned above, one can run them by starting GAP in the tst directory and then calling ReadTest( "docxpl.tst" ).

The file extend.tst in the tst directory contains a few checks of private extensions (see Chapter Private Extensions of the AtlasRep Package). They can be run by starting GAP in the tst directory and then calling ReadTest( "extend.tst" ).

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