% This file was created automatically from technica.msk.
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%W  technica.msk              GAP documentation             Thomas Breuer
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%H  $Id: technica.msk,v 1.16 2002/12/02 15:44:47 gap Exp $
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%Y  Copyright (C) 2001, Lehrstuhl D fuer Mathematik, RWTH Aachen, Germany
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\Chapter{Technicalities of the AtlasRep Package}

This chapter describes those parts of the {\GAP} interface to the
{\ATLAS} of Group Representations that do not belong to the user interface
(cf.~Chapter~"The User Interface of the AtlasRep Package").
Besides global variables used for administrational purposes
(see~"Global Variables Used by the AtlasRep Package")
and some sanity checks
(see~"Sanity Checks for the Atlas of Group Representations"),
they can be regarded as 
the interface between the data actually contained in the files and
the corresponding {\GAP} objects
(see~"Reading and Writing MeatAxe Format Files"
and~"Reading and Writing Atlas Straight Line Programs"),
and the interface between the remote and the local version of the database
(see~"Filenames Used in the Atlas of Group Representations"
and~"The Tables of Contents of the Atlas of Group Representations").
The former interface contains functions to read and write files in
{\MeatAxe} format, which may be interesting for users familiar with
{\MeatAxe} standalones (see for example~\cite{Rin98}).
Other low level functions may be undocumented in the sense that they are
not described in this manual.
Users interested in them may look at the actual implementation in the
`gap' directory of the package, but it may happen that they are changed
in future versions of the package.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\Section{Global Variables Used by the AtlasRep Package}

For debugging purposes, the functions from the {\GAP} interface to the
{\ATLAS} of Group Representations print information depending on the info
level of the info classes `InfoAtlasRep' and `InfoCMeatAxe'
(cf.~"ref:Info Functions" in the {\GAP} Reference Manual).

The info level of an info class can be changed using
`SetInfoLevel' (see~"ref: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> )'.

Information about files being read can be obtained by setting the
value of the global variable `InfoRead1' to `Print'.

\>`InfoAtlasRep' V

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.


\>`InfoCMeatAxe' V

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.




\>`CMeatAxe.FastRead' V

If this component is bound and has the value `true' then `ScanMeatAxeFile'
(see~"ScanMeatAxeFile") reads matrices via `StringFile'
(see~"gapdoc:StringFile" in the {\GAP} Package GapDoc).
Otherwise each file containing a matrix over a finite field is read line by
line via `ReadLine' (see~"ref:ReadLine" in the {\GAP} Reference Manual),
and the {\GAP} matrix is constructed line by line, in a compressed
representation (see~"ref:Row Vectors over Finite Fields"
and~"ref:Matrices over Finite Fields" in the {\GAP} Reference Manual),
which makes it possible to read large matrices in a reasonable amount
of space.
The `StringFile' approach is faster but needs more intermediate space when
matrices over finite fields are read.


\>`AtlasOfGroupRepresentationsInfo' V

`AtlasOfGroupRepresentationsInfo' is a record that is set in the file
`gap/types.g' of the package.
It has the following components.
\beginitems
`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
    (see~"Local or Remote Installation of the AtlasRep Package"),

`compress' &
    \index{gzip}%
    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
    (see~"User Parameters for the AtlasRep Package"),

`wget' (optional) &
    \index{perl}%
    \index{wget}%
    if this is bound to `true' then {\GAP} uses `wget' to fetch data
    files, otherwise `perl' is used
    (see the manual index for references),

`servers' &
    \index{ftp}%
    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
    `ReloadAtlasTableOfContents' (see~"ReloadAtlasTableOfContents"),
    and the values of the components for local data directories are
    created by `AtlasOfGroupRepresentationsNotifyPrivateDirectory'
    (see~"AtlasOfGroupRepresentationsNotifyPrivateDirectory").
\enditems




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\Section{Reading and Writing MeatAxe Format Files}

\index{matrix!{\MeatAxe} format}
\index{permutation!{\MeatAxe} format}

\>ScanMeatAxeFile( <filename>[, <q>] ) F
\>ScanMeatAxeFile( <string>[, <q>], "string" ) F

\index{zcv}
Let <filename> be the name of a {\GAP} readable file (see~"ref: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~\cite{Rin98}),
and let <q> be a prime power.
`ScanMeatAxeFile' returns the corresponding {\GAP} matrix
or list of permutations, respectively.

If the file contains a matrix then the way how it is read depends on the
value of the global variable `CMeatAxe.FastRead'
(see~"Global Variables Used by the AtlasRep Package").
If the parameter <q> is given then the result matrix is represented over
the field with <q> elements.

If the file contains a list of permutations then it is read with
`StringFile' (see~"gapdoc:StringFile" in the {\GAP} package GapDoc);
no parameter <q> is needed in this case.

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~"ref: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.


\>MeatAxeString( <mat>, <q> ) O
\>MeatAxeString( <perms>, <degree> ) O
\>MeatAxeString( <perm>, <q>, <dims> ) O

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 (see~\cite{Rin98}).

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.

When strings are printed to files using `PrintTo' or `AppendTo' then line
breaks are inserted after `SizeScreen()[1]' characters not containing
newline characters
(see~"ref:Operations for Output Streams" in the {\GAP} Reference Manual).
This behaviour is not desirable for creating {\MeatAxe} files.
So the recommended functions for printing the result of `MeatAxeString'
to a file are `FileString' (see~"gapdoc:FileString" in the {\GAP} Package
GapDoc) and `WriteAll'.


\beginexample
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
\endexample

\>FFList( <F> ) F
\>`FFLists' V

`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.


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


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\Section{Reading and Writing Atlas Straight Line Programs}

\>ScanStraightLineProgram( <filename> ) F
\>ScanStraightLineProgram( <string>, "string" ) F

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.
\beginitems
\item{}
`\# <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', $\ldots$, <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',
    $\ldots$, <l>,

`oup <l> <b1> <b2> ... <bl>' &
    means that the next <l> outputs are stored in the labels
    <b1>, <b2>, ... <bl>.
\enditems

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.
For example, an empty file <filename> or an empty string <string>
represent a straight line program with two inputs that are returned as
outputs.

No command (except `cjr') may overwrite its own input.
For example, the line `mu a b a' is not legal. (This is not checked.)

`ScanStraightLineProgram' returns a record containing as the value of its
component `program' the corresponding {\GAP} straight line program
(see~"ref: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~"ref: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.

\begintt
echo "Classes 1A 2A 3A 5A 5B"
oup 5 3 1 2 4 5
\endtt

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'.


\>AtlasStringOfStraightLineProgram( <prog>[, <outputnames>] ) F

For a straight line program <prog> (see~"ref: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.


\beginexample
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
\endexample


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\Section{Data Types Used in the Atlas of Group Representations}

\>AGRDeclareDataType( <kind>, <name>, <record> ) F

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 record that contains the
information about the data will have a component <name> whose value is a
list with the data about the new type.
Examples of <name> are `\"perm\"', `\"matff\"', and `\"classes\"'.

*Compulsory components* of <record> are
\beginitems
`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
    only filenames of the type in question match.

`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 list returned
    by `AGRParseFilenameFormat' for the given type,
    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;
    note that the latter case occurs if the filename matches the format
    description but additional conditions on the parts of the name are
    not satisfied (for example integer parts may be required to be
    positive or prime powers).

`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.
\enditems

*Optional components* of <record> are
\beginitems
`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 `DisplayAtlasInfo' for straight line programs.
    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 returns the list
    of lines (strings) to be printed as the information about the
    available straight line programs of the current type
    and for the given group.
    (The default is to return an empty list.)

`AccessGroupCondition' (for `rep' only) &
    This is used in `DisplayAtlasInfo' 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 function call.
    (The default value is `TOCEntryStringDefault'.)

`PostprocessFileInfo' &
    This is used in the construction of a table of contents via
    `ReloadAtlasTableOfContents', for testing or rearranging the data of
    the current table of contents.
    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 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'
    (see~"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'.
    (see~"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'
    (see~"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'.)
\enditems

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




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\Section{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,
\index{class representatives}
generators of maximal subgroups,
or images of generators under automorphisms
\index{automorphisms}
of a given group $G$ from standard generators of $G$
\index{maximal subgroups}
(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 `<groupname>G<i>', where the integer
<i> denotes the <i>-th set of standard generators for the group $G$, say,
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 `W<n>' means that <n> is the version
number of the straight line program.
\beginitems
`<groupname>G<i>-cycW<n>' &
    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'.

`<groupname>G<i>-cclsW<n>' &
    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'.

`<groupname>G<i>cycW<n>-cclsW<m>' &
    In this case, the file contains a straight line program that takes
    the return value of the program in the file `<groupname>G<i>-cycW<n>'
    (see above),
    and returns a list of conjugacy class representatives of $G$.
    An example is `M11G1cycW1-cclsW1'.

`<groupname>G<i>-max<k>W<n>' &
    In this case, the file contains a 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'.

`<groupname>G<i>max<k>W<n>-<subgroupname>G<j>W<m>' &
    In this case, the file contains a straight line program that takes
    the return value of the program in the file
    `<groupname>G<i>-max<k>W<n>' (see above),
    which are generators for a group $U$, say;
    <subgroupname> is a name for $U$, and the return value is a list of
    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 $J_1$
    consists of groups isomorphic to the linear group $L_2(11)$,
    for which standard generators are defined.

`<groupname>G<i>-a<outname>W<n>' &
    In this case, the file contains a 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 $\alpha$ of $G$ given by the name
    <outname>;
    if this name is empty then $\alpha$ is the unique nontrivial outer
    automorphism of $G$;
    if it is a positive integer $k$ then $\alpha$ is a generator of the
    unique cyclic order $k$ subgroup of the outer automorphism group of
    $G$;
    if it is of the form $2_1$ or $2a$, $4_2$ or $4b$, $3_3$ or $3c$
    $\ldots$ then $\alpha$ generates the cyclic group of automorphisms
    induced on $G$ by $G\.2_1$, $G\.4_2$, $G\.3_3$ $\ldots$;
    finally, if it is of the form `<k>p<d>', 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 $A_5$
    (induced by the action of $S_5$) and the order $2$ automorphisms of
    $L_3(4)$, $U_4(3)$, and $O_8^+(3)$ induced by the actions of
    $L_3(4)\.2_1$, $U_4(3)\.2_2^{\prime}$,
    and $O_8^+(3)\.2_2^{\prime\prime\prime\prime\prime}$, respectively.

`<groupname>G<i>-G<j>W<n>' &
    In this case, the file contains a straight line program that takes
    generators of $G$ w.r.t.~the <i>-th set of standard generators,
    and returns standard generators of $G$ w.r.t.~the <j>-th set of
    standard generators.
    An example is `L35G1-G2W1'.

`<groupname>G<i>-X<descr>W<n>' &
    In this case, the file contains a straight line program that takes
    generators of $G$ w.r.t.~the <i>-th set of standard generators,
    and whose 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").
\enditems

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 lowercase alphabet
letter (see~"ref:IsLowerAlphaChar" in the {\GAP} Reference Manual),
and <m> is a nonnegative integer, meaning that the generators are
written w.r.t.~the <m>-th basis (the meaning is defined by the {\ATLAS}
developers).
\beginitems
`<groupname>G<i>-f<q>r<dim><id>B<m>.m<nr>' &
    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'.

`<groupname>G<i>-p<n><id>B<m>.m<nr>' &
    a file in {\MeatAxe} textfile format
    containing the <nr>-th generator of a permutation representation
    on <n> points.
    An example is `M11G1-p11B0.m1'.

`<groupname>G<i>-Ar<dim><id>B<m>.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'.

`<groupname>G<i>-Zr<dim><id>B<m>.g' &
    a {\GAP} readable file
    containing all generators of a matrix representation
    over the integers, of dimension <dim>.
    An example is `A5G1-Zr4B0.g'.

`<groupname>G<i>-Hr<dim><id>B<m>.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'.

`<groupname>G<i>-Z<n>r<dim><id>B<m>.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'.
\enditems



\>AGRParseFilenameFormat( <string>, <format> ) F

Let <string> be a filename, and <format> be a list
$[ [ c_1, c_2, \ldots, c_n ], [ f_1, f_2, \ldots, f_n ] ]$
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',
and such that each entry $f_i$ is a function for parsing a filename,
such as `ParseForwards' and `ParseBackwards'.

`AGRParseFilenameFormat' returns a list of strings and integers such that
the concatenation of their `String' values yields <string> if <string>
matches <format>, and `fail' otherwise.
Matching is defined as follows.
Splitting <string> at each `-' character yields $m$ parts
$s_1, s_2, \ldots, s_m$.
The string <string> matches <format> if $s_i$ matches the conditions in
$c_i$, for $1 \leq i \leq n$, in the sense that applying $f_i$ to $s_i$
and $c_i$ yields a non-fail result.



\>FilenameAtlas( <dirname>, <groupname>, <filename> ) F

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~"ref: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~"ref:Read" in the {\GAP} Reference Manual).

Note that if a file with name <filename> is already stored in the
<dirname> directory then `FilenameAtlas' does *not* check whether the
table of contents of the {\ATLAS} of Group Representations actually
contains <filename>.




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\Section{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 appropriate function calls for
notifying them, and creates the string that is to 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").

\>AGRGNAN( <gapname>, <atlasname> ) F

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>.

An example of a valid call is
`AGRGNAN(\"A6.2_2\",\"PGL29\")'.



\>AGRFLD( <filename>, <descr> ) F

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, and <descr> be a string describing the field
generated by the matrix entries.
`AGRFLD' adds the triple `[ <filename>, <descr>, <F> ]' to the list
`AtlasOfGroupRepresentationsInfo.fieldinfo'
(see~"AtlasOfGroupRepresentationsInfo"),
where <F> is the field given by <descr>.

An example of a valid call is
`AGRFLD(\"A5G1-Ar3aB0\",\"Field([Sqrt(5)])\")'.




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\Section{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 added 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 `testall.g' in the `tst' directory of the package contains
`ReadTest' (see~"ref:ReadTest" in the {\GAP} Reference Manual) statements
for executing a collection of such sanity checks;
one can run them by starting {\GAP} in the `tst' directory,
and then calling `Read( \"testall.g\" )'.
If no problem occurs then {\GAP} prints only lines starting with one of
the following.
\begintt
+ $Id:
+ GAP4stones:
\endtt

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.
No files are fetched from servers during these tests.

The examples in this manual form a part of these tests,
they are collected in the file `docxpl.tst' in the `tst' directory of the
package.



\>AtlasOfGroupRepresentationsTestFileHeaders( [<tocid>[, <groupname>]] ) F

First suppose that `AtlasOfGroupRepresentationsTestFileHeaders' is called
with two arguments <tocid>, the identifier of a directory
(see~"AtlasOfGroupRepresentationsNotifyPrivateDirectory"), and
<groupname>, a component name in the table of contents of the directory.
The function checks for those data files for <groupname> in the <tocid>
directory that are in {\MeatAxe} text format whether the filename and the
header line are consistent;
it checks the data file in {\GAP} format whether the file name is
consistent with the contents of the file.

If only one argument <tocid> is given then all representations
available for <groupname> are checked with the three argument version.

If only one argument <tocid> is given then all available groups in the
directory with identifier <tocid> are checked;
the contents of the local `dataword' directory can be checked by entering
`\"local\"', which is also the default for <tocid>.

In all cases, the return value is `false' if an error occurred,
and `true' otherwise.


\>AtlasOfGroupRepresentationsTestFiles( [<tocid>[, <groupname>]] ) F

`AtlasOfGroupRepresentationsTestFiles' is an analogue of
`AtlasOfGroupRepresentationsTestFileHeaders'
(see~"AtlasOfGroupRepresentationsTestFileHeaders").
The function does not check if the first line of a {\MeatAxe} file is
consistent with the filename
but checks whether reading the files with `ScanMeatAxeFile' returns
non-`fail' results.

In all cases, the return value is `false' if an error occurred,
and `true' otherwise.


\>AtlasOfGroupRepresentationsTestWords( <tocid> ) F

Called with one argument <tocid>, a string,
`AtlasOfGroupRepresentationsTestWords' reads all straight line programs
that are stored in the directory with identifier <tocid>
(see~"AtlasOfGroupRepresentationsNotifyPrivateDirectory"),
using `ScanStraightLineProgram' (see~"ScanStraightLineProgram"),
and then runs the program on group generators.
The contents of the local `dataword' directory can be checked by entering
`\"local\"'.
The return value is `false' if an error occurs, otherwise `true'.




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%E

