57 Share Libraries

Contributions from people working at Lehrstuhl D, RWTH Aachen, or any other place can become available in GAP3 in two different ways:

1. They can become parts of the main GAP3 library of functions. Their origin will then be rather carefully documented in the respective program files, but will not occur in the description of these functions in the manual. This is e.g. the case -- to mention just one of many such contributions -- with programs for finding composition factors of permutation groups, written by Akos Seress. The reason for this decision about keeping track of the origin of such contributions is that quite often such functions in the main GAP3 library have a complicated history with changes and contributions from various people.

2. On the other hand there are packages written by one or several persons for specific purposes either in the GAP3 language or even in C which are made available en block in GAP3. Such packages will constitute share libraries. A share library will stay under the full responsibility of its author(s), which will be named in the respective chapter in the manual, they will in particular keep the copyright for this package, and they will also have to provide the documentation for it. However provisions will be made to call the functions of such a package like any other GAP3 functions, and to call the documentation via help functions like any other part of the GAP3 documentation. Also these packages will automatically be made available with the main body of GAP3 through ftp and will be sent together with the main body of GAP3 in case we have to fulfill a request to send GAP3 to institutions that cannot obtain GAP3 via electronic networks.

The inclusion of packages as GAP3 share libraries should be negotiated with Lehrstuhl D \fuer Mathematik, RWTH Aachen, for certain standards of the documentation and program organisation that should be met in order to facilitate the use of the packages in the context of GAP3 without problems. A necessary condition for any package to become a GAP3 share library is that it is made available under the conditions formulated in the GAP3 copyright statement, in particular free of any charge, except for refund of expenses for sending, if such occur.

The first section describes how to load a share library package (see RequirePackage).

The next sections describe the ANU pq package and how to install it (see ANU pq Package and Installing the ANU pq Package).

The next sections describe the ANU Sq package and how to install it (see ANU Sq Package and Installing the ANU Sq Package).

The next sections describe the GRAPE package and how to install it (see GRAPE Package and Installing the GRAPE Package).

The next sections describe the MeatAxe package and how to install it (see MeatAxe Package and Installing the MeatAxe Package).

The next sections describe the NQ package and how to install it (see NQ Package and Installing the NQ Package).

The next sections describe the Sisyphos package and how to install it (see SISYPHOS Package and Installing the SISYPHOS Package).

The next sections describe the VE package and how to install it (see Vector Enumeration Package and Installing the Vector Enumeration Package).

The last sections describe the experimental X-Windows interface (see The XGap Package ).

Subsections

57.1 RequirePackage

RequirePackage( name )

RequirePackage will try to initialize the share library name. If the package name is not installed at your site RequirePackage will signal an error. If the package name is already initialized RequirePackage simply returns without any further actions.

    gap> CartanMat( "A", 4 );
    Error, Variable: 'CartanMat' must have a value
    gap> ?CartanMat
    CartanMat ________________________ Root systems and finite Coxeter groups
    
    'CartanMat( <type>, <n> )'
    
    returns the Cartan matrix of Dynkin type  <type> and rank <n>. Admissible
    types are the  strings '"A"',   '"B"',   '"C"',    '"D"',   '"E"',   
    '"F"',    '"G"',   '"H"',   '"I"'.
    
        gap> C := CartanMat( "F", 4 );;
        gap> PrintArray( C );
        [ [   2,  -1,   0,   0 ],
          [  -1,   2,  -1,   0 ],
          [   0,  -2,   2,  -1 ],
          [   0,   0,  -1,   2 ] ]
    
    For type  I_2(m),  which is in fact an infinity of types depending on the
    number  m,  a third argument is needed specifying  the integer  m  so the
    syntax is in fact 'CartanMat(  "I",  2, <m> )':
    
        gap> CartanMat( "I", 2, 5 );
        [ [ 2, E(5)^2+E(5)^3 ], [ E(5)^2+E(5)^3, 2 ] ]
    
    'CartanMat( <type1>, <n1>, ... , <typek>, <nk> )'
                          
    returns the   direct sum  of   'CartanMat( <type1>, <n1> )',   ldots,
    'CartanMat( <typek>, <nk> )'. One can use as argument a computed list of 
    types by 'ApplyFunc( CartanMat, [ <type1>, <n1>, ... , <typek>, <nk> ] )'.
                          
    This function requires the package  "chevie"  (see "RequirePackage").
                          
    gap> RequirePackage( "Chevie" );
    Error, share library "Chevie" is not installed in
    LoadPackage( name ) called from
    RequirePackage( "Chevie" ) called from
    main loop
    brk> quit;
    gap> RequirePackage( "chevie" );
--- Loading package chevie ------- version 4 development of 29Feb2016--------
    If you use this package in your work please cite the authors as follows:
(C) [Jean Michel] The development version of the CHEVIE package of GAP3
     Journal of algebra 435 (2015) 308--336
(C) [Meinolf Geck, Gerhard Hiss, Frank Luebeck, Gunter Malle, Goetz Pfeiffer]
     CHEVIE -- a system for computing and processing generic character tables
     Applicable Algebra in Engineering Comm. and Computing 7 (1996) 175--210

    gap> CartanMat( "A", 4 );;
    gap> PrintArray( last );
    [ [   2,  -1,   0,   0 ],
      [  -1,   2,  -1,   0 ],
      [   0,  -1,   2,  -1 ],
      [   0,   0,  -1,   2 ] ]

57.2 ANU pq Package

The ANU pq provides access to implementations of the following algorithms:

1. A p-quotient algorithm to compute a power-commutator presentation for a group of prime power order. The algorithm implemented here is based on that described in Newman and O'Brien (1996), Havas and Newman (1980), and papers referred to there. Another description of the algorithm appears in Vaughan-Lee (1990). A FORTRAN implementation of this algorithm was programmed by Alford and Havas. The basic data structures of that implementation are retained.

2. A p-group generation algorithm to generate descriptions of groups of prime power order. The algorithm implemented here is based on the algorithms described in Newman (1977) and O'Brien (1990). A FORTRAN implementation of this algorithm was earlier developed by Newman and O'Brien.

3. A standard presentation algorithm used to compute a canonical power-commutator presentation of a p-group. The algorithm implemented here is described in O'Brien (1994).

4. An algorithm which can be used to compute the automorphism group of a p-group. The algorithm implemented here is described in O'Brien (1994).

The following section describes the installation of the ANU pq package, a description of the functions available in the ANU pq package is given in chapter ANU Pq.

A reader interested in details of the algorithms and explanations of terms used is referred to NO96, HN80, OBr90, OBr94, OBr95, New77, Vau84, Vau90a, and Vau90b.

For details about the implementation and the standalone version see the README. This implementation was developed in C by

Eamonn O'Brien
Lehrstuhl D fuer Mathematik
RWTH Aachen

e-mail obrien@math.rwth-aachen.de

57.3 Installing the ANU pq Package

The ANU pq is written in C and the package can only be installed under UNIX. It has been tested on DECstation running Ultrix, a HP 9000/700 and HP 9000/800 running HP-UX, a MIPS running RISC/os Berkeley, a NeXTstation running NeXTSTEP 3.0, and SUNs running SunOS.

If you got a complete binary and source distribution for your machine, nothing has to be done if you want to use the ANU pq for a single architecture. If you want to use the ANU pq for machines with different architectures skip the extraction and compilation part of this section and proceed with the creation of shell scripts described below.

If you got a complete source distribution, skip the extraction part of this section and proceed with the compilation part below.

In the example we will assume that you, as user gap, are installing the ANU pq package for use by several users on a network of two DECstations, called bert and tiffy, and a NeXTstation, called bjerun. We assume that GAP3 is also installed on these machines following the instructions given in Installation of GAP for UNIX.

Note that certain parts of the output in the examples should only be taken as rough outline, especially file sizes and file dates are not to be taken literally.

First of all you have to get the file anupq.zoo (see Getting GAP). Then you must locate the GAP3 directory containing lib/ and doc/, this is usually gap3r4p0 where 0 is to be replaced by the current patch level.

    gap@tiffy:~ > ls -l
    drwxr-xr-x  11 gap     1024 Nov  8  1991 gap3r4p0
    -rw-r--r--   1 gap   360891 Dec 27 15:16 anupq.zoo
    gap@tiffy:~ > ls -l gap3r4p0
    drwxr-xr-x   2 gap     3072 Nov 26 11:53 doc
    drwxr-xr-x   2 gap     1024 Nov  8  1991 grp
    drwxr-xr-x   2 gap     2048 Nov 26 09:42 lib
    drwxr-xr-x   2 gap     2048 Nov 26 09:42 pkg
    drwxr-xr-x   2 gap     2048 Nov 26 09:42 src
    drwxr-xr-x   2 gap     1024 Nov 26 09:42 tst

Unpack the package using unzoo (see Installation of GAP for UNIX). Note that you must be in the directory containing gap3r4p0 to unpack the files. After you have unpacked the source you may remove the archive-file.

    gap@tiffy:~ > unzoo x anupq
    gap@tiffy:~ > cd gap3r4p0/pkg/anupq
    gap@tiffy:../anupq> ls -l
    drwxr-xr-x  5 gap       512 Feb 24 11:17 MakeLibrary
    -rw-r--r--  1 gap     28926 Jun  8 14:21 Makefile
    -rw-r--r--  1 gap      8818 Jun  8 14:21 README
    -rw-r--r--  1 gap       753 Jun 23 18:59 StandardPres
    drwxr-xr-x  2 gap      1024 Jun  8 14:15 TEST
    drwxr-xr-x  2 gap       512 Jun 16 16:03 bin
    drwxr-xr-x  2 gap       512 May 16 06:58 cayley
    drwxr-xr-x  2 gap       512 Jun  8 08:48 doc
    drwxr-xr-x  2 gap      1024 Mar  5 04:01 examples
    drwxr-xr-x  2 gap       512 Jun 23 16:37 gap
    drwxr-xr-x  2 gap       512 Jun 24 10:51 include
    -rw-rw-rw-  1 gap       867 Jun  9 16:12 init.g
    drwxr-xr-x  2 gap      1024 May 21 02:28 isom
    drwxr-xr-x  2 gap       512 May 16 07:58 magma
    drwxr-xr-x  2 gap      6656 Jun 24 11:10 src

Typing make will produce a list of possible target.

gap@tiffy:../anupq > make
usage: 'make <target> EXT=<ext>'  where <target> is one of
'dec-mips-ultrix-gcc2-gmp' for DECstations under Ultrix with gcc/gmp
'dec-mips-ultrix-cc-gmp'   for DECstations under Ultrix with cc/gmp
'dec-mips-ultrix-gcc2'     for DECstations under Ultrix with gcc
'dec-mips-ultrix-cc'       for DECstations under Ultrix with cc
'hp-hppa1.1-hpux-cc-gmp'   for HP 9000/700 under HP-UX with cc/gmp
'hp-hppa1.1-hpux-cc'       for HP 9000/700 under HP-UX with cc
'hp-hppa1.0-hpux-cc-gmp'   for HP 9000/800 under HP-UX with cc/gmp
'hp-hppa1.0-hpux-cc'       for HP 9000/800 under HP-UX with cc
'ibm-i386-386bsd-gcc2-gmp' for IBM PCs under 386BSD with gcc/gmp
'ibm-i386-386bsd-cc-gmp'   for IBM PCs under 386BSD with cc/gmp
'ibm-i386-386bsd-gcc2'     for IBM PCs under 386BSD with gcc2
'ibm-i386-386bsd-cc'       for IBM PCs under 386BSD with cc
'mips-mips-bsd-cc-gmp'     for MIPS under RISC/os Berkeley with cc/gmp
'mips-mips-bsd-cc'         for MIPS under RISC/os Berkeley with cc
'next-m68k-mach-gcc2-gmp'  for NeXT under Mach with gcc/gmp
'next-m68k-mach-cc-gmp'    for NeXT under Mach with cc/gmp
'next-m68k-mach-gcc2'      for NeXT under Mach with gcc
'next-m68k-mach-cc'        for NeXT under Mach with cc
'sun-sparc-sunos-gcc2-gmp' for SUN 4 under SunOs with gcc/gmp
'sun-sparc-sunos-cc-gmp'   for SUN 4 under SunOs with cc/gmp
'sun-sparc-sunos-gcc2'     for SUN 4 under SunOs with gcc2
'sun-sparc-sunos-cc'       for SUN 4 under SunOs with cc
'unix-gmp'                 for a generic unix system with cc/gmp
'unix'                     for a generic unix system with cc
'clean'                    remove all created files

   where <ext> should be a sensible extension, i.e.,
   'EXT=-sun-sparc-sunos' for SUN 4 or 'EXT=' if the PQ only
   runs on a single architecture

   targets are listed according to preference,
   i.e., 'sun-sparc-sunos-gcc2' is better than 'sun-sparc-sunos-cc'.
   additional C compiler and linker flags can be passed with
   'make <target> COPTS=<compiler-opts> LOPTS=<linker-opts>',
   i.e., 'make sun-sparc-sunos-cc COPTS=-g LOPTS=-g'.

   set GAP if gap 3.4 is not started with the command 'gap',
   i.e., 'make sun-sparc-sunos-cc GAP=/home/gap/bin/gap-3.4'.

   in order to use the GNU multiple precision (gmp) set
   'GNUINC' (default '/usr/local/include') and 
   'GNULIB' (default '/usr/local/lib')

Select the target you need. If you have the GNU multiple precision arithmetic (gmp) installed on your system, select the target ending in -gmp. Note that the gmp is not required. In our case we first compile the DECstation version. We assume that the command to start GAP3 is /usr/local/bin/gap for tiffy and bjerun and /rem/tiffy/usr/local/bin/gap for bert.

    gap@tiffy:../anupq > make dec-mips-ultric-cc \ 
                               GAP=/usr/local/bin/gap \ 
			       EXT=-dec-mips-ultrix
    # you will see a lot of messages and a few warnings

Now repeat the compilation for the NeXTstation. Do not forget to clean up.

    gap@tiffy:../anupq > rlogin bjerun
    gap@bjerun:~ > cd gap3r4p0/pkg/anupq
    gap@bjerun:../anupq > make clean
    gap@bjerun:../src > make next-m68k-mach-cc \ 
                             GAP=/usr/local/bin/gap \ 
			     EXT=-next-m68k-mach
    # you will see a lot of messages and a few warnings
    gap@bjerun:../anupq > exit
    gap@tiffy:../anupq >

Switch into the subdirectory bin/ and create a script which will call the correct binary for each machine. A skeleton shell script is provided in bin/pq.sh.

    gap@tiffy:../anupq > cd bin
    gap@tiffy:../bin > cat > pq

!/bin/csh
    switch ( `hostname` )
      case 'tiffy':
        exec $0-dec-mips-ultrix $* ;
        breaksw ;
      case 'bert':
        setenv ANUPQ_GAP_EXEC /rem/tiffy/usr/local/bin/gap ;
        exec $0-dec-mips-ultrix $* ;
        breaksw ;
      case 'bjerun':
        limit stacksize 2048 ;
        exec $0-next-m68k-mach $* ;
        breaksw ;
      default:
        echo "pq: sorry, no executable exists for this machine" ;
        breaksw ;
    endsw

ctr-D

    gap@tiffy:../bin > chmod 755 pq
    gap@tiffy:../bin > cd ..

Note that the NeXTstation requires you to raise the stacksize. If your default limit on any other machine for the stack size is less than 1024 you might need to add the limit stacksize 2048 line.

If the documentation is not already installed or an older version is installed, copy the file gap/anupq.tex into the doc/ directory and run latex again (see Installation of GAP for UNIX). In general the documentation will already be installed so you can just skip the following step.

    gap@tiffy:../anupq > cp gap/anupq.tex ../../doc
    gap@tiffy:../anupq > cd ../../doc
    gap@tiffy:../doc > latex manual
    # a few messages about undefined references
    gap@tiffy:../doc > latex manual
    # a few messages about undefined references
    gap@tiffy:../doc > makeindex manual
    # makeindex prints some diagnostic output
    gap@tiffy:../doc > latex manual
    # there should be no warnings this time
    gap@tiffy:../doc cd ../pkg/anupq

Now it is time to test the installation. The first test will only test the ANU pq.

    gap@tiffy:../anupq > bin/pq < gap/test1.pga
    # a lot of messages ending in
    **************************************************
    Starting group: c3c3

#2;2 #

4;3
    Order: 3^7
    Nuclear rank: 3
    3-multiplicator rank: 4

 of immediate descendants of order 3^8 is 7

 of capable immediate descendants is 5

    **************************************************
    34 capable groups saved on file c3c3_class4
    Construction of descendants took 1.92 seconds

    Select option: 0 
    Exiting from p-group generation

    Select option: 0 
    Exiting from ANU p-Quotient Program
    Total user time in seconds is 1.97
    gap@tiffy:../anupq > ls -l c3c3*
    total 89
    -rw-r--r--    1 gap    3320 Jun 24 11:24 c3c3_class2
    -rw-r--r--    1 gap    5912 Jun 24 11:24 c3c3_class3
    -rw-r--r--    1 gap   56184 Jun 24 11:24 c3c3_class4
    gap:../anupq > rm c3c3_class*

The second test will test the stacksize. If it is too small you will get a memory fault, try to raise the stacksize as described above.

    gap@tiffy:../anupq > bin/pq < gap/test2.pga
    # a lot of messages ending in
    **************************************************
    Starting group: c2c2

#1;1 #1;1 #

1;1
    Order: 2^5
    Nuclear rank: 1
    2-multiplicator rank: 3
    Group c2c2

#1;1 #1;1 #

1;1 is an invalid starting group

    **************************************************
    Starting group: c2c2

#2;1 #1;1 #

1;1
    Order: 2^5
    Nuclear rank: 1
    2-multiplicator rank: 3
    Group c2c2

#2;1 #1;1 #

1;1 is an invalid starting group
    Construction of descendants took 0.47 seconds

    Select option: 0 
    Exiting from p-group generation

    Select option: 0 
    Exiting from ANU p-Quotient Program
    Total user time in seconds is 0.50
    gap@tiffy:../anupq > ls -l c2c2*
    total 45
    -rw-r--r--    1 gap   6228 Jun 24 11:25 c2c2_class2
    -rw-r--r--    1 gap  11156 Jun 24 11:25 c2c2_class3
    -rw-r--r--    1 gap   2248 Jun 24 11:25 c2c2_class4
    -rw-r--r--    1 gap      0 Jun 24 11:25 c2c2_class5
    gap:../anupq > rm c2c2_class*

The third example tests the link between the ANU pq and GAP3. If there is a problem you will get a error message saying Error in system call to GAP; if this happens, check the environment variable ANUPQ_GAP_EXEC.

    gap@tiffy:../anupq > bin/pq < gap/test3.pga
    # a lot of messages ending in
    **************************************************
    Starting group: c5c5

#1;1 #

1;1
    Order: 5^4
    Nuclear rank: 1
    5-multiplicator rank: 2

 of immediate descendants of order 5^5 is 2

    **************************************************
    Starting group: c5c5

#1;1 #

2;2
    Order: 5^5
    Nuclear rank: 3
    5-multiplicator rank: 3

 of immediate descendants of order 5^6 is 3

 of immediate descendants of order 5^7 is 3

 of capable immediate descendants is 1

 of immediate descendants of order 5^8 is 1

 of capable immediate descendants is 1

    **************************************************
    2 capable groups saved on file c5c5_class4

    **************************************************
    Starting group: c5c5

#1;1 #2;2 #

4;2
    Order: 5^7
    Nuclear rank: 1
    5-multiplicator rank: 2

 of immediate descendants of order 5^8 is 2

 of capable immediate descendants is 2

    **************************************************
    Starting group: c5c5

#1;1 #2;2 #

7;3
    Order: 5^8
    Nuclear rank: 2

 of immediate descendants of order 5^9 is 1

 of capable immediate descendants is 1

 of immediate descendants of order 5^10 is 1

 of capable immediate descendants is 1

    **************************************************
    4 capable groups saved on file c5c5_class5
    Construction of descendants took 0.62 seconds

    Select option: 0 
    Exiting from p-group generation

    Select option: 0 
    Exiting from ANU p-Quotient Program
    Total user time in seconds is 0.68
    gap@tiffy:../anupq > ls -l c5c5*
    total 41
    -rw-r--r--    1 gap     924 Jun 24 11:27 c5c5_class2
    -rw-r--r--    1 gap    2220 Jun 24 11:28 c5c5_class3
    -rw-r--r--    1 gap    3192 Jun 24 11:30 c5c5_class4
    -rw-r--r--    1 gap    7476 Jun 24 11:32 c5c5_class5
    gap:../anupq > rm c5c5_class*

The fourth test will test the standard presentation part of the pq.

    gap@tiffy:../anupq > bin/pq -i -k < gap/test4.sp
    # a lot of messages ending in
    Computing standard presentation for class 9 took 0.43 seconds
    The largest 5-quotient of the group has class 9

    Select option: 0 
    Exiting from ANU p-Quotient Program
    Total user time in seconds is 2.17
    gap@tiffy:../anupq > ls -l SPRES
    -rw-r--r--  1 gap     768 Jun 24 11:33 SPRES
    gap@tiffy:../anupq > diff SPRES gap/out4.sp
    # there should be no difference if compiled with -gmp
    156250000
    gap@tiffy:../anupq > rm SPRES

The last test will test the link between GAP3 and the ANU pq. If everything goes well you should not see any message.

    gap@tiffy:../anupq > gap -b
    gap> RequirePackage( "anupq" );
    gap> ReadTest( "gap/anupga.tst" );
    gap>

You may now repeat the tests for the other machines.

57.4 ANU Sq Package

Sq( G, L )

The function Sq is the interface to the Soluble Quotient standalone program.

Let G be a finitely presented group and let L be a list of lists. Each of these lists is a list of integer pairs [p_i,c_i], where p_i is a prime and c_i is a non-negative integer and p_i ≠ p_i+1 and c_i positive for i < k. Sq computes a consistent power conjugate presentation for a finite soluble group given as a quotient of the finitely presented group G which is described by L as follows.

Let H be a group and p a prime. The series

H = P^p₀(H) ≥ P^p₁(H) ≥...\hbox to 1.5 cm\hfil with P^p_i(H) = [P^p_i-1(H),H] (P^p_i-1 (H))^p

for i ≥ 1 is the lower exponent-p central series of H.

For 1 ≤ i ≤ k and 0 ≤ j ≤ c_i define the list L_i,j = [(p₁,c₁),..., (p_i-1,c_i-1),(p_i, j) ]. Define L_1,0(G) = G. For 1 ≤ i ≤ k and 1 ≤ j ≤ c_i define the subgroups

L_i,j(G) = P_j^p_i( L_i,0(G) )

and for 1 ≤ i < k define the subgroups

L_i+1,0(G) = L_{i,c_i}(G)

and L(G) = L_{k,c_k}(G). Note that L_i,j(G) ≥ L_i,j+1(G) holds for j < c_i.

The chain of subgroups

G = L_1,0(G) ≥ L_1,1(G) ≥ ... ≥ L_1,c₁(G) = L_2,0(G) ≥ ... ≥ L_{k,c_k}(G) = L(G)

is called the soluble L-series of G.

Sq computes a consistent power conjugate presentation for G/ L(G), where the presentation exhibits a composition series of the quotient group which is a refinement of the soluble L-series. An epimorphism from G onto G/ L(G) is listed in comments.

The algorithm proceeds by computing power conjugate presentations for the quotients G/ L_i,j(G) in turn. Without loss of generality assume that a power conjugate presentation for G/ L_i,j(G) has been computed for j < c_i. The basic step computes a power conjugate presentation for G/ L_i,j+1(G). The group L_i,j(G)/ L_i,j+1(G) is a p_i-group. If during the basic step it is discovered that L_i,j(G) = L_i,j+1(G), then L_i+1,0(G) is set to L_i,j(G).

Note that during the basic step the vector enumerator is called.

    gap> RequirePackage("anusq");
    gap> f := FreeGroup( "a", "b" );;
    gap> f := f/[ (f.1*f.2)^2*f.2^-6, f.1^4*f.2^-1*f.1*f.2^-9*f.1^-1*f.2 ];
    Group( a, b )
    gap> g := Sq( f, [[2,1],[3,1],[2,2],[3,2]] );
    rec(
      generators := [ a.1, a.2, a.3, a.4, a.5, a.6, a.7, a.8 ],
      relators :=
       [ a.1^2*a.3^-1, a.1^-1*a.2*a.1*a.4^-1*a.2^-2, a.2^3*a.5^-1,
          a.1^-1*a.3*a.1*a.3^-1,
          a.2^-1*a.3*a.2*a.6^-1*a.5^-1*a.4^-1*a.3^-1, a.3^2*a.7^-1*a.5^-1,
          a.1^-1*a.4*a.1*a.7^-1*a.4^-1*a.3^-1,
          a.2^-1*a.4*a.2*a.8^-1*a.7^-1*a.6^-2*a.3^-1,
          a.3^-1*a.4*a.3*a.8^-2*a.7^-2*a.5^-1*a.4^-1,
          a.4^2*a.8^-2*a.7^-2*a.6^-2*a.5^-1,
          a.1^-1*a.5*a.1*a.8^-1*a.7^-1*a.6^-1*a.5^-1,
          a.2^-1*a.5*a.2*a.5^-1, a.3^-1*a.5*a.3*a.8^-2*a.6^-1*a.5^-1,
          a.4^-1*a.5*a.4*a.7^-1*a.5^-1, a.5^2,
          a.1^-1*a.6*a.1*a.8^-1*a.7^-2*a.6^-1,
          a.2^-1*a.6*a.2*a.8^-2*a.6^-2,
          a.3^-1*a.6*a.3*a.8^-2*a.7^-2*a.6^-2,
          a.4^-1*a.6*a.4*a.8^-1*a.7^-2, a.5^-1*a.6*a.5*a.8^-2*a.6^-2,
          a.6^3, a.1^-1*a.7*a.1*a.6^-2, a.2^-1*a.7*a.2*a.7^-2*a.6^-2,
          a.3^-1*a.7*a.3*a.8^-1*a.7^-1*a.6^-2, a.4^-1*a.7*a.4*a.6^-1,
          a.5^-1*a.7*a.5*a.7^-2, a.6^-1*a.7*a.6*a.8^-1*a.7^-1, a.7^3,
          a.1^-1*a.8*a.1*a.8^-2, a.2^-1*a.8*a.2*a.8^-1,
          a.3^-1*a.8*a.3*a.8^-1, a.4^-1*a.8*a.4*a.8^-1,
          a.5^-1*a.8*a.5*a.8^-1, a.6^-1*a.8*a.6*a.8^-1,
          a.7^-1*a.8*a.7*a.8^-1, a.8^3 ] )

This implementation was developed in C by

Alice C. Niemeyer
Department of Mathematics
University of Western Australia
Nedlands, WA 6009
Australia

email:: alice@maths.uwa.edu.au

57.5 Installing the ANU Sq Package

The ANU Sq is written in C and the package can only be installed under UNIX. It has been tested on DECstation running Ultrix, a HP 9000/700 and HP 9000/800 running HP-UX, a MIPS running RISC/os Berkeley, a PC running NnetBSD 0.9, and SUNs running SunOS.

It requires Steve Linton's vector enumerator (either as standalone or as GAP share library). Make sure that it is installed before trying to install the ANU Sq.

If you have a complete binary and source distribution for your machine, nothing has to be done if you want to use the ANU Sq for a single architecture. If you want to use the ANU Sq for machines with different architectures skip the extraction and compilation part of this section and proceed with the creation of shell scripts described below.

If you have a complete source distribution, skip the extraction part of this section and proceed with the compilation part below.

In the example we will assume that you, as user gap, are installing the ANU Sq package for use by several users on a network of two DECstations, called bert and tiffy, and a Sun running SunOS 5.3, called galois. We assume that GAP3 is also installed on these machines following the instructions given in Installation of GAP for UNIX.

Note that certain parts of the output in the examples should only be taken as rough outline, especially file sizes and file dates are not to be taken literally.

First of all you have to get the file anusq.zoo (see Getting GAP). Then you must locate the GAP3 directory containing lib/ and doc/, this is usually gap3r4p0 where 0 is to be replaced by the current patch level.

    gap@tiffy:~ > ls -l
    drwxr-xr-x  11 gap     1024 Nov  8  1991 gap3r4p0
    -rw-r--r--   1 gap   360891 Dec 27 15:16 anusq.zoo
    gap@tiffy:~ > ls -l gap3r4p0
    drwxr-xr-x   2 gap     3072 Nov 26 11:53 doc
    drwxr-xr-x   2 gap     1024 Nov  8  1991 grp
    drwxr-xr-x   2 gap     2048 Nov 26 09:42 lib
    drwxr-xr-x   2 gap     2048 Nov 26 09:42 pkg
    drwxr-xr-x   2 gap     2048 Nov 26 09:42 src
    drwxr-xr-x   2 gap     1024 Nov 26 09:42 tst

    gap@tiffy:~ > unzoo x anusq
    gap@tiffy:~ > cd gap3r4p0/pkg/anusq
    gap@tiffy:../anusq> ls -l
    -rw-r--r--   1 gap     5232 Apr 10 12:40 Makefile
    -rw-r--r--   1 gap    13626 Mar 28 16:31 README
    drwxr-xr-x   2 gap      512 Apr 10 13:30 bin
    drwxr-xr-x   2 gap      512 Apr  9 20:28 examples
    drwxr-xr-x   2 gap      512 Apr 10 14:22 gap
    -rw-r--r--   1 gap     5272 Apr 10 13:34 init.g
    drwxr-xr-x   2 gap     1024 Apr 10 13:41 src
    -rwxr-xr-x   1 gap      525 Mar 28 15:50 testSq

Typing make will produce a list of possible target.

    gap@tiffy:../anusq > make
    usage: 'make <target> EXT=<ext>'  where <target> is one of
    'bsd-gcc'    for Berkeley UNIX with GNU cc 2
    'bsd-cc'     for Berkeley UNIX with cc
    'usg-gcc'    for System V UNIX with cc
    'usg-cc'     for System V UNIX with cc
    'clean'      remove all created files

       where <ext> should be a sensible extension, i.e.,
       'EXT=-sun-sparc-sunos' for SUN 4 or 'EXT=' if the SQ only
       runs on a single architecture

       additional C compiler and linker flags can be passed with
       'make <target> COPTS=<compiler-opts> LOPTS=<linker-opts>',
       i.e., 'make bsd-cc COPTS="-DTAILS -DCOLLECT"', see the
       README file for details on TAILS and COLLECT.

       set ME if the vector enumerator is not started with the
       command '`pwd`/../ve/bin/me',
       i.e., 'make bsd-cc ME=/home/ve/bin/me'.

Select the target you need. The DECstations are running Ultrix, so we chose bsd-gcc.

    gap@tiffy:../anusq > make bsd-gcc EXT=-dec-mips-ultrix
    # you will see a lot of messages

Now repeat the compilation for the Sun run SunOS 5.3. Do not forget to clean up.

    gap@tiffy:../anusq > rlogin galois
    gap@galois:~ > cd gap3r4p0/pkg/anusq
    gap@galois:../anusq > make clean
    gap@galois:../src > make usg-cc EXT=-sun-sparc-sunos
    # you will see a lot of messages and a few warnings
    gap@galois:../anusq > exit
    gap@tiffy:../anusq >

Switch into the subdirectory bin/ and create a script which will call the correct binary for each machine. A skeleton shell script is provided in bin/Sq.sh.

    gap@tiffy:../anusq > cd bin
    gap@tiffy:../bin > cat > sq

!/bin/csh
    switch ( `hostname` )
      case 'tiffy':
        exec $0-dec-mips-ultrix $* ;
        breaksw ;
      case 'bert':
        setenv ANUSQ_ME_EXEC /rem/tiffy/usr/local/bin/me ;
        exec $0-dec-mips-ultrix $* ;
        breaksw ;
      case 'galois':
        exec $0-sun-sparc-sunos $* ;
        breaksw ;
      default:
        echo "sq: sorry, no executable exists for this machine" ;
        breaksw ;
    endsw

ctr-D

    gap@tiffy:../bin > chmod 755 Sq
    gap@tiffy:../bin > cd ..

Now it is time to test the installation. The first test will only test the ANU Sq.

    gap@tiffy:../anusq > ./testSq
    Testing examples/grp1.fp  . . . . . . . . succeeded
    Testing examples/grp2.fp  . . . . . . . . succeeded
    Testing examples/grp3.fp  . . . . . . . . succeeded

If there is a problem and you get an error message saying me not found, set the environment variable ANUSQ_ME_EXEC to the module enumerator executable and try again.

The second test will test the link between GAP3 and the ANU Sq. If everything goes well you should not see any message.

    gap@tiffy:../anusq > gap -b
    gap> RequirePackage( "anusq" );
    gap> ReadTest( "gap/test1.tst" );
    gap>

You may now repeat the tests for the other machines.

57.6 GRAPE Package

GRAPE (Version 2.2) is a system for computing with graphs, and is primarily designed for constructing and analysing graphs related to groups and finite geometries.

The vast majority of GRAPE functions are written entirely in the GAP3 language, except for the automorphism group and isomorphism testing functions, which use Brendan McKay's \nauty (Version 1.7) package Nau90.

Except for the \nauty 1.7 package included with GRAPE, the GRAPE system was designed and written by Leonard H. Soicher, School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London E1 4NS, U.K., email: L.H.Soicher@qmw.ac.uk.

Please tell Leonard Soicher if you install GRAPE. Also, if you use GRAPE to solve a problem then also tell him about it, and reference

L.H.Soicher, GRAPE: a system for computing with graphs and groups, in Groups and Computation (L. Finkelstein and W.M. Kantor, eds.), DIMACS Series in Discrete Mathematics and Theoretical Computer Science 11, pp. 287--291.

If you use the automorphism group and graph isomorphism testing functions of GRAPE then you are also using Brendan McKay's \nauty package, and should also reference

B.D.McKay, \nauty users guide (version 1.5), Technical Report TR-CS-90-02, Computer Science Department, Australian National University, 1990.

This document is in nauty17/nug.alw in postscript form. There is also a readme for \nauty in nauty17/read.me.

Warning A canonical labelling given by \nauty can depend on the version of \nauty (Version 1.7 in GRAPE 2.2), certain parameters of \nauty (always set the same by GRAPE 2.2) and the compiler and computer used. If you use a canonical labelling (say by using the IsIsomorphicGraph function) of a graph stored on a file, then you must be sure that this field was created in the same environment in which you are presently computing. If in doubt, unbind the canonicalLabelling field of the graph.

The only incompatible changes from GRAPE 2.1 to GRAPE 2.2 are that Components is now called ConnectedComponents, and Component is now called ConnectedComponent, and only works for simple graphs.

GRAPE is provided "as is", with no warranty whatsoever. Please read the copyright notice in the file COPYING.

Please send comments on GRAPE, bug reports, etc. to L.H.Soicher@qmw.ac.uk.

57.7 Installing the GRAPE Package

GRAPE consists of two parts. The first part is a set of GAP3 functions for constructing and analysing graphs, which will run on any machine that supports GAP3. The second part is based on the \nauty package written in C and computes automorphism groups of graphs, and tests for graph isomorphisms. This part of the package can only be installed under UNIX.

If you got a complete binary and source distribution for your machine, nothing has to be done if you want to use GRAPE for a single architecture. If you want to use GRAPE for machines with different architectures skip the extraction and compilation part of this section and proceed with the creation of shell scripts described below.

If you got a complete source distribution, skip the extraction part of this section and proceed with the compilation part below.

In the example we will assume that you, as user gap, are installing the GRAPE package for use by several users on a network of two DECstations, called bert and tiffy, and a PC running 386BSD, called waldorf. We assume that GAP3 is also installed on these machines following the instructions given in Installation of GAP for UNIX.

Note that certain parts of the output in the examples should only be taken as rough outline, especially file sizes and file dates are not to be taken literally.

First of all you have to get the file grape.zoo (see Getting GAP). Then you must locate the GAP3 directories containing lib/ and doc/, this is usually gap3r4p0 where 0 is to be replaced by current the patch level.

    gap@tiffy:~ > ls -l
    drwxr-xr-x  11 gap      gap          1024 Nov  8  1991 gap3r4p0
    -rw-r--r--   1 gap      gap        342865 May 27 15:16 grape.zoo
    gap@tiffy:~ > ls -l gap3r4p0
    drwxr-xr-x   2 gap      gap          3072 Nov 26 11:53 doc
    drwxr-xr-x   2 gap      gap          1024 Nov  8  1991 grp
    drwxr-xr-x   2 gap      gap          2048 Nov 26 09:42 lib
    drwxr-xr-x   2 gap      gap          2048 Nov 26 09:42 src
    drwxr-xr-x   2 gap      gap          1024 Nov 26 09:42 tst

    gap@tiffy:~ > unzoo x grape.zoo
    gap@tiffy:~ > ls -l gap3r4p0/pkg/grape
    -rw-r--r--    1 gap   1063 May 22 14:40 COPYING
    -rw-r--r--    1 gap   2636 May 28 09:58 Makefile
    -rw-r--r--    1 gap   4100 May 24 14:57 README
    drwxr-xr-x    2 gap    512 May 28 11:36 bin
    drwxr-xr-x    2 gap    512 May 25 14:52 doc
    drwxr-xr-x    2 gap    512 May 22 16:59 grh
    -rw-r--r--    1 gap  82053 May 27 12:19 init.g
    drwxr-xr-x    2 gap    512 May 27 14:18 lib
    drwxr-xr-x    2 gap    512 May 28 11:36 nauty17
    drwxr-xr-x    2 gap    512 May 22 12:32 prs
    drwxr-xr-x    2 gap    512 May 28 11:36 src

You are now able to use the all functions described in chapter Grape except AutGroupGraph and IsIsomorphicGraph which use the \nauty package.

    gap> RequirePackage("grape");

    Loading  GRAPE 2.2  (GRaph Algorithms using PErmutation groups),
    by L.H.Soicher@qmw.ac.uk.

    gap> gamma := JohnsonGraph( 4, 2 );
    rec(
      isGraph := true,
      order := 6,
      group := Group( (1,5)(2,6), (1,3)(4,6), (2,3)(4,5) ),
      schreierVector := [ -1, 3, 2, 3, 1, 2 ],
      adjacencies := [ [ 2, 3, 4, 5 ] ],
      representatives := [ 1 ],
      names := [ [ 1, 2 ], [ 1, 3 ], [ 1, 4 ], [ 2, 3 ], [ 2, 4 ],
          [ 3, 4 ] ],
      isSimple := true )

If the documentation is not already installed or an older version is installed, copy the file doc/grape.tex into the doc/ directory and run latex again (see Installation of GAP for UNIX). In general the documentation will already be installed so you can just skip the following step.

    gap@tiffy:~ > cd gap3r4p0/pkg/grape
    gap@tiffy:../grape > cp doc/grape.tex ../../doc
    gap@tiffy:../grape > cd ../../doc
    gap@tiffy:../doc > latex manual
    # a few messages about undefined references
    gap@tiffy:../doc > latex manual
    # a few messages about undefined references
    gap@tiffy:../doc > makeindex manual
    # makeindex prints some diagnostic output
    gap@tiffy:../doc > latex manual
    # there should be no warnings this time
    gap@tiffy:../doc cd ../pkg/grape

In order to compile \nauty and the filters used by GRAPE to interact with \nauty type make to get a list of support machines.

    gap@tiffy:../grape > make
    usage: 'make <target>' EXT=<ext> where target is one of
    'dec-mips-ultrix-cc'   for DECstations running Ultrix with cc
    'hp-hppa1.1-hpux-cc'   for HP 9000/700 under HP-UX with cc
    'hp-hppa1.0-hpux-cc'   for HP 9000/800 under HP-UX with cc
    'ibm-i386-386bsd-gcc2' for IBM PCs under 386BSD with GNU cc 2
    'ibm-i386-386bsd-cc'   for IBM PCs under 386BSD with cc (GNU)
    'sun-sparc-sunos-cc'   for SUN 4 under SunOS with cc
    'bsd'                  for others under Berkeley UNIX with cc
    'usg'                  for others under System V UNIX with cc

    where <ext> should be a sensible extension, i.e.,
    'EXT=.sun' for SUN or 'EXT=' if GRAPE only runs
    on a single architecture

Select the target you need. In your case we first compile the DECstation version. We use the extension -dec-mips-ultrix, which creates the binaries
dreadnaut-dec-mips-ultrix, drcanon3-dec-mips-ultrix,
gap3todr-dec-mips-ultrix and drtogap3-dec-mips-ultrix
in the bin/ directory.

    gap@tiffy:../grape > make dec-mips-ultric-cc EXT=-dec-mips-ultrix
    # you will see a lot of messages

Now repeat the compilation for the PC. Do not forget to clean up.

    gap@tiffy:../grape > rlogin waldorf
    gap@waldorf:~ > cd gap3r4p0/pkg/grape
    gap@waldorf:../grape > make clean
    gap@waldorf:../grape > make ibm-i386-386bsd-gcc2 EXT=-ibm-i386-386bsd
    # you will see a lot of messages
    gap@waldorf:../grape > exit
    gap@tiffy:../grape >

Switch into the subdirectory bin/ and create four shell scripts which will call the correct binary for each machine. Skeleton shell scripts are provided in bin/dreadnaut.sh, bin/drcanon3.sh, etc.

    gap@tiffy:../grape > cat > bin/dreadnaut

!/bin/csh
    switch ( `hostname` )
      case 'tiffy':
      case 'bert':
        exec $0-dec-mips-ultrix $* ;
        breaksw ;
      case 'waldorf':
        exec $0-ibm-i386-386bsd $* ;
        breaksw ;
      default:
        echo "dreadnaut: sorry, no executable exists for this machine" ;
        breaksw ;
    endsw

ctr-D

    gap@tiffy:../grape > chmod 755 bin/dreadnaut

You must also create similar shell scripts for drcanon3, drtogap3, and gap3todr. Note that if you are using GRAPE only on a single architecture you can specify an empty extension using EXT= as a parameter to make. In this case do not create the above shell scripts. The following example will test the interface between GRAPE and \nauty.

    gap> IsIsomorphicGraph( JohnsonGraph(7,3), JohnsonGraph(7,4) );
    true
    gap> AutGroupGraph( JohnsonGraph(4,2) );
    Group( (3,4), (2,3)(4,5), (1,2)(5,6) )

57.8 MeatAxe Package

The MeatAxe package provides algorithms for computing with finite field matrices, permutations, matrix groups, matrix algebras, and their modules.

Every such object exists outside GAP3 on a file, and GAP3 is only responsible for handling these files using the appropriate programs.

Details about the standalone can be found in Rin93. This implementation was developed in C by

Michael Ringe
Lehrstuhl D für Mathematik
RWTH Aachen
52062 Aachen, Germany

e-mail mringe@math.rwth-aachen.de

57.9 Installing the MeatAxe Package

The MeatAxe is written in C, and it is assumed that the package is installed under UNIX. Some other systems --currently MS-DOS and VM/CMS-- are supported, but this applies only for the standalone and not for the use of the MeatAxe from within GAP3 (see the MeatAxe manual Rin93 for details of the installation in these cases).

If you got a complete binary and source distribution, skip the extraction and compilation part of this section. All what you have to do in this case is to make the executables accessible via a pathname that contains the hostname of the machine; this is best done by creating suitable links, as is described at the end of this section.

If you got a complete source distribution, skip the extraction part of this section and proceed with the compilation part below.

In the example we will assume that you, as user gap, are installing the MeatAxe package for use by several users on a network of two DECstations, called bert and tiffy, and a NeXTstation, called bjerun. We assume that GAP3 is also installed on these machines following the instructions given in Installation of GAP for UNIX.

Note that certain parts of the output in the examples should only be taken as rough outline, especially file sizes and file dates are not to be taken literally.

First of all you have to get the file meataxe.zoo (see Getting GAP). Then you must locate the GAP3 directory containing lib/ and doc/, this is usually gap3r4p0 where 0 is to be be replaced by the patch level.

    gap@tiffy:~ > ls -l
    drwxr-xr-x  11 gap      gap          1024 Nov  8  1991 gap3r4p0
    -rw-r--r--   1 gap      gap        359381 May 11 11:34 meataxe.zoo
    gap@tiffy:~ > ls -l gap3r4p0
    drwxr-xr-x    2 gap          3072 Nov 26 11:53 doc
    drwxr-xr-x    2 gap          1024 Nov  8  1991 grp
    drwxr-xr-x    2 gap          2048 Nov 26 09:42 lib
    drwxr-xr-x    2 gap          2048 Nov 26 09:42 src
    drwxr-xr-x    2 gap          1024 Nov 26 09:42 tst

    gap@tiffy:~ > unzoo x meataxe.zoo
    gap@tiffy:~ > ls -l gap3r4p0/pkg/meataxe
    -rw-r--r--    1 gap         17982 Aug  6  1993 COPYING
    -rw-r--r--    1 gap          3086 Mar 15 15:07 README
    drwxr-xr-x    3 gap           512 Mar 26 18:01 bin
    drwxr-xr-x    2 gap           512 Feb 25 12:07 doc
    drwxr-xr-x    2 gap           512 May 11 09:34 gap
    -rw-r--r--    1 gap          1023 May 11 09:34 init.g
    drwxr-xr-x    2 gap          1024 Mar 26 18:02 lib
    drwxr-xr-x    2 gap          1536 Mar 26 18:02 src
    drwxr-xr-x    2 gap           512 Mar 15 11:36 tests

Switch into the directory bin/, edit the Makefile, and follow the instructions given there. In most cases it will suffice to choose the right COMPFLAGS. Then type make to compile the MeatAxe. In your case we first compile the DECstation version.

    gap@tiffy:~ > cd gap3r4p0/pkg/meataxe/bin
    gap@tiffy:../bin > make

# you will see a lot of messages

The executables reside in a directory with the same name as the host, in this case this is tiffy. The programs will be called from GAP3 using the hostname, thus for every machine that shall run the MeatAxe under GAP3 such a directory is necessary. In your case there is a second DEC-station called bert which can use the same executables, we make them available via a link.

gap@tiffy:../bin > ln -s tiffy bert

Now repeat the compilation for the NeXTstation. If you want to save space you can clean up using make clean but this is not necessary. If the make run was interrupted you can return to the prior situation using make delete, and then call make again.

    gap@tiffy:../bin > rlogin bjerun
    gap@bjerun:~ > cd gap3r4p0/pkg/meataxe/bin
    gap@bjerun:../bin > make clean
    gap@bjerun:../bin > make

 you will see a lot of messages
    gap@bjerun:../bin > exit
    gap@tiffy:../bin >

Now it is time to test the package. Switch into the directory ../tests/ and type ./testmtx. You should get no error messages, and end up with the message all tests passed.

    gap@tiffy:../bin > cd ../tests
    gap@tiffy:../tests > ./testmtx

 you will see a lot of messages
    gap@tiffy:../tests >

57.10 NQ Package

NilpotentQuotient( F )
NilpotentQuotient( F, c )

NilpotentQuotient computes the quotient groups of the finitely presented group F successively modulo the terms of the lower central series of F. If it terminates, it returns a list L. The i-th entry of L contains the non-trivial abelian invariants of the i-th factor of the lower central series of F (the largest abelian quotient being the first factor).

NilpotentQuotient accepts a positive integer c as an optional second argument. If the second argument is present, the function computes the quotient group of F modulo the c-th term of the lower central series of F (the commutator subgroup is the first term).

    gap> RequirePackage("nq");
    gap> a := AbstractGenerator( "a" );;
    gap> b := AbstractGenerator( "b" );;
    gap>
    gap> G := rec( generators := [a, b],
    >     relators   := [ LeftNormedComm( b,a,a,a,a ),
    >                     LeftNormedComm( b,a,b,b,b ),
    >                     LeftNormedComm( b,a,a*b,a*b,a*b ),
    >                     LeftNormedComm( b,a,a*b^2,a*b^2,a*b^2 ),
    >                     LeftNormedComm( b,a,b,a,a,a ),
    >                     LeftNormedComm( b,a,a,b,b,b ) ]
    >    );;
    gap>
    gap> NilpotentQuotient( G, 6 );
    [ [ 0, 0 ], [ 0 ], [ 0, 0 ], [ 0, 0, 0 ], [ 2, 0, 0 ], [ 2, 10, 0 ] ]

This implementation was developed in C by

Werner Nickel
School of Mathematical Sciences
Australian National University
Canberra, ACT 0200

e-mail werner@pell.anu.edu.au

57.11 Installing the NQ Package

The NQ is written in C and the package can only be installed under UNIX. It has been tested on DECstation running Ultrix, a NeXTstation running NeXT-Step 3.0, and SUNs running SunOS. It requires the GNU multiple precision arithmetic. Make sure that this library is installed before trying to install the NQ.

If you got a complete binary and source distribution for your machine, nothing has to be done if you want to use the NQ for a single architecture. If you want to use the NQ for machines with different architectures skip the extraction and compilation part of this section and proceed with the creation of shell scripts described below.

If you got a complete source distribution, skip the extraction part of this section and proceed with the compilation part below.

In the example we will assume that you, as user gap, are installing the NQ package for use by several users on a network of two DECstations, called bert and tiffy, and a NeXTstation, called bjerun. We assume that GAP3 is also installed on these machines following the instructions given in Installation of GAP for UNIX.

Note that certain parts of the output in the examples should only be taken as rough outline, especially file sizes and file dates are not to be taken literally.

First of all you have to get the file nq.zoo (see Getting GAP). Then you must locate the GAP3 directories containing lib/ and doc/, this is usually gap3r4p0 where 0 is to be be replaced by the patch level.

    gap@tiffy:~ > ls -l
    drwxr-xr-x  11 gap      gap          1024 Nov  8  1991 gap3r4p0
    -rw-r--r--   1 gap      gap        106307 Jan 24 15:16 nq.zoo
    gap@tiffy:~ > ls -l
    drwxr-xr-x   2 gap      gap          3072 Nov 26 11:53 doc
    drwxr-xr-x   2 gap      gap          1024 Nov  8  1991 grp
    drwxr-xr-x   2 gap      gap          2048 Nov 26 09:42 lib
    drwxr-xr-x   2 gap      gap          2048 Nov 26 09:42 src
    drwxr-xr-x   2 gap      gap          1024 Nov 26 09:42 tst

    gap@tiffy:~ > unzoo x nq.zoo
    gap@tiffy:~ > ls -l gap3r4p0/pkg/nq
    drwxr-xr-x   2 gap    gap      1024 Jan 24 21:00 bin
    drwxr-xr-x   2 gap    gap      1024 Jan 19 11:33 examples
    drwxr-xr-x   2 gap    gap      1024 Jan 24 21:03 gap
    lrwxrwxrwx   1 gap    gap         8 Jan 19 11:33 init.g
    drwxr-xr-x   2 gap    gap      1024 Jan 24 21:04 src
    -rwxr--r--   1 gap    gap       144 Dec 28 15:08 testNq

Switch into the directory src/ and type make to compile the NQ. If the header files for the GNU multiple precision arithmetic are not in /usr/local/include you must set GNUINC to the correct directory. If the library for the GNU multiple precision arithmetic is not /usr/local/lib/libmp.a you must set GNULIB. In your case we first compile the DECstation version. If your operating system does not provide a function getrusage start make with COPTS=-DNO_GETRUSAGE.

    gap@tiffy:~ > cd gap3r4p0/pkg/nq/src
    gap@tiffy:../src > make GNUINC=/usr/gnu/include \ 
                            GNULIB=/usr/gnu/lib/libmp.a

# you will see a lot of messages

Now it is possible to test the standalone.

    gap@tiffy:../src > cd ..
    gap@tiffy:../nq > testNq

If testNq reports a difference others then machine name, runtime or size, check the GNU multiple precision arithmetic and warnings generated by make. If testNq succeeded , move the executable to the bin/ directory.

gap@tiffy:../nq > mv src/nq bin/nq-dec-mips-ultrix

Now repeat the compilation for the NeXTstation. Do not forget to clean up.

    gap@tiffy:../nq > rlogin bjerun
    gap@bjerun:~ > cd gap3r4p0/pkg/nq/src
    gap@bjerun:../src > make clean
    gap@bjerun:../src > make

 you will see a lot of messages
    gap@bjerun:../src > mv nq ../bin/nq-next-m68k-mach
    gap@bjerun:../src > exit
    gap@tiffy:../src >

Switch into the subdirectory bin/ and create a script which will call the correct binary for each machine. A skeleton shell script is provided in bin/nq.sh.

    gap@tiffy:../src > cd ..
    gap@tiffy:../nq > cat > bin/nq

!/bin/csh
    switch ( `hostname` )
      case 'bert':
      case 'tiffy':
        exec $0-dec-mips-ultrix $* ;
        breaksw ;
      case 'bjerun':
        exec $0-next-m68k-mach $* ;
        breaksw ;
      default:
        echo "nq: sorry, no executable exists for this machine" ;
        breaksw ;
    endsw

ctr-D

    gap@tiffy:../nq > chmod 755 bin/nq

Now it is time to test the package. Assuming that testNq worked the following will test the link to GAP3.

    gap@tiffy:../nq > gap -b
    gap> RequirePackage( "nq" );
    gap> ReadTest( "gap/nq.tst" );
    gap>

57.12 SISYPHOS Package

Sisyphos provides access to implementations of algorithms for dealing with p-groups and their modular group algebras. At the moment only the programs for p-groups are accessible via GAP3. They can be used to compute isomorphisms between p-groups, and automorphism groups of p-groups.

The description of the functions available in the Sisyphos package is given in chapter Sisyphos.

For details about the implementation and the standalone version see the README. This implementation was developed in C by

Martin Wursthorn
Math. Inst. B, 3. Lehrstuhl
Universität Stuttgart

e-mail pluto@machnix.mathematik.uni-stuttgart.de

Tel.:: +49 (0)711 685 5517
Fax.: +49 (0)711 685 5322

57.13 Installing the SISYPHOS Package

Sisyphos is written in ANSI-C and should run on every UNIX system (and some non-UNIX systems) that provides an ANSI-C Compiler, e.g., the GNU C compiler. Sisyphos has been ported to IBM RS6000 running AIX 3.2, HP9000 7xx running HP-UX 8.0/9.0, PC 386/486 running Linux, PC 386/486 running DOS or OS/2 with emx and ATARI ST/TT running TOS.

In the example we will assume that you, as user gap, are installing the Sisyphos package for use by several users on a network of two DECstations, called bert and tiffy, and a 486 PC, called waldorf. We assume that GAP3 is also installed on these machines following the instructions given in Installation of GAP for UNIX.

Note that certain parts of the output in the examples should only be taken as rough outline, especially file sizes and file dates are not to be taken literally.

First of all you have to get the file sisyphos.zoo (see Getting GAP). Then you must locate the GAP3 directories containing lib/ and doc/, this is usually gap3r4p0 where 0 is to be be replaced by the patch level.

    gap@tiffy:~ > ls -l
    drwxr-xr-x  11 gap     1024 Nov  8  1991 gap3r4p0
    -rw-r--r--   1 gap   245957 Dec 27 15:16 sisyphos.zoo
    gap@tiffy:~ > ls -l gap3r4p0
    drwxr-xr-x   2 gap     3072 Nov 26 11:53 doc
    drwxr-xr-x   2 gap     1024 Nov  8  1991 grp
    drwxr-xr-x   2 gap     2048 Nov 26 09:42 lib
    drwxr-xr-x   2 gap     2048 Nov 26 09:42 src
    drwxr-xr-x   2 gap     1024 Nov 26 09:42 tst

    gap@tiffy:~ > unzoo x sisyphos.zoo
    gap@tiffy:~ > ls -l gap3r4p0/pkg/sisyphos
    -rw-r--r--  1 gap          9496 Feb 11  1993 README
    drwxr-xr-x  3 gap           512 Oct 19 10:24 doc
    drwxr-xr-x  2 gap           512 Oct 15 14:30 groups
    drwxr-xr-x  2 gap           512 Apr  1  1993 ideal
    -rw-r--r--  1 gap         22072 Oct 19 10:23 init.g
    drwxr-xr-x  2 gap          1536 Oct 15 14:49 src

Switch into the directory src/. It contains the makefile for Sisyphos.

gap@tiffy:../src > make
usage: 'make <target>'  where target is one of
'hp700-hpux-gcc2'    for HP 9000/7xx under HP-UX with GNU cc 2
'hp700-hpux-cc'      for HP 9000/7xx under HP-UX with cc
'hp700-hpux-cci'     for HP 9000/7xx under HP-UX with cc -
                       generate version for profile dependent optimization
'hp700-hpux-ccp'     for HP 9000/7xx under HP-UX with cc -
                       relink with profile dependent optimization
'ibm6000-aix-cc'     for IBM RS/6000 under AIX with cc
'ibmpc-linux-gcc2'   for IBM PCs under Linux with GNU cc 2
'ibmpc-emx-gcc2'     for IBM PCs under DOS or OS/2 2.0 with emx
'generic-unix-gcc2'  for other UNIX machines with GNU cc 2
                     this should work on most machines

Select the target you need. In our case we first compile the DECstation version. We assume that the command to start GAP3 is /usr/local/bin/gap for tiffy and waldorf and /rem/tiffy/usr/local/bin/gap for bert.

    gap@tiffy:../src > make generic-unix-gcc2
    # you will see a lot of messages and maybe a few warnings

You should test the standalone now. The following command should run without any comment. This will work, however, only for UNIX machines.

gap@tiffy:../src > testsis

The executables will be collected in the /bin directory, so we move that for the DECstation there.

gap@tiffy:../src > mv sis ../bin/sis.ds

Now repeat the compilation for the PC. Do not forget to clean up.

    gap@tiffy:../src > rlogin waldorf
    gap@waldorf:~ > cd gap3r4p0/pkg/sisyphos/src
    gap@waldorf:../src > make clean
    gap@waldorf:../src > make generic-unix-gcc2
    # you will see a lot of messages and maybe a few warnings

Test the executable (under UNIX only), and move it to the right place.

    gap@waldorf:../src > testsis
    gap@waldorf:../src > mv sis ../bin/sis.386bsd
    gap@waldorf:../src > exit
    gap@tiffy:../src >

Switch into the subdirectory bin/ and create a script which will call the correct binary for each machine.

    gap@tiffy:../src > cd ..
    gap@tiffy:../sisyphos > cat > bin/sis

!/bin/csh
    switch ( `hostname` )
      case 'bert':
      case 'tiffy':
        exec ~gap/3.2/pkg/sisyphos/bin/sis.ds $* ;
        breaksw ;
      case 'waldorf':
        exec ~gap/3.2/pkg/sisyphos/bin/sis.386bsd $* ;
        breaksw ;
      default:
        echo "sis: sorry, no executable exists for this machine" ;
        breaksw ;
    endsw

ctr-D

    gap@tiffy:../sisyphos > chmod 755 bin/sis

57.14 Vector Enumeration Package

The VE package provides access to the implementation of the ``linear Todd-Coxeter'' method for computing matrix representations of finitely presented algebras.

The description of the functions available in the VE package is given in chapter Vector Enumeration.

For details about the implementation and the standalone version see the README. This implementation was developed in C by

Stephen A. Linton
Division of Computer Science
School of Mathematical and Computational Science
University of St. Andrews
North Haugh
St. Andrews
Fife
KY10 2SA
SCOTLAND

e-mail sal@cs.at-andrews.ac.uk

Tel.:: +44 334 63239
Fax.: +44 334 63278

57.15 Installing the Vector Enumeration Package

The Vector Enumerator (VE) is written in C and the package can only be installed under UNIX. It has been tested on DECstation running Ultrix, a 486 running NetBSD, and SUNs running SunOS.

The parts of the package that deal with rationals require the GNU multiple precision arithmetic library GMP. Make sure that this library is installed before trying to install VE.

If you got a complete binary and source distribution for your machine, nothing has to be done if you want to use the VE for a single architecture. If you want to use the VE for machines with different architectures skip the extraction and compilation part of this section and proceed with the creation of shell scripts described below.

If you got a complete source distribution, skip the extraction part of this section and proceed with the compilation part below.

In the example we will assume that you, as user gap, are installing the VE package for use by several users on a network of two DECstations, called bert and tiffy, and a NeXTstation, called bjerun. We assume that GAP3 is also installed on these machines following the instructions given in Installation of GAP for UNIX.

Note that certain parts of the output in the examples should only be taken as rough outline, especially file sizes and file dates are not to be taken literally.

First of all you have to get the file ve.zoo (see Getting GAP). Then you must locate the GAP3 directories containing lib/ and doc/, this is usually gap3r4p0 where 0 is to be be replaced by the patch level.

    gap@tiffy:~ > ls -l
    drwxr-xr-x  11 gap      gap          1024 Nov  8  1991 gap3r4p0
    -rw-r--r--   1 gap      gap        106307 Jan 24 15:16 ve.zoo
    gap@tiffy:~ > ls -l gap3r4p0
    drwxr-xr-x   2 gap      gap          3072 Nov 26 11:53 doc
    drwxr-xr-x   2 gap      gap          1024 Nov  8  1991 grp
    drwxr-xr-x   2 gap      gap          2048 Nov 26 09:42 lib
    drwxr-xr-x   2 gap      gap          2048 Nov 26 09:42 src
    drwxr-xr-x   2 gap      gap          1024 Nov 26 09:42 tst

    gap@tiffy:~ > unzoo x ve.zoo
     gap@tiffy:~ > ls -l gap3r4p0/pkg/ve
     -rw-r--r--  1 sam         16761 May 10 17:39 Makefile
     -rw-r-----  1 sam          1983 May  6  1993 README
     drwxr-xr-x  2 sam           512 May 10 17:41 bin
     drwxr-xr-x  2 sam           512 May 10 17:34 docs
     drwxr-xr-x  2 sam           512 May 10 17:34 examples
     drwxr-xr-x  3 sam           512 Mar 28 17:55 gap
     -rw-r--r--  1 sam           553 Mar 24 18:18 init.g
     drwxr-xr-x  5 sam          1024 May 10 17:36 src

Switch into the directory ve/ and type make to see a list of targets for compilation; then type make target to compile VE, where target is the target that is closest to your machine. If the header files for the GNU multiple precision arithmetic are not in /usr/local/include you must set INCDIRGMP to the correct directory. If the library for the GNU multiple precision arithmetic is not /usr/local/lib/libgmp.a you must set LIBDIRGMP. In this case we first compile the DECstation version.

    gap@tiffy:~ > cd gap3r4p0/pkg/ve
    gap@tiffy:../ve > make INCDIRGMP=/usr/gnu/include \ 
                       LIBDIRGMP=/usr/gnu/lib/ dec-mips-ultrix-gcc2

# you will see a lot of messages

Now repeat the compilation for the NeXTstation. Do not forget to clean up.

    gap@tiffy:../ve > mv bin/me.exe bin/me.dec
    gap@tiffy:../ve > mv bin/qme.exe bin/qme.dec
    gap@tiffy:../ve > rlogin bjerun
    gap@bjerun:~ > cd gap3r4p0/pkg/ve
    gap@bjerun:../ve > make clean

 you will see some messages
    gap@bjerun:../ve > make next-m68k-mach-gcc2

 you will see a lot of messages
    gap@bjerun:../ve > mv bin/me.exe bin/me.next
    gap@bjerun:../ve > mv bin/qme.exe bin/qme.next
    gap@bjerun:../ve > exit
    gap@tiffy:../ve >

Switch into the subdirectory bin/ and create scripts which will call the correct binary for each machine. The shell scripts that are already contained in `bin/me.sgl` and `bin/qme.sgl` are suitable only for a single architecture installation.

    gap@tiffy:../ve > cat > bin/me

!/bin/csh
    switch ( `hostname` )
      case 'bert':
      case 'tiffy':
        exec $0.dec $* ;
        breaksw ;
      case 'bjerun':
        exec $0.next $* ;
        breaksw ;
      default:
        echo "me/qme/zme: sorry, no executable exists for this machine" ;
        breaksw ;
    endsw

ctr-D

    gap@tiffy:../ve > chmod 755 bin/me
    gap@tiffy:../ve > ln bin/me bin/qme

57.16 The XGap Package

\XGAP is a graphical user interface for GAP3, it extends the GAP3 library with functions dealing with graphic sheets and objects. Using these functions it also supplies a graphical interface for investigating the subgroup lattice of a group, giving you easy access to the low index subgroups, prime quotient and Reidemeister-Schreier algorithms and many other GAP3 functions for groups and subgroups. At the moment the only supported window system is X-Windows X11R5, however, programs using the \XGAP library functions will run on other platforms as soon as \XGAP is available on these. We plan to release a Windows 3.11 version in the near future.

In order to produce a preliminary manual and installation guide for the \XGAP package, switch into the directory gap3r4p4/pkg/xgap/doc and latex the document latexme.tex.

\centerlineFrank Celler \& Susanne Keitemeier

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gap3-jm
27 Nov 2023