%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %A share.tex GAP documentation Frank Celler %% %A @(#)$Id: share.tex,v 3.32 1994/07/07 11:07:18 mschoene Rel $ %% %Y Copyright 1990-1992, Lehrstuhl D fuer Mathematik, RWTH Aachen, Germany %% %H $Log: share.tex,v $ %H Revision 3.32 1994/07/07 11:07:18 mschoene %H changed introduction for GRAPE to avoid two overfull hboxes %H %H Revision 3.31 1994/07/01 08:24:40 fceller %H updated GRAPE to 2.2 %H %H Revision 3.30 1994/06/20 14:46:12 vfelsch %H corrected xgap example %H %H Revision 3.29 1994/06/17 19:03:58 vfelsch %H examples adjusted to version 3.4 %H %H Revision 3.28 1994/06/03 08:57:20 mschoene %H changed a few things to avoid LaTeX warnings %H %H Revision 3.27 1994/05/31 11:37:51 vfelsch %H updated introduction %H %H Revision 3.26 1994/05/22 12:41:04 fceller %H added smash package %H %H Revision 3.25 1994/05/19 13:43:36 sam %H bug fixes %H %H Revision 3.23 1994/05/10 16:00:36 sam %H changes in section about VE installation %H %H Revision 3.22 1994/04/28 10:16:34 fceller %H added Alice's SQ %H %H Revision 3.21 1994/04/27 08:59:33 fceller %H chnaged ANU PQ section (srce is now src) %H %H Revision 3.20 1994/04/12 14:14:35 sam %H added section about the VE package %H %H Revision 3.19 1994/03/23 09:39:21 fceller %H changed "srce" to "src" in PQ section %H %H Revision 3.18 1993/11/09 00:08:10 martin %H fixed references to installation sections %H %H Revision 3.17 1993/10/21 17:15:24 fceller %H added xgap and sisyphos %H %H Revision 3.16 1993/10/20 12:25:58 fceller %H distribution is now done using zoo archives not tar archives %H %H Revision 3.15 1993/07/27 08:21:28 fceller %H clearified example in 'RequirePackage' %H %H Revision 3.14 1993/07/20 11:07:11 fceller %H updated GRAPE section %H %H Revision 3.13 93/06/28 10:01:52 fceller %H new ANU pq version %H %H Revision 3.12 1993/05/28 13:37:26 gap %H added GRAPE %H %H Revision 3.11 1993/02/19 10:48:42 gap %H adjustments in line length and spelling %H %H Revision 3.10 1993/02/18 09:50:38 felsch %H examples fixed %H %H Revision 3.9 1993/02/01 11:36:55 fceller %H added reference to "weyl.tex" and "anupq.tex" %H %H Revision 3.8 1993/01/25 22:16:09 fceller %H added Werner's NQ %H %H Revision 3.7 1993/01/05 11:41:05 fceller %H added ANU pq in the introduction %H %H Revision 3.6 1993/01/04 11:01:25 fceller %H fixed some misspellings %H %H Revision 3.5 1992/12/29 15:56:35 fceller %H add the ANU pq %H %H Revision 3.4 1992/12/04 11:11:58 fceller %H added Neubueser's introduction %H %H Revision 3.3 1992/12/02 10:08:45 fceller %H fixed a few bad text alignments %H %H Revision 3.2 92/11/30 15:17:32 fceller %H initial GAP 3.2 revision %% \def\fuer{f{\accent127 u}r} \def\GRAPE{\sf GRAPE} \def\MeatAxe{\sf MeatAxe} \def\SISYPHOS{\sc SISYPHOS} \def\VE{Vector Enumeration} \def\nauty{\it nauty} \Chapter{Share Libraries} Contributions from people working at Lehrstuhl D, RWTH Aachen, or any other place can become available in {\GAP} in two different ways\: 1. They can become parts of the main {\GAP} 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 {\GAP} 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 {\GAP} language or even in C which are made available en block in {\GAP}. 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 {\GAP} functions, and to call the documentation via help functions like any other part of the {\GAP} documentation. Also these packages will automatically be made available with the main body of {\GAP} through ftp and will be sent together with the main body of {\GAP} in case we have to fulfill a request to send {\GAP} to institutions that cannot obtain {\GAP} via electronic networks. The inclusion of packages as {\GAP} 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 {\GAP} without problems. A necessary condition for any package to become a {\GAP} share library is that it is made available under the conditions formulated in the {\GAP} 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 smash package and how to install it (see "Smash Package" and "Installing the Smash Package"). The next sections describe the {\VE} package and how to install it (see "Vector Enumeration Package" and "Installing the Vector Enumeration Package"). The next sections describe the Weyl package and how to install it (see "Weyl Package" and "Installing the Weyl Package"). The last sections describe the experimental X-Windows interface and how to install it (see "The XGap Package" and "Installing the XGap Package"). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \Section{RequirePackage} 'RequirePackage( )' 'RequirePackage' will try to initialize the share library . If the package is not installed at your site 'RequirePackage' will signal an error. If the package is already initialized 'RequirePackage' simply returns without any further actions. | gap> CartanMat( "A", 4 ); Error, Variable: 'CartanMat' must have a value gap> ?Cartan 'CartanMat( , )' returns the Cartan matrix of Dynkin type and rank . gap> CartanMat( "F", 4 ); [ [ 2, -1, 0, 0 ], [ -1, 2, -1, 0 ], [ 0, -2, 2, -1 ], [ 0, 0, -1, 2 ] ] This function requires the package "weyl" (see "RequirePackage"). # on some system is case-sensitive, so watch out for typos gap> RequirePackage( "Weyl" ); Error, share library "Weyl" is not installed gap> RequirePackage( "weyl" ); gap> CartanMat( "A", 4 );; gap> PrintArray( last ); [ [ 2, -1, 0, 0 ], [ -1, 2, -1, 0 ], [ 0, -1, 2, -1 ], [ 0, 0, -1, 2 ] ]| %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \Section{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 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 (1993). 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 \cite{HN80}, \cite{OBr90}, \cite{OBr93}, \cite{OBr94}, \cite{New77}, \cite{Vau84}, \cite{Vau90a}, and \cite{Vau90b}. For details about the implementation and the standalone version see the README. This implementation was developed in C by Eamonn O\'Brien\\ School of Mathematical Sciences\\ Australian National University\\ Canberra, ACT 0200 e-mail obrien@maths.anu.edu.au %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \Section{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 {\GAP} 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 {\GAP} 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 EXT=' where 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 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 COPTS= LOPTS=', 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 {\GAP} 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 |-'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 {\GAP}. 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 {\GAP} 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. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \Section{ANU Sq Package} \index{Sq} 'Sq( , )' The function 'Sq' is the interface to the Soluble Quotient standalone program. Let be a finitely presented group and let 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 $p_i \not= p_{i+1}$ 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 which is described by as follows. Let $H$ be a group and $p$ a prime. The series $$H = {P}^p_0(H)\ge {P}^p_1(H)\ge\cdots\,\,\hbox to 1.5 cm{\hfil with\ } {P}^p_i(H) = [{P}^p_{i-1}(H),H] \left({P}^p_{i-1} (H)\right)^p$$ for $i \ge 1$ is the {\it lower exponent-$p$ central series} of $H.$ For $1 \le i \le k$ and $0 \le j \le c_i$ define the list ${\rm L}_{i,j} = [(p_1,c_1),\ldots, (p_{i-1},c_{i-1}),(p_{i}, j) ].$ Define ${\rm L}_{1,0}(G) = G.$ For $1 \le i \le k$ and $1 \le j \le c_i$ define the subgroups $${\rm L}_{i,j}(G) = {\rm P}_{j}^{p_i}( {\rm L}_{i,0}(G) )$$ and for $1 \le i \< k$ define the subgroups $${\rm L}_{i+1,0}(G) = {\rm L}_{i,c_i}(G)$$ and ${\rm L}(G) = {\rm L}_{k,c_k}(G).$ Note that ${\rm L}_{i,j}(G) \ge {\rm L}_{i,j+1}(G)$ holds for $j \< c_i$. The chain of subgroups $$G = {\rm L}_{1,0}(G) \ge {\rm L}_{1,1}(G) \ge \cdots \ge {\rm L}_{1,c_1}(G) = {\rm L}_{2,0}(G)\ge \cdots \ge {\rm L}_{k,c_k}(G) = {\rm L}(G) $$ is called the {\it soluble ${\rm L}$-series} of $G.$ 'Sq' computes a consistent power conjugate presentation for $G/{\rm L}(G),$ where the presentation exhibits a composition series of the quotient group which is a refinement of the soluble ${\rm L}$-series. An epimorphism from $G$ onto $G/{\rm L}(G)$ is listed in comments. The algorithm proceeds by computing power conjugate presentations for the quotients $G/{\rm L}_{i,j}(G)$ in turn. Without loss of generality assume that a power conjugate presentation for $G/{\rm L}_{i,j}(G)$ has been computed for $j \< c_i.$ The basic step computes a power conjugate presentation for $G/{\rm L}_{i,j+1}(G).$ The group ${\rm L}_{i,j}(G)/{\rm L}_{i,j+1}(G)$ is a $p_{i}$-group. If during the basic step it is discovered that ${\rm L}_{i,j}(G) = {\rm L}_{i,j+1}(G),$ then ${\rm L}_{i+1,0}(G)$ is set to ${\rm L}_{i,j}(G).$ 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 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \Section{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 {\GAP} 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 {\GAP} 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| 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 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 EXT=' where 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 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 COPTS= LOPTS=', 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 |-'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 {\GAP} 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. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \Section{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 {\GAP} language, except for the automorphism group and isomorphism testing functions, which use Brendan McKay\'s {\nauty} (Version~1.7) package \cite{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 (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. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \Section{Installing the GRAPE Package} {\GRAPE} consists of two parts. The first part is a set of {\GAP} functions for constructing and analysing graphs, which will run on any machine that supports {\GAP}. 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 {\GAP} 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 {\GAP} 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| 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 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 ' 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 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 |-'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) ) | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \Section{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 {\GAP} on a file, and {\GAP} is only responsible for handling these files using the appropriate programs. Details about the standalone can be found in~\cite{Rin93}. This implementation was developed in C by Michael Ringe\\ Lehrstuhl D f{\accent127 u}r Mathematik\\ RWTH Aachen\\ 52062 Aachen, Germany e-mail mringe@math.rwth-aachen.de %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \Section{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 {\GAP} (see the {\MeatAxe} manual~\cite{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 {\GAP} 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 {\GAP} 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| 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 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 {\GAP} using the hostname, thus for every machine that shall run the {\MeatAxe} under {\GAP} 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 > | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \Section{NQ Package} \index{NilpotentQuotient} 'NilpotentQuotient( )' \\ 'NilpotentQuotient( , )' 'NilpotentQuotient' computes the quotient groups of the finitely presented group successively modulo the terms of the lower central series of . 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 (the largest abelian quotient being the first factor). 'NilpotentQuotient' accepts a positive integer as an optional second argument. If the second argument is present, the function computes the quotient group of modulo the -th term of the lower central series of (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 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \Section{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 {\GAP} 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 {\GAP} 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| 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 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 |-'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 {\GAP}. | gap@tiffy:../nq > gap -b gap> RequirePackage( "nq" ); gap> ReadTest( "gap/nq.tst" ); gap> | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \Section{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 {\GAP}. 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". % A reader interested in details of the algorithms and explanations of % terms used is referred to \cite{...} 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\\ Universit{\accent127 a}t Stuttgart e-mail pluto@machnix.mathematik.uni-stuttgart.de\\ Tel.: +49 (0)711 685 5517\\ Fax.: +49 (0)711 685 5322 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \Section{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 {\GAP} 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 {\GAP} 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 | 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 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 ' 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 {\GAP} 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 |-'D'| gap@tiffy:../sisyphos > chmod 755 bin/sis| %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \Section{Smash Package} This share library provides functions which may be used to construct and investigate the structure of matrix groups defined over finite fields. These functions permit the user to construct certain types of matrix groups and G-modules; to test whether a G-module is irreducible or absolutely irreducible; to decide whether a group has certain decomposition with respect to a normal subgroup; and to select random elements with certain properties. The code was developed as part of the on-going project to \"recognise\" the Aschbacher categories of matrix groups defined over finite fields. The interested reader is referred to \cite{HR94}, \cite{HLOR94a}, and \cite{HLOR94b} for details of the algorithms used. Smash was developed by Derek Holt, Mathematics Institute, Warwick \\ dfh@maths.warwick.ac.uk Charles Leedham-Green, School of Mathematical Studies, QMW \\ C.R.Leedham-Green@qmw.ac.uk Eamonn O\'Brien, School of Mathematical Sciences, ANU \\ Eamonn.OBrien@maths.anu.edu.au Sarah Rees, Department of Mathematics and Statistics, Newcastle \\ Sarah.Rees@newcastle.ac.uk %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \Section{Installing the Smash Package} The smash package is completely written in the {\GAP} language, it does not require any additional programs and/or compilations. It will run on any computer that runs {\GAP}. To access smash, use 'RequirePackage' (see "RequirePackage"). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \Section{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 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \Section{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 {\GAP} 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 {\GAP} 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| 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 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 ' to compile VE, where 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 |-'D'| gap@tiffy:../ve > chmod 755 bin/me gap@tiffy:../ve > ln bin/me bin/qme | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \Section{Weyl Package} There is a collection of programs for dealing with finite Weyl groups, associated (Iwahori-) Hecke algebras, and their representations. These programs were written by Meinolf Geck (Lehrstuhl D \fuer\ Mathematik, RWTH Aachen, Templergraben 64, 5100 Aachen, Germany, e-mail\: geck@tiffy.math.rwth-aachen.de). On a low level, these programs provide the basic data about a fixed finite Weyl group $W$\: \\ having specified a Cartan matrix, they compute the root system, the reflection representation, and the permutation representation on the root vectors. Elements of $W$ can be given either as permutations or as reduced words in the standard generators (i.e., simply as a list of integers labelling the generators), and there are functions to convert these expressions into each other. In particular, all functions of {\GAP} for working with permutation groups can be applied. On a higher level, it is possible to compute distinguished coset representatives and representatives of the conjugacy classes of $W$ of minimal length. Furthermore, there are functions for calculating Kazhdan-Lusztig polynomials, left cells, and the corresponding representations of the associated Hecke algebra $H$ (for groups of rank $\leq$ 5, say). Also, computations inside $H$ are possible, such as multiplying two arbitrary elements of $H$ and expressing the result as a linear combination in the basis elements $T_w$, $w \in W$. The following section describes the installation of the Weyl package, a description of the functions available in the Weyl package is given in chapter "Weyl Groups and Hecke Algebras". %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \Section{Installing the Weyl Package} The Weyl package is completely written in the {\GAP} language, it does not require any additional programs and/or compilations. It will run on any computer that runs {\GAP}. In the following we will describe the installation under UNIX. The installation on the Atari ST, TT or IBM PC is similar. If you got a complete source distribution, nothing has to be done. In the example we give we will assume that {\GAP} is installed in the home directory of a pseudo user 'gap' and that you, as user 'gap', want to install the Weyl package. 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 'weyl.zoo' (see "Getting GAP"). Then you must locate the {\GAP} directories containing 'lib/' and 'doc/', this is usually 'gap3r4p0' where '0' is to be replaced by the current the patch level. | gap:~ > ls -l drwxr-xr-x 11 gap gap 1024 Nov 8 1991 gap3r4p0 -rw-r--r-- 1 gap gap 35870 Nov 26 12:33 weyl.zoo gap:~ > 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| 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:~ > unzoo x weyl.zoo gap:~ > ls -l gap3r4p0/pkg/weyl -rw-r--r-- 1 gap gap 1536 Nov 22 04:16 README -rw-r--r-- 1 gap gap 57058 Nov 22 04:02 init.g -rw-r--r-- 1 gap gap 40304 Nov 22 04:18 weyl.tex -rw-r--r-- 1 gap gap 57058 Nov 22 03:41 weylgrp.g| If the documentation is not already installed or an older version is installed, copy the file 'weyl.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:~ > cd gap3r4p0/pkg/weyl gap:../weyl > cp weyl.tex ../../doc gap:../weyl > cd ../../doc gap:../doc > latex manual # a few messages about undefined references gap:../doc > latex manual # a few messages about undefined references gap:../doc > makeindex manual # 'makeindex' prints some diagnostic output gap:../doc > latex manual # there should be no warnings this time | Now it is time to test the installation. Let us assume that the executable of {\GAP} lives in 'src/' and is called 'gap'. | gap:~/gap3r4p0 > src/gap -b gap> ?CartanMat CartanMat ____________________________ Weyl Groups and Hecke Algebras 'CartanMat( , )' returns the Cartan matrix of Dynkin type and rank . gap> CartanMat( "F", 4 ); [ [ 2, -1, 0, 0 ], [ -1, 2, -1, 0 ], [ 0, -2, 2, -1 ], [ 0, 0, -1, 2 ] ] This function requires the package "weyl" (see "RequirePackage"). gap> RequirePackage( "weyl" ); gap> CartanMat( "F", 4 ); [ [ 2, -1, 0, 0 ], [ -1, 2, -1, 0 ], [ 0, -2, 2, -1 ], [ 0, 0, -1, 2 ] ] | If 'RequirePackage' signals an error check the permissions of the subdirectories 'pkg/' and 'weyl/'. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\XGap{{\sf XGap}} \Section{The XGap Package} {\XGap} is an experimental graphical user interface for {\GAP}. The only supported window system at the moment is X-Windows 11R5, however, programs written for {\XGap} will run on other platforms as soon as an user interface is available on these platforms. Right now, no documentation is available, manual entries are delivered as soon as the system is stable. If you want to play with {\XGap} try | fceller@tiffy:~ > xgap gap> GraphicLattice( Group( (1,2,3,4), (1,3) ), 400, 600 );; gap> s := GraphicSheet( "Hallo World", 300, 300 );; gap> c := Circle( s, 100, 100, 50 );; gap> c.operations.MoveDelta( c, 10, 10 ); gap> for i in [ 1 .. 10 ] do > c.operations.MoveDelta( c, i, -i ); > od; gap> Delete( s, c ); gap> Close(s); | Please send comments, bug reports, etc. to | fceller@math.rwth-achen.de| or | gap-trouble@math.rwth-aachen.de| %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \Section{Installing the XGap Package} {\XGap} is written in C and the package can only be installed under UNIX running X-Windows 11R5. It has been tested on a DECstation running Ultrix, a SUN running SunOS, a PC running 386bsd, and a NeXTstation running NeXTSTEP 3.0 and MouseX. If you got a complete binary and source distribution for your machine, no compilation is necessary, you must however adapted the shell script 'gap3r4p0/pkg/xgap/bin/xgap'. 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 {\XGap} package for use by several users on a network of two DECstations, called 'bert' and 'tiffy'. We assume that {\GAP} 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 'xgap.zoo' (see "Getting GAP"). Then you must locate the {\GAP} 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 xgap gap@tiffy:~ > ls -l gap3r4p0/pkg/xgap -rw-rw-rw- 1 gap 120 4401 Oct 18 12:12 Makefile drwxr-xr-x 2 gap 120 512 Oct 21 11:28 bin drwxr-xr-x 3 gap 120 512 Oct 18 12:06 lib drwxr-xr-x 3 gap 120 512 Oct 21 11:29 src drwxr-xr-x 2 gap 120 512 Apr 19 1993 tst| Switch into the directory 'gap3r4p0/pkg/xgap/src/' and type 'make'. Note that we do *not* supply an 'Imakefile'. |gap@tiffy:~ > cd gap3r4p0/pkg/xgap/src gap@tiffy:../src > make usage: 'make ' where target is one of 'next-m68k-mach-gcc2' for NeXT under Mach with X11R5 and GNU cc 2 'ibm-i386-386bsd-gcc2' for IBM PCs under 386BSD with X386 and GNU cc 2 'dec-mips-ultrix-gcc2' for DECstations under Ultrix with X11R5 and GNU cc 2 'dec-mips-ultrix-cc' for DECstations under Ultrix with X11R5 and cc 'sun-sparc-sunos-cc' for SUN SPARC under SunOS with X11R5 and cc 'sun-sparc-sunos-gcc' for SUN SPARC under SunOS with X11R5 and GNU cc 2 if the X11 include files directory does not live in "/usr/include", you must set 'X11INC' to point to the correct directory if the X11 library files do not live in "/usr/lib", you must set 'X11LIB' to point to the correct directory | Select the target you need. In our case we use 'dec-mips-ultrix-gcc2' in order to compile the DECstation version. | gap@tiffy:../src > make dec-mips-ultrix-gcc2 # you will see a lot of messages | This create a executable 'xgap' in the current directory. If {\GAP} lives in the directory '~gap/gap3r4p0/src/gap' try the following: | gap@tiffy:../src > ./xgap -G ~gap/gap3r4p0/src/gap| This command should create a new window in which {\GAP} is awaiting your input, type 'quit;' inside this window. Strip the executable and move it into the directory 'bin/', but *do not* call it 'xgap'. | gap@tiffy:../src > strip xgap gap@tiffy:../src > mv xgap ../bin/xgap-dec-mips-ultrix | Switch into the directory 'bin/' and adapted the shell script 'xgap', you must at least set the environment variables 'EXEC', 'LIB', 'DOC', and 'GAP', where 'EXEC' should point to your newly created executable of {\XGap}, 'LIB' should (after the first semicolon) point to the directory where {\GAP}\'s libraries files live (it *must* end with a '/'), 'DOC' should point to the directory containing the TeX files, and 'GAP' should point to the executable of {\GAP}.