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| Title: | Mathematics at DEC |
|
| Moderator: | RUSURE::EDP |
|
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
1593.0. "Free system for computational discrete algebra." by CADSYS::COOPER (Topher Cooper) Wed Apr 15 1992 13:25
<<Crossposted to MAPLE>>
------------------------------------------------------------------------------
Newsgroups: sci.math,sci.math.symbolic
From: [email protected] ( Martin Schoenert)
Subject: Announcement of GAP 3.1
Message-ID: <martin.703247020@bert>
Summary: GAP 3.1 is finally available
Keywords: Computational Group Theory
Sender: [email protected] (Newsfiles Owner)
Nntp-Posting-Host: bert.math.rwth-aachen.de
Organization: RBI - RWTH Aachen
Date: 14 Apr 92 10:23:40 GMT
Introduction
============
GAP is a system for computational discrete algebra, which we have
developed with particular emphasis on computational group theory, but
which has already proved useful also in other areas. The name GAP is an
acronym for *Groups, Algorithms, and Programming*. This (long) document
announces the availability of GAP version 3 release 1, GAP 3.1 for short.
It is an *advertisement* for GAP, but not a *commercial*, since we give
GAP away for free. Hit 'n' now if you are not interested.
This document begins with the section "Announcement", which contains the
announcment proper. The next section "Analyzing Rubik's Cube with GAP"
contains an extensive example. This example is followed by a general
disscussion of GAP's capabilities in the section "An Overview of GAP".
The next sections "How to get GAP" and "How to install GAP" describe how
you can get GAP running on your computer. Then we tell you about our
plans for the future in the section "The Future of GAP". The final
section "The GAP Forum" introduces the GAP forum, where interested users
can discuss GAP related topics by e-mail messages.
Announcement
============
Il est trop tard,
maintenant,
il sera toujours trop tard.
Heureusement!
(A. Camus, La chute)
######## Lehrstuhl D fuer Mathematik
### #### RWTH Aachen
## ##
## # ####### #########
## # ## ## # ##
## # # ## # ##
#### ## ## # # ##
##### ### ## ## ## ##
######### # ######### #######
# #
## Version 3 #
### Release 1 #
## # 7 Apr 92 #
## #
## # Johannes Meier, Martin Schoenert
## # Alice Niemeyer, Werner Nickel
## # Alex Wegner, Thomas Bischops
### ## Juergen Mnich, Frank Celler
###### Thomas Breuer, Goetz Pfeiffer
Udo Polis
Lehrstuhl D f"ur Mathematik, RWTH Aachen, announces the availability of
GAP version 3 release 1, or GAP 3.1 for short. This is the first
publicly available release of GAP since version 2.4, which was
distributed since January 1989.
Analyzing Rubik's Cube with GAP
===============================
Ideal Toy Company stated on the package of
the original Rubik cube that there were more than
three billion possible states the cube could attain.
It's analogous to Mac Donald's proudly announcing
that they've sold more than 120 hamburgers.
(J. A. Paulos, Innumeracy)
To show you what GAP can do a short example is probably best. If you are
not interested in this example skip to the section "An Overview of GAP".
For the example we consider the group of transformations of Rubik's magic
cube. If we number the faces of this cube as follows
+--------------+
| 1 2 3 |
| 4 top 5 |
| 6 7 8 |
+--------------+--------------+--------------+--------------+
| 9 10 11 | 17 18 19 | 25 26 27 | 33 34 35 |
| 12 left 13 | 20 front 21 | 28 right 29 | 36 rear 37 |
| 14 15 16 | 22 23 24 | 30 31 32 | 38 39 40 |
+--------------+--------------+--------------+--------------+
| 41 42 43 |
| 44 bottom 45 |
| 46 47 48 |
+--------------+
then the group is generated by the following generators, corresponding
to the six faces of the cube (the two semicolons tell GAP not to print
the result, which is identical to the input here).
gap> cube := Group(
> ( 1, 3, 8, 6)( 2, 5, 7, 4)( 9,33,25,17)(10,34,26,18)(11,35,27,19),
> ( 9,11,16,14)(10,13,15,12)( 1,17,41,40)( 4,20,44,37)( 6,22,46,35),
> (17,19,24,22)(18,21,23,20)( 6,25,43,16)( 7,28,42,13)( 8,30,41,11),
> (25,27,32,30)(26,29,31,28)( 3,38,43,19)( 5,36,45,21)( 8,33,48,24),
> (33,35,40,38)(34,37,39,36)( 3, 9,46,32)( 2,12,47,29)( 1,14,48,27),
> (41,43,48,46)(42,45,47,44)(14,22,30,38)(15,23,31,39)(16,24,32,40)
> );;
First we want to know the size of this group.
gap> Size( cube );
43252003274489856000
Since this is a little bit unhandy, let us factorize this number.
gap> Collected( Factors( last ) );
[ [ 2, 27 ], [ 3, 14 ], [ 5, 3 ], [ 7, 2 ], [ 11, 1 ] ]
(The result tells us that the size is 2^27 3^14 5^3 7^2 11.)
Next let us investigate the operation of the group on the 48 points.
gap> orbits := Orbits( cube, [1..48] );
[ [ 1, 3, 17, 14, 8, 38, 9, 41, 19, 48, 22, 6, 30, 33, 43, 11, 46,
40, 24, 27, 25, 35, 16, 32 ],
[ 2, 5, 12, 7, 36, 10, 47, 4, 28, 45, 34, 13, 29, 44, 20, 42,
26, 21, 37, 15, 31, 18, 23, 39 ] ]
The first orbit contains the points at the corners, the second those at
the edges; clearly the group cannot move a point at a corner onto a point
at an edge.
So to investigate the cube group we first investigate the operation on
the corner points. Note that the constructed group that describes this
operation will operate on the set [1..24], not on the original set
[1,3,17,14,8,38,9,41,19,48,22,6,30,33,43,11,46,40,24,27,25,35,16,32].
gap> cube1 := Operation( cube, orbits[1] );
Group( ( 1, 2, 5,12)( 3, 7,14,21)( 9,16,22,20),
( 1, 3, 8,18)( 4, 7,16,23)(11,17,22,12),
( 3, 9,19,11)( 5,13, 8,16)(12,21,15,23),
( 2, 6,15, 9)( 5,14,10,19)(13,21,20,24),
( 1, 4,10,20)( 2, 7,17,24)( 6,14,22,18),
( 4,11,13, 6)( 8,15,10,17)(18,23,19,24) )
gap> Size( cube1 );
88179840
Now this group obviously operates transitively, but let us test whether
it is also primitive.
gap> corners := Blocks( cube1, [1..24] );
[ [ 1, 7, 22 ], [ 2, 14, 20 ], [ 3, 12, 16 ], [ 4, 17, 18 ],
[ 5, 9, 21 ], [ 6, 10, 24 ], [ 8, 11, 23 ], [ 13, 15, 19 ] ]
Those eight blocks correspond to the eight corners of the cube; on the
one hand the group permutes those and on the other hand it permutes the
three points at each corner cyclically.
So the obvious thing to do is to investigate the operation of the group
on the eight corners.
gap> cube1b := Operation( cube1, corners, OnSets );
Group( (1,2,5,3), (1,3,7,4), (3,5,8,7),
(2,6,8,5), (1,4,6,2), (4,7,8,6) )
gap> Size( cube1b );
40320
Now a permutation group of degree 8 that has order 40320 must be the full
symmetric group S(8) on eight points.
The next thing then is to investigate the kernel of this operation on
blocks, i.e., the subgroup of 'cube1' of those elements that fix the
blocks setwise.
gap> blockhom1 := OperationHomomorphism( cube1, cube1b );;
gap> Factors( Size( Kernel( blockhom1 ) ) );
[ 3, 3, 3, 3, 3, 3, 3 ]
gap> IsElementaryAbelian( Kernel( blockhom1 ) );
true
We can show that the product of this elementary abelian group 3^7 with
the S(8) is semidirect by finding a complement, i.e., a subgroup that has
trivial intersection with the kernel and that generates 'cube1' together
with the kernel.
gap> cmpl1 := Stabilizer( cube1, [1,2,3,4,5,6,8,13], OnSets );;
gap> Size( cmpl1 );
40320
gap> Size( Intersection( cmpl1, Kernel( blockhom1 ) ) );
1
gap> Closure( cmpl1, Kernel( blockhom1 ) ) = cube1;
true
There is even a more elegant way to show that 'cmpl1' is a complement.
gap> IsIsomorphism( OperationHomomorphism( cmpl1, cube1b ) );
true
Of course, theoretically it is clear that 'cmpl1' must indeed be a
complement.
In fact we know that 'cube1' is a subgroup of index 3 in the wreath
product of a cylic 3 with S(8). This missing index 3 tells us that we do
not have total freedom in turning the corners. The following tests show
that whenever we turn one corner clockwise we must turn another corner
counterclockwise.
gap> (1,7,22) in cube1;
false
gap> (1,7,22)(2,20,14) in cube1;
true
More or less the same things happen when we consider the operation of the
cube group on the edges.
gap> cube2 := Operation( cube, orbits[2] );;
gap> Size( cube2 );
980995276800
gap> edges := Blocks( cube2, [1..24] );
[ [ 1, 11 ], [ 2, 17 ], [ 3, 19 ], [ 4, 22 ], [ 5, 13 ], [ 6, 8 ],
[ 7, 24 ], [ 9, 18 ], [ 10, 21 ], [ 12, 15 ], [ 14, 20 ], [ 16, 23 ] ]
gap> cube2b := Operation( cube2, edges, OnSets );;
gap> Size( cube2b );
479001600
gap> blockhom2 := OperationHomomorphism( cube2, cube2b );;
gap> Factors( Size( Kernel( blockhom2 ) ) );
[ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]
gap> IsElementaryAbelian( Kernel( blockhom2 ) );
true
gap> cmpl2 := Stabilizer(cube2,[1,2,3,4,5,6,7,9,10,12,14,16],OnSets);;
gap> IsIsomorphism( OperationHomomorphism( cmpl2, cube2b ) );
true
This time we get a semidirect product of a 2^11 with an S(12), namely a
subgroup of index 2 of the wreath product of a cyclic 2 with S(12). Here
the missing index 2 tells us again that we do not have total freedom in
turning the edges. The following tests show that whenever we flip one
edge we must also flip another edge.
gap> (1,11) in cube2;
false
gap> (1,11)(2,17) in cube2;
true
Since 'cube1' and 'cube2' are the groups describing the actions on the
two orbits of 'cube', it is clear that 'cube' is a subdirect product of
those groups, i.e., a subgroup of the direct product. Comparing the
sizes of 'cube1', 'cube2', and 'cube' we see that 'cube' must be a
subgroup of index 2 in the direct product of those two groups.
gap> Size( cube );
43252003274489856000
gap> Size( cube1 ) * Size( cube2 );
86504006548979712000
This final missing index 2 tells us that we cannot operate on corners and
edges totally independently. The following tests show that whenever we
exchange a pair of corners we must also exchange a pair of edges (and
vice versa).
gap> (17,19)(11,8)(6,25) in cube;
false
gap> (7,28)(18,21) in cube;
false
gap> (17,19)(11,8)(6,25)(7,28)(18,21) in cube;
true
Finally let us compute the centre of the cube group, i.e., the subgroup
of those operations that can be performed either before or after any
other operation with the same result.
gap> Centre( cube );
Subgroup( cube, [ ( 2,34)( 4,10)( 5,26)( 7,18)(12,37)(13,20)
(15,44)(21,28)(23,42)(29,36)(31,45)(39,47) ] )
We see that the centre contains one nontrivial element, namely the
operation that flips all 12 edges simultaneously.
This concludes our example. Of course, GAP can do much more, and the
next section gives an overview of its capabilities, but demonstrating
them all would take too much room.
An Overview of GAP
==================
Though this be madness,
yet there is method in't.
(W. Shakespeare, Hamlet)
GAP consists of several parts: the kernel, the library of functions, the
library of groups and related data, and the documentation.
The *kernel* implements an automatic memory management, a PASCAL-like
programming language, also called GAP, with special datatypes for
computations in group theory, and an interactive programming environment
to run programs written in the GAP programming language.
The automatic *memory management* allows programmers to concentrate on
implementing the algorithm without needing to care about allocation and
deallocation of memory. It includes a garbage collection that
automatically throws away objects that are no longer accessible.
The GAP programming language supports a number of datatypes for elements
of fields. *Integers* can be arbitrarily large, and are implemented in
such a way that operations with small integers are reasonably fast.
Building on this large-integer arithmetic GAP supports *rationals* and
elements from *cyclotomic fields*. Also GAP allows one to work with
elements from *finite fields* of size (at present) at most 2^16.
The special datatypes of group elements are *permutations* (currently
operating on at most 2^16 points, but we are going to remove this
restriction soon), *matrices* over the rationals, cyclotomic fields, and
finite fields, *words in abstract generators*, and *words in solvable
groups*.
GAP also contains a very flexible *list* datatype. A list is simply a
collection of objects that allows you to access the components using an
integer position. Lists grow automatically when you add new elements to
them. Lists are used to represent sets, vectors, and matrices. A *set*
is represented by a sorted list without duplicates. A list whose
elements all lie in a common field is a *vector*. A list of vectors of
the same length over a common field is a *matrix*. Since sets, vectors,
and matrices are lists, all list operations and functions are applicable.
You can, for example, find a certain element in a vector with the general
function 'Position'. There are also *ranges*, i.e., lists of
consecutive integers, and *boolean lists*, i.e., lists containing only
'true' and 'false'. Vectors, ranges, and boolean lists have special
internal representations to ensure efficient operations and memory usage.
For example, a boolean list requires only one bit per element.
*Records* in GAP are similar to lists, except that accessing the
components of a record is done using a name instead of an index. Records
are used to collect objects of different types, while lists usually only
contain elements of one type. Records are for example used to represent
groups and other domains; there is *no* group datatype in the GAP
language . Because of this all information that GAP knows about a group
is also accessible to you by simply investigating the record.
The control structures of GAP are PASCAL-like. GAP has *if* statements,
*while*, *repeat*, and *for* loops. The for loop is a little bit
uncommon in that it always loops over the elements of a list. The usual
semantics can be obtained by looping over the elements of a range. Using
those building blocks you can write *functions*. Functions can be
recursive, and are first class objects in the sense that you can collect
functions in lists, pass them as arguments to other functions and also
return them.
It is important to note that GAP has dynamic typing instead of static
typing. That means that the datatype is a property of the object, not of
the variable. This allows you to write general functions. For example
the generic function that computes an orbit can be used to compute the
orbit of an integer under a permutation group, the orbit of a vector
under a matrix group, the conjugacy class of a group element, and many
more.
The kernel also implements an *interactive environment* that allows you
to use GAP. This environment supports debugging; in case of an error a
break loop is entered in which you can investigate the problem, and maybe
correct it and continue. You also have online access to the manual,
though sections that contain larger formulas do not look nice on the
screen.
The *library of functions*, simply called library in the following,
contains implementations of various group theoretical algorithms written
in the GAP language. Because all the group theoretical functions are in
this library it is easy for you to look at them to find out how they
work, and change them if they do almost, but not quite, what you want.
The whole library is centered around the concept of domains and
categories. A *domain* is a structured set, e.g., a group is a domain as
is the ring of Gaussian integers. Each domain in GAP belongs to one or
more *categories*, which are simply sets of domains, e.g., the set of all
groups forms a category. The categories in which a domain lies determine
the functions that are applicable to this domain and its elements.
To each domain belongs a set of functions, in a so called operations
record, that are called by dispatchers like 'Size'. For example, for a
permutation group <G>, '<G>.operations.Size' is a function implementing
the Schreier Sims algorithm. Thus if you have any domain <D>, simply
calling 'Size( <D> )' will return the size of the domain <D>, computed by
an appropriate function. Domains *inherit* such functions from their
category, unless they redefine them. For example, for a permutation
group <G>, the derived subgroup will be computed by the generic group
function, which computes the normal closure of the subgroup generated by
the commutators of the generators.
Of course the most important category is the category of *groups*. There
are about 100 functions applicable to groups. These include general
functions such as 'Centralizer' and 'SylowSubgroup', functions that
compute series of subgroups such as 'LowerCentralSeries', a function that
computes the whole lattice of subgroups, functions that test predicates
such as 'IsSimple', functions that are related to the operations of
groups such as 'Stabilizer', and many more. Most of these functions are
applicable to all groups, e.g., permutation groups, finite polycyclic
groups, factor groups, direct products of arbitrary groups, and even new
types of groups that you create by simply specifying how the elements are
multiplied and inverted (actually it is not quite so simple, but you can
do it).
Where the general functions that are applicable to all groups are not
efficient enough, we have tried to overlay them by more efficient
functions for special types of groups. The prime example is the category
of *permutation groups*, which overlays 'Size', 'Elements',
'Centralizer', 'Normalizer', 'SylowSubgroup', and a few more functions by
functions that employ stabilizer chains and backtracking algorithms.
Also many of the functions that deal with operations of groups are
overlayed for permutation groups for the operation of a permutation group
on integers or lists of integers.
For *finitely presented groups* only some functions are as yet
implemented. They include finding the index of a subgroup via a
Todd-Coxeter coset enumeration, computing the abelian invariants of the
commutator factor group, intersecting two subgroups, finding the
normalizer of a subgroup, and finding all subgroups of small index. Of
course it is possible to go to a permutation group operating on the
cosets of a subgroup and then to work with this permutation group.
Clearly there is still much to be done in this area, most notably
computing presentations for subgroups and simplifying presentations. We
hope to be able to add such functions in the near future.
For *finite polycyclic groups* a special kind of presentation
corresponding to a composition series is used. Such a presentation
implies a canonical form for the elements and thus allows efficient
operations with the elements of such a group. This presentation is used
to make functions such as 'Centralizer', 'Normalizer', 'Intersection',
and 'ConjugacyClasses' very efficient. GAP's capabilities for finite
polycyclic groups exceed those of the computer system SOGOS (which was
developed at Lehrstuhl D f"ur Mathematik for the last decade).
There is also support for *mappings* and *homomorphisms*. Since they
play such a ubiquitous role in mathematics, it is only natural that they
should also play an important role in a system like GAP. Mappings and
homomorphisms are objects in their own right in GAP. You can apply a
mapping to an element of its source, multiply mappings (provided that the
range of the first is a subset of the source of the second), invert
mappings (even if what you get is a multi-valued mapping), and perform a
few more operations. Important examples are the 'NaturalHomomorphism'
onto a factor group, 'OperationsHomomorphism' mapping a group that
operates on a set of <n> elements into the symmetric group on [1..<n>],
'Embeddings' into products of groups, 'Projections' from products of
groups onto the components, and the general 'GroupHomomorphismByImages'
for which you only specify the images of a set of generators.
The library contains a package for handling character tables of finite
groups. This includes almost all possibilities of the computer system
CAS (which was developed at Lehrstuhl D f"ur Mathematik in the last
decade), and many new functions. You can compute character tables of
groups, or construct character tables using other tables, or do some
calculations within known character tables. You can, for example,
compute a list of candidates for permutation characters. Of course there
are many character tables (at the moment more than 650 ordinary tables)
in the data library, including all those in the ATLAS of finite groups.
For large integers we now also have a package for *elementary number
theory*. There are functions in this package to test primality, factor
integers of reasonable size, compute the size phi(<n>) of the prime
residue group modulo an integer <n>, compute roots modulo an integer <n>,
etc. Also based on this there is a package to do calculations in the
ring of Gaussian integers.
The library also includes a package for *combinatorics*. This contains
functions to find all selections of various flavours of the elements of a
set, e.g., 'Combinations' and 'Tuples', or the number of such selections,
e.g., 'Binomial'. Other functions are related to partitions of sets or
integers, e.g., 'PartitionsSet' and 'RestrictedPartitions', or the number
of such, e.g., 'NrPartitions' and 'Bell'. It also contains some
miscellaneous functions such as 'Fibonacci' and 'Bernoulli'.
The *data library* at present contains the primitive permutation groups
of degree up to 50 from C. Sims, the 2-groups of size dividing 256 from
E. O'Brien and M. F. Newman, the solvable groups of size up to 100 from
M. Hall, J. K. Senior, R. Laue, and J. Neub"user, and a library of
character tables including all of the ATLAS. We plan to extend the data
library with more data in the future.
How to get GAP
==============
Ceterum censeo:
Nobody has ever paid a licence fee
for using a proof
that shows Sylow's subgroups to exist.
Nobody should ever pay a licence fee
for using a program
that computes Sylow's subgroups.
(J. Neub"user)
GAP is distributed *free of charge*. You can obtain it via 'ftp' or
electronic mail and give it away to your colleagues. GAP is *not* in the
public domain, however. In particular you are not allowed to incorporate
GAP or parts thereof into a commercial product.
If you get GAP, we would appreciate it if you could notify us, e.g., by
sending a short e-mail message to '[email protected]',
containing your full name and address, so that we have a rough idea of
the number of users. We also hope that this number will be large enough
to convince various agencies that GAP is a project worthy of (financial)
support. If you publish some result that was partly obtained using GAP,
we would appreciate it if you would cite GAP, just as you would cite
another paper that you used. Again we would appreciate if you could
inform us about such a paper.
We distribute the *full source* for everything, the C code for the
kernel, the GAP code for the library, and the LaTeX code for the manual,
which has at present about 700 pages. So it should be no problem to get
GAP, even if you have a rather uncommon system. Of course, ports to non
UNIX systems may require some work. We already have a port to the Atari
ST. A port to IBM PC compatibles with an Intel 80386 or 80486 is under
way. We also hope to provide a port to the Apple Macintosh in the near
future. Note that about 4 MByte of main memory and a harddisk are
required to run GAP.
GAP 3.1 can be obtained by anonymous *ftp* from the following servers.
'samson.math.rwth-aachen.de':
Lehrstuhl D fur Mathematik, RWTH Aachen, Germany (137.226.152.6).
'dimacs.rutgers.edu':
DIMACS, Rutgers, New Brunswick, New Jersey (128.6.75.16).
'math.ucla.edu':
Math. Dept., Univ. of California at Los Angeles (128.97.4.254).
'pell.anu.edu.au':
Math. Dept., Australian National Univ., Canberra (150.203.15.5).
'ftp' to the server *closest* to you, login as user 'ftp' and give your
full e-mail address as password. GAP is in the directory 'pub/gap'.
Remember when you transmit the files to set the file transfer type to
*binary image*, otherwise you will only receive unusable garbage. Those
servers will always have the latest version of GAP available.
GAP can also be obtained via *electronic mail*. To get one of the files
mentioned below send a message to '[email protected]'
containing a line 'get GAP <file-name>', e.g., 'get GAP src3r1.tar.Z'.
'listserv' will reply by sending you the file as e-mail message.
Because most files are large binary files they will be uuencoded and
split into several parts, each at most 64 kBytes large. You can
concatenate the parts by hand, removing the mail header, and then use
'uudecode' to decode them. We suggest however that you also get 'uud.c',
which skips the mail headers automatically and is also able to fix up
transmission errors caused by 'EBCDIC' machines. You can also get single
parts of a file by sending 'get GAP <file-name> <part-nr>'.
For users in the United Kingdom with only Janet access, neither 'ftp' nor
the mail server will work (please do *not* try to use the mail server).
Please contact Derek Holt (e-mail address '[email protected]'). He
has kindly offered us to distribute GAP in the United Kingdom.
The 'ftp' directory and the 'listserv' archive contain the following
files. Please check first which files you need, to avoid transferring
those that you don't need.
'README': the file you are currently reading.
GAP version 3 release 1 itself comes in several files. You do not need
all of those files. All files are 'compress'-ed 'tar' archives.
'src3r1.tar.Z': the *source code* for the GAP kernel. You need
this unless you get one of the executables below.
This file is about 600 KBytes long.
'lib3r1.tar.Z': the *library of functions*. You need this. This
file is about 700 KBytes long.
'doc3r1.tar.Z': the *documentation*. Serves as LaTeX source
for the printed manual and online documentation.
Contains further installation information. This
file is about 700 KBytes long.
'doc3r1.dvi.Z': the preformatted documentation. You need this
if you do not have a *big* TeX. This file is
about 900 KByte long.
'grp3r1.tar.Z': various *group libraries*. Contains for example
all primitive permutation groups of degree at
most 50. This file is about 50 KByte long.
'two3r1.tar.Z': the library of *2-group* of size at most 256.
This file is about 630 KByte long.
'tbl3r1.tar.Z': a library of *character tables* including all of
the ATLAS. This file is about 2000 KByte long.
'src3r1.zoo', 'lib3r1.zoo', 'doc3r1.zoo',
'grp3r1.zoo', 'tbl3r1.zoo', 'two3r1.zoo':
'zoo' archives containing *exactly* the same
files as the 'compress'-ed 'tar' archives above.
The advantage of 'compress'-ed 'tar' archives is
that 'uncompress' and 'tar' are widely available
on UNIX systems. The advantage of 'zoo' archives
is that they are smaller (about 30 percent) and
that 'zoo' is more common on PC-s and Atari ST-s.
(These files may not be available on all servers)
We supply executables for some of the more popular machines. If you have
one of those machines it will be easier for you to get this executable
instead of compiling GAP yourself. The following executables are
available (again these files may not be available on all servers)
'gapexe.st': executable for Atari ST (680?0) running TOS
compiled with the GNU C compiler. This file is
about 360 KByte long.
'gapexe.su3': executable for SUN 3 (680?0) running SunOS 4.0 or
higher compiled with SunOS C. This file is about
410 KByte long.
'gapexe.su4': executable for SUN 4 (Sparc) running SunOS 4.0 or
higher compiled with SunOS C. This file is about
450 KByte long.
'gapexe.dec': executable for DECstation (MIPS) running Ultrix
4.0 or higher compiled with Ultrix C. This file
is about 500 KByte long.
The following support files are also available (and again these files may
not be available on all servers)
'compress.tar': 'compress' version 4.1. You need this program
to uncompress the compressed tar files. Note
however, that almost all UNIX systems these days
already come with an executable 'compress'. This
file is about 90 KByte long.
'uud.c': 'uud' version 3.4. 'uud' is much better than the
'uudecode' that comes with most UNIX systems.
This file is about 12 KByte long.
'zoo21.tar.Z': Rahul Dhesi's 'zoo' archiver version 2.1. You
need this to unpack the *zoo-archives*. Note
that the widespread version 2.01 will *not* work.
This file is about 250 KByte long.
'zooexe.st': Executable of 'zoo' for the Atari ST. This file
is about 80 KByte long.
How to install GAP
==================
The file 'install.tex' in 'doc3r1.tar.Z' contains extensive installation
instructions. If however, you are one of those who never read manuals,
here is a quick installation guide.
Make a directory for GAP, e.g., '~/gap/' or '/usr/local/lib/gap/'.
Unpack the source archive 'src3r1.tar.Z' into the subdirectory 'src/';
unpack the library archive 'lib3r1.tar.Z' into the subdirectory 'lib/';
unpack the documentation 'doc3r1.tar.Z' into the subdirectory 'doc/'.
If you have obtained the optional groups and character tables libraries
'grp3r1.tar.Z', 'tbl3r1.tar.Z', and 'two3r1.tar.Z', unpack them into
the subdirectories 'grp/', 'tbl/', and 'two/'.
Change into 'src/' and execute 'make' to see a list of possible targets;
select a target, if in doubt use 'bsd' or 'usg', and make the kernel.
In an appropriate directory, e.g., '~/bin/' or '/usr/local/bin/', create
a shell script that executes the GAP kernel. This should look like
exec <gap-directory>/src/gap -m 4m -l <gap-directory>/lib/ $*
The option '-m' specifies the amount of initial memory; the option '-l'
specifies where to find the library, if you get it wrong GAP complains
gap: hmm, I cannot find 'lib/init.g', maybe use option '-l <libname>'?
Change into 'doc/' and make the printed manual with the commands
latex manual; latex manual; lp -dvi manual.dvi
or something similar, according to your local custom for using LaTeX.
Try something in GAP, e.g., the following exercises GAP quite a bit
gap> m11 := Group( (1,2,3,4,5,6,7,8,9,10,11), (3,7,11,8)(4,10,5,6) );;
gap> Number( ConjugacyClasses( m11 ) );
The result should be 10.
The Future of GAP
=================
See ye not all these things?
Verily I say unto you,
there shall not be left here
one stone upon another,
that shall not be thrown down.
(Matthew 24:2)
Clearly GAP will contain bugs, as any system of this size, though
currently we know none. Also there are things that we feel are still
missing, and that we would like to include into GAP. We will continue to
improve and extend GAP. We will release new versions quite regulary now,
about three or four upgrades a year are planned.
We are committed however, to staying upward compatible from now on in
future releases. That means that everything that works now will also
work in those future releases. This is different from the quite radical
step from GAP 2.4 to GAP 3.1, in which almost everything was changed.
Of course, we have ideas about what we want to have in future versions of
GAP. However we are also looking forward to your comments or
suggestions.
The GAP Forum
=============
We have also established a GAP forum, where interested users can discuss
GAP related topics by e-mail. In particular this forum is for questions
about GAP, general comments, bug reports, and maybe bug fixes. We, the
developers of GAP, will read this forum and answer questions and
comments, and distribute bug fixes. Of course others are also invited to
answer questions, etc. We will also announce future releases of GAP on
this forum. So in order to be informed about bugs and their fixes as
well as about additions to GAP we recommend that you subscribe to the GAP
forum.
To subscribe send a message to '[email protected]'
containing the line 'subscribe gap-forum <your-name>', where <your-name>
should be your full name, not your e-mail address. You will receive an
acknowledgement, and from then on all e-mail messages sent to
'[email protected]'.
'[email protected]' also accepts the following
requests: 'help' for a short help on how to use 'listserv', 'unsubscribe
gap-forum' to unsubscribe again, 'recipients gap-forum' to get a list of
subscribers, and 'statistics gap-forum' to see how many e-mail messages
each subscriber has sent so far.
If you have further questions or comments do not hesitate to write to me
'[email protected]'.
Thank you for your attention, Martin.
--
Martin Sch"onert, [email protected], +49 241 804551
Lehrstuhl D f"ur Mathematik, Templergraben 64, RWTH, D 51 Aachen, Germany
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