This file contains the mails sent to the GAP forum in July-September 1993.

Name               Email address                           Mails    Lines
Frank Celler       fceller@math.rwth-aachen.de                 9      335
Martin Schoenert   martin@math.rwth-aachen.de                  9      210
Joachim Neubueser  neubuese@math.rwth-aachen.de                7      221
Dima Pasechnik     dima@maths.uwa.edu.au                       4       68
Leonard Soicher    L.H.Soicher@qmw.ac.uk                       3       60
Jaroslav Gurican   gurican@alpha.dcs.mff.uniba.cs              2       94
Alexander Hulpke   hulpke@abacus.concordia.ca                  2       55
Eamonn O'Brien     obrien@pell.anu.edu.au                      2       48
Dana-Picard Noah   dana@bimacs.cs.biu.ac.il                    2       44
Toni Greil         greil@guug.de                               2       32
Dave Donaghy       Dave.Donaghy@bristol.ac.uk                  2       17
Philip Osterlund   osterlu@s5.math.umn.edu                     1       58
Harald Boegeholz   hwblist@machnix.mathematik.uni-stuttgart.de 1       49
Luis Valero        valero@s5.math.umn.edu                      1       41
Thomas Breuer      sam@math.rwth-aachen.de                     1       31
Hiroshi Matsuyama  f50014@sakura.kudpc.kyoto-u.ac.jp           1       26
Johannes Mueller   Johannes_Mueller@su.maus.de                 1       18
Norai Rocco        norai@ime.unicamp.br                        1       15
Ruth Schwingel     RUTH@brunb                                  1       14
Michael Smith      smith@pell.anu.edu.au                       1       12
David Sibley       sibley@math.psu.edu                         1       12
Prof. Knapp        knapp@donau.mathematik.uni-tuebingen.de     1       10
N. S. Mendelsohn   mendel@ccu.umanitoba.ca                     1        9
Daniel Ruberman    RUBERMAN@binah.cc.brandeis.edu              1        9
Yasuhiro HONDA     honda@smlab.tutkie.tut.ac.jp                1        7
Bill Bogley        bogley@math.orst.edu                        1        4
Steve Linton       sl25@cus.cam.ac.uk                          1        3
Jackie Ford        ffor@gauss.math.rochester.edu               1        2

This  file is in Berkeley mail drop format, which means you can read this
file with 'mail -f <name-of-the-file>'  or 'mailx -f <name-of-the-file>'.
It is also possible however to read this file with any text editor.



From obrien@pell.anu.edu.au Sun Jul  4 08:16:24 1993
From:        obrien@pell.anu.edu.au "Eamonn O'Brien"
Date:        Sun, 4 Jul 93 08:16:24 +0200
Subject:     ANU p-Quotient Program Version 1.1

Version 1.1 of the ANU p-Quotient Program is now available
by anonymous FTP. This version can be run as part of the
share library of GAP 3.2.  

The files "anupq.tar.Z" and "anupq.zoo" are available by 
anonymous ftp from "pub/gap" on "samson.math.rwth-aachen.de"  
They are also available in "pub/gap-3.2" from "pell.anu.edu.au"

This program provides access to implementations of 
the following algorithms:

-- p-quotient computations;

-- p-group generation;

-- a "standard presentation" algorithm which permits 
   isomorphism testing for p-groups;

-- an algorithm to compute a description of the
   automorphism group of a p-group.

New features of the first two implementations are now accessible 
via GAP; the latter two are publicly available for the first time.

Feedback and bug reports are welcomed.

++++++++++++++++++++++++++++++++++++++++++++++
Eamonn O'Brien
School of Mathematical Sciences
Australian National University
Canberra, 0200 

FAX +61-(0)6-249 5549 
Telephone +61-(0)6-249 2963 (office)
e-mail obrien@pell.anu.edu.au
++++++++++++++++++++++++++++++++++++++++++++++



From dana@bimacs.cs.biu.ac.il Wed Jul 14 13:34:34 1993
From:        dana@bimacs.cs.biu.ac.il "Dana-Picard Noah"
Date:        Wed, 14 Jul 93 13:34:34 +0200
Subject:     DimensionLoewyFactors

Dear Forum,
I entered some small p-groups as finitely presented groups and used
the function DimensionsLoewyFactors. For the first ones everything
seemed OK, but once I got the following:

gap> g:=Group(a,b,c);
Group( a, b, c )
gap> g.name:="g";
"g"
gap> g.relators:=[a^3,b^3,c^3,a*b*a^2*b^2,a*c*b*a^2*c^2,b*c*b^2*c^2];
[ a^3, b^3, c^3, a*b*a^2*b^2, a*c*b*a^2*c^2, b*c*b^2*c^2 ]
gap> Size(g);
27
gap> DimensionsLoewyFactors(g);
Error, This function will not work for finitely presented groups.
Please use 'OperationCosetsFpGroup' in order to construct
an isomorphic permutation group in
G.operations.ConjugacyClasses( G ) called from
ConjugacyClasses( G ) called from
G.operations.Agemo( G, p ) called from
AgemoAbove( L[i], C, p ) called from
G.operations.JenningsSeries( G ) called from
..
brk> 

What happens here? 

Furthermore, I got the same
> Please use 'OperationCosetsFpGroup' in order to construct
> an isomorphic permutation group 
when trying to compute Centre or ConjugacyClasses of a finitely
presented group.
Could somebody send more information and/or examples?

Thanks a lot,
Thierry Dana-Picard.



From neubuese@math.rwth-aachen.de Wed Jul 14 15:33:02 1993
From:        neubuese@math.rwth-aachen.de "Joachim Neubueser"
Date:        Wed, 14 Jul 93 15:33:02 +0200
Subject:     Re: DimensionLoewyFactors

Thierry Dana-Picard asked:
> I entered some small p-groups as finitely presented groups and used
> the function DimensionsLoewyFactors. For the first ones everything
> seemed OK, but once I got the following:
> 
> gap> g:=Group(a,b,c);
> Group( a, b, c )
> gap> g.name:="g";
> "g"
> gap> g.relators:=[a^3,b^3,c^3,a*b*a^2*b^2,a*c*b*a^2*c^2,b*c*b^2*c^2];
> [ a^3, b^3, c^3, a*b*a^2*b^2, a*c*b*a^2*c^2, b*c*b^2*c^2 ]
> gap> Size(g);
> 27
> gap> DimensionsLoewyFactors(g);
> Error, This function will not work for finitely presented groups.
> Please use 'OperationCosetsFpGroup' in order to construct
> an isomorphic permutation group in
> G.operations.ConjugacyClasses( G ) called from
> ConjugacyClasses( G ) called from
> G.operations.Agemo( G, p ) called from
> AgemoAbove( L[i], C, p ) called from
> G.operations.JenningsSeries( G ) called from
> ..
> brk> 
> 
> What happens here? 
> 
> Furthermore, I got the same
> > Please use 'OperationCosetsFpGroup' in order to construct
> > an isomorphic permutation group 
> when trying to compute Centre or ConjugacyClasses of a finitely
> presented group.
> Could somebody send more information and/or examples?

The answer is fairly  simple: There are  no general algorithms to find
for  a finitely   presented  group its  conjugacy  classes, centre  or
Jennings series (from  which in turn the  dimensions of the factors of
the  Loewy series  are  obtained).   This   is a  consequence   of the
unsolvability of the word problem.  However, if the finitely presented
group is indeed  finite, a faithful  permutation representation can be
found and used. GAP does not try to do this automatically but asks the
user to use 'OperationCosetsFpGroup' to do just that.

Just in very special cases, e.g. if the presentation exhibits that the
group is in fact finite abelian, the function 'DimensionsLoewyFactors'
will recognise this and  directly give the answer.   This is perhaps a
slightly misleading act of courtesy since  it is then in fact puzzling
why a  function that did answer for  some very small examples suddenly
does not work.

By the way, if you want to compute the dimensions of the Loewy factors
of a  p-group  it  is  advisable to  describe   the  group by an    AG
(polycyclic) presentation from which GAP can work directly.

I hope that this clarifies the situation.      Joachim Neubueser



From mendel@ccu.umanitoba.ca Mon Jul 19 22:25:17 1993
From:        mendel@ccu.umanitoba.ca "N. S. Mendelsohn"
Date:        Mon, 19 Jul 93 22:25:17 +0200
Subject:     GAP 3.2 on the Mac

For those not contacted by H. Lakser, Gap 32 on the Mac may be obtained
from ftp anonymous at the address ccu.umanitoba.ca.  It is archived as
/pub/mac/macgap32.
The directory of macgap32 contains the following four files for
downloading: MacGap32.sea.hqx; doc32.sea.hqx; lib32.sea.hqx; and
macgap32.info.  These files are all self extracting. 

N. S. Mendelsohn



From dana@bimacs.cs.biu.ac.il Wed Jul 21 11:02:25 1993
From:        dana@bimacs.cs.biu.ac.il "Dana-Picard Noah"
Date:        Wed, 21 Jul 93 11:02:25 +0200
Subject:     Conjugacy classes

Dear Forum,
Let t be the character table of a group g, given by GAP. Is there a
way to get the elements of the various conjugacy classes of g and the
correspondence between these classes and the columns of t?
Thanks a lot,
Thierry Dana-Picard.



From sam@math.rwth-aachen.de Wed Jul 21 11:40:23 1993
From:        sam@math.rwth-aachen.de "Thomas Breuer"
Date:        Wed, 21 Jul 93 11:40:23 +0200
Subject:     Re: Conjugacy classes

Dear Mrs. and Mr. Forum,
Thierry Dana-Picard asks the following question.

> Let <t> be the character table of a group <g>, given by GAP. Is there a
> way to get the elements of the various conjugacy classes of <g> and the
> correspondence between these classes and the columns of <t>?

If <t> has been computed from <g> using 'CharTable' then the conjugacy
classes of <g> are stored in the component '<g>.conjugacyClasses', and
their ordering is the same as that of the columns in <t>.

If <t> is a library table then there is no particular representation of
the underlying group <g> attached to <t>, so it is not clear what it means
to ``get the elements'' of a conjugacy class corresponding to a particular
column of <t>.  So the problem might be to identify the columns of a
library table <t> with the conjugacy classes of a group <g> for which <t>
is the character table.  Probably many of the classes of <g> will be easily
identified by their element and centralizer orders, and maybe other
invariants.  If this is not sufficient, one can compute the character
table of <g>, and then find permutations of columns and rows that transform
this table into <t> (e.g. using 'TransformingPermutationsCharTables').

In some cases there is a generic description of conjugacy classes, e.g.,
the classes of symmetric groups are parametrized by partitions, and the
classes of general linear groups are parametrized by normal forms of
matrices.  This may make it easier to identify the columns and the classes.

Kind regards
Thomas Breuer
(sam@ernie.math.rwth-aachen.de)



From fceller@math.rwth-aachen.de Wed Jul 21 12:52:35 1993
From:        fceller@math.rwth-aachen.de "Frank Celler"
Date:        Wed, 21 Jul 93 12:52:35 +0200
Subject:     New Grape (Version 2.1)

Dear Forum,
Leonard Soicher's new version of GRAPE (Version 2.1), a GAP share
library package for graph algorithms, is available on our ftp server
(samson.math.rwth-aachen.de) as zoo and tar archive.

  -r--r--r--  1 ftp         60365 Feb 19 17:28 grp3r2.tar.Z
  -r--r--r--  1 ftp         35194 Feb 19 17:28 grp3r2.zoo

The following is an extract from the README.

-----------------------------------------------------------------------------
    GRAPE (GRaph Algorithms using PErmutation groups),
    Version 2.1, L.H.Soicher@qmw.ac.uk, 12 July 1993.

    Changes from previous versions of GRAPE other than new functions and new 
    function parameters:
       (1) Nauty Version 1.7 is now used. Note that canonical labellings could 
           be different from those produced by nauty 1.4, which was used in 
           previous versions of GRAPE.
       (2) EnumColadj now returns an intersection matrix for the trivial
	   orbital graph, in addition to the intersection matrices for the 
	   other orbital graphs.
       (3) MakeIntransitiveGroupGenerators now called 
	   IntransitiveGroupGenerators.
       (4) VertexName now returns a copy (of the vertex name).

    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.  
-----------------------------------------------------------------------------

best wishes
  Frank



From fceller@math.rwth-aachen.de Wed Jul 21 14:32:49 1993
From:        fceller@math.rwth-aachen.de "Frank Celler"
Date:        Wed, 21 Jul 93 14:32:49 +0200
Subject:     Re: New Grape (Version 2.1)

Dear Forum,
>>     -r--r--r--  1 ftp         60365 Feb 19 17:28 grp3r2.tar.Z
>>     -r--r--r--  1 ftp         35194 Feb 19 17:28 grp3r2.zoo

this should be

    -r--r--r--  1 ftp        456034 Jul 21 12:22 grape.tar.Z
    -r--r--r--  1 ftp        366431 Jul 21 12:22 grape.zoo

best wishes
  Frank



From L.H.Soicher@qmw.ac.uk Wed Jul 21 18:12:58 1993
From:        L.H.Soicher@qmw.ac.uk "Leonard Soicher"
Date:        Wed, 21 Jul 93 18:12:58 +0200
Subject:     Important information on the new GRAPE 2.1

            The new GRAPE 2.1 gap share library package
                    for computing with graphs
           -------------------------------------------

                     *Important Information*

This GAP 3.2 share library package is the latest version of GRAPE.  

Old GRAPE users should note that it includes online documentation, new
functions, some new (optional) function parameters, and the nauty
version 1.7 system (and they should alter their .gaprc so that an old
version of GRAPE is not read, and insert  RequirePackage("grape");
instead!).

As well as being available from Aachen, GRAPE 2.1 is available via
anonymous ftp from galois.maths.qmw.ac.uk (138.37.80.15)  in the file
pub/grape/2.1/grape.tar.Z.  Also available is the file
pub/grape/2.1/grapedoc.dvi.Z,  the uncompressed version of which
includes a description of GRAPE, the installation instructions, and
documentation for GRAPE functions (when GRAPE is installed, all this
documentation is available online in the usual GAP way).  The file
grapedoc.dvi is also part of the grape.tar archive, and you should read
it!

Please email L.H.Soicher@qmw.ac.uk if you install GRAPE 2.1.

If you use GRAPE to solve a problem then also tell me about it,
and reference

L.H.Soicher, GRAPE: a system for computing with graphs and groups, in
Proc. 1991 DIMACS Workshop on Groups and Computation, DIMACS Series in
Discrete Mathematics and Theoretical Computer Science, to appear.

If you use the automorphism group and graph isomorphism testing
functions of GRAPE 2.1 then you are also using Brendan McKay's nauty 1.7
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.  

I hope you find GRAPE useful.  Please send comments on GRAPE, bug
reports, etc. to L.H.Soicher@qmw.ac.uk.



From honda@smlab.tutkie.tut.ac.jp Thu Jul 22 07:32:02 1993
From:        honda@smlab.tutkie.tut.ac.jp "Yasuhiro HONDA"
Date:        Thu, 22 Jul 93 07:32:02 +0200
Subject:     Gr\"{o}bner bases software

Does anyone have software for Gr\"{o}bner bases algorithm on GAP?

Thanks.

--
              Yasuhiro HONDA @ Toyohashi Univ. of Tech.



From f50014@sakura.kudpc.kyoto-u.ac.jp Fri Jul 23 02:06:20 1993
From:        f50014@sakura.kudpc.kyoto-u.ac.jp "Hiroshi Matsuyama"
Date:        Fri, 23 Jul 93 02:06:20 +0200
Subject:     Problem in FactorsInt

Dear Gap Forum,

I use Gap on SVR4/386 (Japanese version) with intel 80486/60MHz.
I tried factoring the 17-th repunit as follows.
But Gap does not factorize it, and exits to shell. 

---------------------------------------
gap> FactorsInt((10^17-1)/9);
   Gasman: last bag of type str and size     4 has overwritten the free bag.
$
---------------------------------------

Of course, Gap on Sparc station and Gap386.exe 
can factor (10^17-1)/9 corrrectly.
This implies that the problem is in the machine (NEC) or
in the Japanes version of UNIX SVR4/386.

What the message means ?
Please give me any advice.

Hiroshi Matsuyama
F50014@sakura.kudpc.kyoto-u.ac.jp
Dept. of Math.
Hyougo Univ. of Teacher Edu.
Japan



From gurican@alpha.dcs.mff.uniba.cs Fri Jul 23 09:48:22 1993
From:        gurican@alpha.dcs.mff.uniba.cs "Jaroslav Gurican"
Date:        Fri, 23 Jul 93 09:48:22 +0200
Subject:     PQ on VAX/VMS

Dear Professor,
I would like to get sources of PQ and/or NQ for VAX/VMS if you provide
them. I tried to get something from your ftp server pell.anu.edu.au,
but acces bits are bad, I got message : permission denied for files in 
PQ, NQ and gap-3.2 directories (but I could list these directories).
Sincerely, 
	Jaroslav Gurican, 
	Dept. of Algebra, 
	Comenius University at Bratislava,
	Slovakia (former Czechoslovakia)



From martin@math.rwth-aachen.de Mon Jul 26 14:53:10 1993
From:        martin@math.rwth-aachen.de "Martin Schoenert"
Date:        Mon, 26 Jul 93 14:53:10 +0200
Subject:     Upgrade for GAP 3.2 patchlevel 2 (V3R2P2) to patchlevel 3 (V3R2P3)

This is  to announce the availibility of  the third  upgrade for GAP 3.2.
This upgrade brings version 3 release  2 patchlevel 2 (V3R2P2) to version
3 release 2   patchlevel 3 (V3R2P3).  The   priority of  this upgrade  is
medium.

This  upgrade adds  adds a  group of  size  96 that  was missing from the
library of solvable groups of size <= 100.  It also adds symmetric groups
on 0 and 1 points.

This upgrade  fixes the reported  problem with subgroups in a composition
series of  a permutation group having  a trivial elements list.  Also the
functions for permutation groups are a little  bit more carefull to avoid
creation of unnecessary  lists.  Coset enumerations in finitely presented
groups  will now enter  a  break loop  if more than  a  certain number of
cosets have been  defined,  to give the user   the choice to  abandon the
enumeration.  A problem  with  the computation  of double cosets  in very
small groups is fixed.  A problem in the implementation of Dixon's method
to compute the character table of  a group is  fixed.  Two functions that
assumed that the trivial character is always first in the character table
were fixed.  'DisplayCharTable' now handles character tables that have no
powermap.  A function  'InterpolatedPolynomial' was added.  The  function
that divides polynomials now  checks if the  divisor and not the dividend
is nonzero.  An incorrect test in the function  that composes mappings is
fixed.

A function 'LogInputTo' was added to the  kernel.  The kernel didn't know
about the  new  ranges with  three  operands, so  the  third operand  was
sometimes  deleted by the garbage collection,  leading  to address errors
and core dumps.

The upgrade is available as  file  'upg3r2p3.dif.Z'  on the  'ftp' server
'samson.math.rwth-aachen.de'.  It should be  available on the other 'ftp'
servers soon.  This time I do not send out this  upgrade as e-mail, it is
simply too large (about 100 KBytes 'compress'-ed).

First unpack the upgrade with 'uncompress upg3r1p3.dif.Z'.  Then read the
beginning   of   the   unpacked   file  'upg3r2p3.dif',   which  contains
instructions how to apply this upgrade.

Martin.

-- .- .-. - .. -.  .-.. --- ...- . ...  .- -. -. .. -.- .-
Martin Sch"onert,   Martin.Schoenert@Math.RWTH-Aachen.DE,   +49 241 804551
Lehrstuhl D f"ur Mathematik, Templergraben 64, RWTH, 52056 Aachen, Germany



From hulpke@abacus.concordia.ca Mon Jul 26 16:49:52 1993
From:        hulpke@abacus.concordia.ca "Alexander Hulpke"
Date:        Mon, 26 Jul 93 16:49:52 +0200
Subject:     Re: Conjugacy classes

Dear Mrs. and Mr. Forum,
Thomas Breuer already answered the question of Thierry Dana-Picard.
however, there are two minor comments, I'd like to add:

When the ``easy'' invariants (orders, centralizers, permutation
character etc.) are not sufficient, and one has to compute the character
table of <g>, it may be sufficient, to compute this table only
partially (especially, if the group is large, the computation of the
whole table is not feasible at all). 

A lot of this identification process could be automized. The routine
would be given a group, a character table and (if possible) further
informations, as the type of the permutation character (when using
permutation representations of small degree, this character is sometimes
determined unique by the degree, even without knowing the values on the
conjugacy classes). The routine then would try to find a unique mapping
and compute further information (conjugacy classes, powermap, partial
character table) etc. itself until the correspondence is determined
completely (As the character table is known already, some of these
computations would be much more easy, then in  the general case, as
sometimes the character table will give information, that can save
tedious computations, e.g. conjugacy tests).

Some time ago, I had considered writing a routine of this type, since I
needed something similar, but for the particular case, working ``by
hand'' had been faster. If there is sufficiently demand for that kind of
routine, I would reconsider my decision. (I can not promise anything
about availiability of a routine of this type yet.)
In case, you would be interested in such a routine please send me a
short eMail message (to the adress in the footer, not to the gap-forum
itself, as most readers won't be interested in particular answers).

Alexander Hulpke
(hulpke@bert.math.rwth-aachen.de)



From martin@math.rwth-aachen.de Tue Jul 27 07:19:48 1993
From:        martin@math.rwth-aachen.de "Martin Schoenert"
Date:        Tue, 27 Jul 93 07:19:48 +0200
Subject:     Re: Gr\"{o}bner bases software

Yasuhiro Honda writes in his e-mail message of 1993/07/22
    Does anyone have software for Gr\"{o}bner bases algorithm on GAP?

Unfortunately no.  Note that the current implementation of multivarite
polynomials in GAP is not very efficient.

Martin.

-- .- .-. - .. -.  .-.. --- ...- . ...  .- -. -. .. -.- .-
Martin Sch"onert,   Martin.Schoenert@Math.RWTH-Aachen.DE,   +49 241 804551
Lehrstuhl D f"ur Mathematik, Templergraben 64, RWTH, 52056 Aachen, Germany



From martin@math.rwth-aachen.de Tue Jul 27 07:33:24 1993
From:        martin@math.rwth-aachen.de "Martin Schoenert"
Date:        Tue, 27 Jul 93 07:33:24 +0200
Subject:     Re: Problem in FactorsInt

Hiroshi Matsuyama writes in his e-mail message of 1993/07/23
    I use Gap on SVR4/386 (Japanese version) with intel 80486/60MHz.
    I tried factoring the 17-th repunit as follows.
    But Gap does not factorize it, and exits to shell. 

    ---------------------------------------
    gap> FactorsInt((10^17-1)/9);
    Gasman: last bag of type str and size     4 has overwritten the free bag.
    $
    ---------------------------------------

    Of course, Gap on Sparc station and Gap386.exe 
    can factor (10^17-1)/9 corrrectly.
    This implies that the problem is in the machine (NEC) or
    in the Japanes version of UNIX SVR4/386.

    What the message means ?
    Please give me any advice.

This is a message from Gasman -- GAP's storage manager.  Each time an
object is allocated Gasman checks that the word behind the previously
allocated object has not been overwritten.  This check failed in the
example above.  I.e. the last bag, which was a string with 3 characters
(plus a terminating '\0' character) has overwritten the following word.

Does the executable work for other problems?  Or does it fail for any
nontrivial computation?  Which C compiler did you use?  Have you compiled
GAP without the optimizer (i.e., without the '-O' option)?

Please send your answer to 'gap-trouble@samson.math.rwth-aachen.de'.  If
anything interesting comes out of this I will summarize in the GAP
forum.

Martin.

-- .- .-. - .. -.  .-.. --- ...- . ...  .- -. -. .. -.- .-
Martin Sch"onert,   Martin.Schoenert@Math.RWTH-Aachen.DE,   +49 241 804551
Lehrstuhl D f"ur Mathematik, Templergraben 64, RWTH, 52056 Aachen, Germany



From martin@math.rwth-aachen.de Tue Jul 27 07:39:53 1993
From:        martin@math.rwth-aachen.de "Martin Schoenert"
Date:        Tue, 27 Jul 93 07:39:53 +0200
Subject:     Re: PQ on VAX/VMS

Jaroslav Gurican writes in his e-mail message of 1993/07/23
    I would like to get sources of PQ and/or NQ for VAX/VMS if you provide
    them. I tried to get something from your ftp server pell.anu.edu.au,
    but acces bits are bad, I got message : permission denied for files in 
    PQ, NQ and gap-3.2 directories (but I could list these directories).

Very strange.  I could get the files from 'pell.anu.edu.au' in the
directories 'pub/PQ', 'pub/NQ', and 'pub/gap' without any problems.  Be
that as it may.  You can also take the files 'anupq.tar.Z' and 'nq.tar.Z'
from 'samson.math.rwth-aachen.de'.

Martin.

-- .- .-. - .. -.  .-.. --- ...- . ...  .- -. -. .. -.- .-
Martin Sch"onert,   Martin.Schoenert@Math.RWTH-Aachen.DE,   +49 241 804551
Lehrstuhl D f"ur Mathematik, Templergraben 64, RWTH, 52056 Aachen, Germany



From osterlu@s5.math.umn.edu Tue Jul 27 07:51:57 1993
From:        osterlu@s5.math.umn.edu "Philip Osterlund"
Date:        Tue, 27 Jul 93 07:51:57 +0200
Subject:     Redefining "+, -, *, =," etc.

Dear Forum:
	I would like to be able to create a domain in which I redefine addition
and multiplication.  I was able to do so in version 3.1, but I'm having
difficulty in version 3.2.  These are defined as functios, as shown below.

gap>  G := SymmetricGroup(5);;
gap> a := AbstractGenerator("a");;b :=AbstractGenerator("b");;
gap> a5:= Group(a,b);;a5.relators := [a^2,b^3,(a*b)^5];;
gap> D := DirectProduct(G,a5);
Group( DirectProductElement( (1,5), IdWord ), DirectProductElement( 
(2,5), IdWord ), DirectProductElement( (3,5), IdWord ), DirectProductElement( 
(4,5
 ), IdWord ), DirectProductElement( (), a ), DirectProductElement( (), b ) )
gap>  ops := D.identity.operations;
rec(
  = := function ( a, b ) ... end,
  < := function ( a, b ) ... end,
  * := function ( a, b ) ... end,
  / := function ( a, b ) ... end,
  mod := function ( a, b ) ... end,
  ^ := function ( a, b ) ... end,
  Comm := function ( a, b ) ... end,
  Print := function ( a ) ... end )


But I can't access these functions.  The obvious guess is:


gap> ops.=;
Syntax error: record component name expected
ops.=;
    ^

What used to work is:


gap> ops.'=';
Syntax error: record component name expected
ops.'=';
      ^

Another possible guess is:


gap> ops."=";
Syntax error: record component name expected
ops."=";
      ^

Just to check that I'm looking at the right object:


gap> ops.Print;
function ( a ) ... end

Thanks for any suggestions.
			-Philip Osterlund



From martin@math.rwth-aachen.de Tue Jul 27 08:01:39 1993
From:        martin@math.rwth-aachen.de "Martin Schoenert"
Date:        Tue, 27 Jul 93 08:01:39 +0200
Subject:     Re: Redefining "+, -, *, =," etc.

Philip Osterlund writes in his e-mail message of 1993/07/27
    I would like to be able to create a domain in which I redefine addition
    and multiplication.  I was able to do so in version 3.1, but I'm having
    difficulty in version 3.2.  These are defined as functios, as shown
    below.

    ...example deleted...

    But I can't access these functions.  The obvious guess is:

    gap> ops.=;
    Syntax error: record component name expected

    What used to work is:

    gap> ops.'=';
    Syntax error: record component name expected

    Another possible guess is:

    gap> ops."=";
    Syntax error: record component name expected

The single quotes are now used to specify character constants, i.e.,
'=' is the equal character.  There are two possibilities.

    gap> ops.\=;
    function ( left, right ) ... end
    gap> ops.("=");
    function ( left, right ) ... end

The first is preferrable, because in the second one the string value is
looked up at runtime.

Martin.

-- .- .-. - .. -.  .-.. --- ...- . ...  .- -. -. .. -.- .-
Martin Sch"onert,   Martin.Schoenert@Math.RWTH-Aachen.DE,   +49 241 804551
Lehrstuhl D f"ur Mathematik, Templergraben 64, RWTH, 52056 Aachen, Germany



From ffor@gauss.math.rochester.edu Tue Jul 27 14:18:28 1993
From:        ffor@gauss.math.rochester.edu "Jackie Ford"
Date:        Tue, 27 Jul 93 14:18:28 +0200
Subject:     

unsubscribe



From RUBERMAN@binah.cc.brandeis.edu Tue Aug 10 16:28:35 1993
From:        RUBERMAN@binah.cc.brandeis.edu "Daniel Ruberman"
Date:        Tue, 10 Aug 93 16:28:35 +0200
Subject:     SL_2

Dear Gap Forum--I was hoping to do some investigations concerning
SL_2 and PSL_2 of the ring of integers in Q(sqrt(p)).  These groups are
finitely presented (I believe) but I haven't been able to find an explicit
presentation in the literature.  Specific examples (e.g. p=5) would be of
interest as well as the general case.

Thank you,
Daniel Ruberman



From greil@guug.de Tue Aug 10 16:55:13 1993
From:        greil@guug.de "Toni Greil"
Date:        Tue, 10 Aug 93 16:55:13 +0200
Subject:     Re: SL_2

> 
> Dear Gap Forum--I was hoping to do some investigations concerning
> SL_2 and PSL_2 of the ring of integers in Q(sqrt(p)).  These groups are
> finitely presented (I believe) but I haven't been able to find an explicit
> presentation in the literature.  Specific examples (e.g. p=5) would be of
> interest as well as the general case.
> 
> Thank you,
> Daniel Ruberman
> 

One reference is:

Benjamin Fine,
"Algebraic Theory of the Bianchi Groups"
- Monographs and textbooks in pure and applied mathematics; 129 -
Marcel Dekker, Inc. New York and Basel (1989)

Toni Greil, Muenchen (Germany)
greil@guug.de



From obrien@pell.anu.edu.au Tue Aug 10 19:38:33 1993
From:        obrien@pell.anu.edu.au "Eamonn O'Brien"
Date:        Tue, 10 Aug 93 19:38:33 +0200
Subject:     break command in GAP language

As a follow-up to recent discussions with Gap developers
I propose that a "break;" command be provided in the GAP 
language. It would perform an identical function to the 
comparable command in C -- namely to exit from a loop.

Are there other GAP users who wish to have such provided?
Martin has given public assurance that he will be guided
by the opinion of the forum on this topic.

Eamonn O'Brien



From sibley@math.psu.edu Tue Aug 10 21:37:56 1993
From:        sibley@math.psu.edu "David Sibley"
Date:        Tue, 10 Aug 93 21:37:56 +0200
Subject:     Re: break command in GAP language

> As a follow-up to recent discussions with Gap developers
> I propose that a "break;" command be provided in the GAP 
> language. It would perform an identical function to the 
> comparable command in C -- namely to exit from a loop.
> 
> Are there other GAP users who wish to have such provided?
> Martin has given public assurance that he will be guided
> by the opinion of the forum on this topic.


Yes.  I would certainly use such a command.



From bogley@math.orst.edu Tue Aug 10 23:23:29 1993
From:        bogley@math.orst.edu "Bill Bogley"
Date:        Tue, 10 Aug 93 23:23:29 +0200
Subject:     Re: break command in GAP language 

A built-in command to abort runaway processes would be very helpful.

Bill Bogley



From dima@maths.uwa.edu.au Wed Aug 11 04:57:05 1993
From:        dima@maths.uwa.edu.au "Dima Pasechnik"
Date:        Wed, 11 Aug 93 04:57:05 +0200
Subject:     Re: break command in GAP language

> 
> As a follow-up to recent discussions with Gap developers
> I propose that a "break;" command be provided in the GAP 
> language. It would perform an identical function to the 
> comparable command in C -- namely to exit from a loop.
> 
> Are there other GAP users who wish to have such provided?
> Martin has given public assurance that he will be guided
> by the opinion of the forum on this topic.
> 
> Eamonn O'Brien

Yes, such a command would be quite useful.
(Adepts of "structural" programming would disagree.)

Dmitri Pasechnik



From dima@maths.uwa.edu.au Wed Aug 11 05:04:08 1993
From:        dima@maths.uwa.edu.au "Dima Pasechnik"
Date:        Wed, 11 Aug 93 05:04:08 +0200
Subject:     stack overflow

Dear Forum,
How one can recognise the sutuation when a recursive GAP function
causes the stack overflow. How one can find the size of space avaliable
for such a stack.
Thanks in advance,

Dima Pasechnik



From martin@math.rwth-aachen.de Tue Aug 24 01:18:28 1993
From:        martin@math.rwth-aachen.de "Martin Schoenert"
Date:        Tue, 24 Aug 93 01:18:28 +0200
Subject:     Re: stack overflow

Dima Pasechnik writes in his e-mail message of 1993/08/11
    How one can recognise the sutuation when a recursive GAP function
    causes the stack overflow. How one can find the size of space avaliable
    for such a stack.

The answer to the first question is unfortunatly ``not at all''.  Apart
from getting a core dump, that is.  The answer to the second question
depends on the operating system.  Under most variants of UNIX there is
something called 'limit' or 'ulimit', which can be used to get and set
the process parameters, such as maximal data space or stack space.

Martin.

-- .- .-. - .. -.  .-.. --- ...- . ...  .- -. -. .. -.- .-
Martin Sch"onert,   Martin.Schoenert@Math.RWTH-Aachen.DE,   +49 241 804551
Lehrstuhl D f"ur Mathematik, Templergraben 64, RWTH, 52056 Aachen, Germany



From martin@math.rwth-aachen.de Tue Aug 24 01:27:10 1993
From:        martin@math.rwth-aachen.de "Martin Schoenert"
Date:        Tue, 24 Aug 93 01:27:10 +0200
Subject:     Re: break command in GAP language

Eamonn O'Brien writes his e-mail message of 1993/08/10
    As a follow-up to recent discussions with Gap developers
    I propose that a "break;" command be provided in the GAP 
    language. It would perform an identical function to the 
    comparable command in C -- namely to exit from a loop.

Ok, I have 6 votes for a 'break' statement, and no vote against it.
I will put this on my to-do list.

Martin.

-- .- .-. - .. -.  .-.. --- ...- . ...  .- -. -. .. -.- .-
Martin Sch"onert,   Martin.Schoenert@Math.RWTH-Aachen.DE,   +49 241 804551
Lehrstuhl D f"ur Mathematik, Templergraben 64, RWTH, 52056 Aachen, Germany



From dima@maths.uwa.edu.au Tue Aug 24 03:15:43 1993
From:        dima@maths.uwa.edu.au "Dima Pasechnik"
Date:        Tue, 24 Aug 93 03:15:43 +0200
Subject:     Re: stack overflow

>     How one can recognise the sutuation when a recursive GAP function
>     causes the stack overflow. How one can find the size of space avaliable
>     for such a stack.
> 
> The answer to the first question is unfortunatly ``not at all''.  Apart
> from getting a core dump, that is.  The answer to the second question
> depends on the operating system.  Under most variants of UNIX there is
> something called 'limit' or 'ulimit', which can be used to get and set
> the process parameters, such as maximal data space or stack space.

Let me suggest the memory control to be implemented in future versions,
to avoid those problems. I'd guess it wouldn't affect the speed.

Regards,
Dima Pasechnik



From martin@math.rwth-aachen.de Tue Aug 24 07:58:04 1993
From:        martin@math.rwth-aachen.de "Martin Schoenert"
Date:        Tue, 24 Aug 93 07:58:04 +0200
Subject:     Unsubscriptions

This is a reminder that to unsubscribe one should send an e-mail message
to 'listserv@samson.math.rwth-aachen.de' (not to 'gap-forum') containing
the line 'unsubscribe gap-forum'.

Thank you, Martin.

-- .- .-. - .. -.  .-.. --- ...- . ...  .- -. -. .. -.- .-
Martin Sch"onert,   Martin.Schoenert@Math.RWTH-Aachen.DE,   +49 241 804551
Lehrstuhl D f"ur Mathematik, Templergraben 64, RWTH, 52056 Aachen, Germany



From Dave.Donaghy@bristol.ac.uk Tue Aug 24 10:34:47 1993
From:        Dave.Donaghy@bristol.ac.uk "Dave Donaghy"
Date:        Tue, 24 Aug 93 10:34:47 +0200
Subject:     Calculating Invariants

I know this isn't really a GAP question, but does anyone out there know if
there's a package available that will calculate the invariants of the
action of a (small) finite group on a purely transcendental field
extension over some (arbitrary but infinite) base field? The action can be
given explicitly as the action on the transcendental generators, but ISN'T
a permutation action. (Even though the group is often the symmetric group.)

Hopeful thanks,

Dave Donaghy



From knapp@donau.mathematik.uni-tuebingen.de Tue Aug 24 11:54:35 1993
From:        knapp@donau.mathematik.uni-tuebingen.de "Prof. Knapp"
Date:        Tue, 24 Aug 93 11:54:35 +0200
Subject:     GAP3.3

While attending the group theory conference in Galway I was told by the GAP
people who ran the GAP workshop that the new release GAP3.3 were available
since August 1st. I tried to get the new release from the samson server in
Aachen, but apparently the new release is not yet available on pub/gap as
all file names indicate the release 3.2 . What has happened? A readme file
on the directory pub/gap would also be desirable.

       Wolfgang Knapp , University of Tuebingen, Germany
       KnappWD@mailserv.zdv.uni-tuebingen.de



From neubuese@math.rwth-aachen.de Tue Aug 24 12:02:38 1993
From:        neubuese@math.rwth-aachen.de "Joachim Neubueser"
Date:        Tue, 24 Aug 93 12:02:38 +0200
Subject:     Re: Calculating Invariants

I do not have an answer to Dave Donaghy's question:
> I know this isn't really a GAP question, but does anyone out there know
> if there's a package available that will calculate the invariants of
> the action of a (small) finite group on a purely transcendental field
> extension over some (arbitrary but infinite) base field? The action can be
> given explicitly as the action on the transcendental generators, but ISN'T
> a permutation action. (Even though the group is often the symmetric group.)
 
but  the   recommendation      to contact   Larry    Grove    (Tucson)
(grove@math.arizona.edu)   who has  used    GAP   and Maple   in   the
investigation of invariants during  a visit to  Aachen and  might have
some advice. 

Since this  is an area  that we have   been asked about more  often, I
would welcome further comments in the  GAP-forum, if somebody has some
hints.

Joachim Neubueser



From neubuese@math.rwth-aachen.de Tue Aug 24 12:28:47 1993
From:        neubuese@math.rwth-aachen.de "Joachim Neubueser"
Date:        Tue, 24 Aug 93 12:28:47 +0200
Subject:     Re: GAP3.3

Wolfgang Knapp writes:
> While attending the group theory conference in Galway I was told by the GAP
> people who ran the GAP workshop that the new release GAP3.3 were available
> since August 1st. I tried to get the new release from the samson server in
> Aachen, but apparently the new release is not yet available on pub/gap as
> all file names indicate the release 3.2 . What has happened? A readme file
> on the directory pub/gap would also be desirable.

Sorry, this must be a misunderstanding.  We  did use a prerelease copy
of GAP 3.3  in Galway, but the  release  of this version should  still
take a few  weeks, e.g.  we want  to fix a  few things that we learned
through the use in Galway. At present the latest version is still 3.2,
patchlevel 3, i.e.  three patches for version 3.2 have been issued. As
a  general remark,  let  me  add  that  version  3.3 will not   differ
dramatically from  version 3.2,  it  is more   a consolidation of  the
latter, fixing  the   bugs that have    been noticed, of   course, and
replacing some functions by  more efficient ones,  having some but not
very many  new functions. Note  that recently some new share libraries
have become available  . We hope to bring  in more new  stuff with the
next version  after   3.3,  which  however should   definitely not  be
expected before the end of the year.

The readme  file  with the   GAP  announcement  is  contained in   the
directory pub/gap as pub/gap/README.

Joachim Neubueser



From martin@math.rwth-aachen.de Tue Aug 24 12:50:04 1993
From:        martin@math.rwth-aachen.de "Martin Schoenert"
Date:        Tue, 24 Aug 93 12:50:04 +0200
Subject:     Re: Re: stack overflow

Dima Pasechnik writes in his e-mail message of 1993/08/24
    Let me suggest the memory control to be implemented in future versions,
    to avoid those problems. I'd guess it wouldn't affect the speed.

I never tried it, but I think that it would indeed affect the
performance.  It would mean (at least) one more increment/decrement and
test of a global variable in 'EvFuncCall', and this function is already a
series bottleneck for many computations.

Martin.

-- .- .-. - .. -.  .-.. --- ...- . ...  .- -. -. .. -.- .-
Martin Sch"onert,   Martin.Schoenert@Math.RWTH-Aachen.DE,   +49 241 804551
Lehrstuhl D f"ur Mathematik, Templergraben 64, RWTH, 52056 Aachen, Germany



From dima@maths.uwa.edu.au Tue Aug 24 13:29:58 1993
From:        dima@maths.uwa.edu.au "Dima Pasechnik"
Date:        Tue, 24 Aug 93 13:29:58 +0200
Subject:     Re: Re: stack overflow

> 
> Dima Pasechnik writes in his e-mail message of 1993/08/24
> 
>     Let me suggest the memory control to be implemented in future versions,
>     to avoid those problems. I'd guess it wouldn't affect the speed.
> 
> I never tried it, but I think that it would indeed affect the
> performance.  It would mean (at least) one more increment/decrement and
> test of a global variable in 'EvFuncCall', and this function is already a
> series bottleneck for many computations.

I'd give it less than 0.1% of the speed anyway. Indeed, each memory allocation
in the interpreted languages (say, Basic, or GAP) takes hundreds of commands.

> 
> Martin.
> 
> -- .- .-. - .. -.  .-.. --- ...- . ...  .- -. -. .. -.- .-
> Martin Sch"onert,   Martin.Schoenert@Math.RWTH-Aachen.DE,   +49 241 804551
> Lehrstuhl D f"ur Mathematik, Templergraben 64, RWTH, 52056 Aachen, Germany

-- 
Dima Pasechnik, 
Dept. of Mathematics, 
Univ. of Western Australia, Nedlands WA 6009, Australia
e-mail:dima@maths.uwa.edu.au



From sl25@cus.cam.ac.uk Tue Aug 24 13:39:43 1993
From:        sl25@cus.cam.ac.uk "Steve Linton"
Date:        Tue, 24 Aug 93 13:39:43 +0200
Subject:     Re: Calculating Invariants 

I believe Leonard Soicher had  a program to do domething of this kind.
	Steve



From valero@s5.math.umn.edu Tue Aug 24 23:16:47 1993
From:        valero@s5.math.umn.edu "Luis Valero"
Date:        Tue, 24 Aug 93 23:16:47 +0200
Subject:     GroupHomomorphismByImages

I have been having trouble using GroupHomomorphismByImages, which seems
to take a very long time in a fairly straightforward situation. Here is
an example:

g:=Group((1,2,3,4,5,6),(1,2));
R:=[];
for k in [1..2] do
   M:=NullMat(6,6,GF(3));
   for i in [1..6] do
      j:=i^g.generators[k];
      M[i][j]:=Z(3)^0;
   od;
   R[k]:=M;
od;
GroupHomomorphismByImages(g,GeneralLinearGroup(6,3),g.generators,R);

This piece of code sets up a pair of matrices R{1] and R[2] which represent
the permutation action of the two generators of the symmetric group of
degree 6 on the natural permutation representation. Everything except the
last line takes hardly any time. The final line then takes some minutes
to run.

Evidently GroupHomomorphismByImages is doing a lengthy computation, but
by looking at the manual I can't tell what it is. From looking at
interrupt messages it appears to be computing a stablizer chain. I can think
of several things it might be doing that would take rather a long time, but
am not sure which is actually taking place.
Could you please shed some light on this situation?

My main aim is to set up a record which stores some of the information
in GroupHomomorphismByImages, but I don't necessarily need all this
information. Is there any way to bypass the computation that
GroupHomomorphismByImages is doing?

I am running version 3.2 of GAP without any of the subsequent patches.

With thanks for your help,
Luis Valero
valero@math.umn.edu
School of Mathematics, University of Minnesota, Minneapolis MN 55455



From fceller@math.rwth-aachen.de Wed Aug 25 14:26:26 1993
From:        fceller@math.rwth-aachen.de "Frank Celler"
Date:        Wed, 25 Aug 93 14:26:26 +0200
Subject:     Re: GroupHomomorphismByImages

Dear Luis Valero,
>>   I have been having trouble using GroupHomomorphismByImages, which seems
>>   to take a very long time in a fairly straightforward situation. Here is
>>   an example:

unfortunately 'GroupHomomorphismByImages' has a lot of hidden
pitfalls, we are still trying to clean this up.  The following is
going wrong: the function tries to decide if the set <R> is a subset
if the general linear group, although this should be straight forward,
this is done at the moment using a permutation representation for GL.
You can avoid this check by calling

  h := g.operations.GroupHom..(g,GL(6,3),g.generators,R)

directly instead of

>>   GroupHomomorphismByImages(g,GeneralLinearGroup(6,3),g.generators,R);

>>   Could you please shed some light on this situation?
>>   in GroupHomomorphismByImages, but I don't necessarily need all this
>>   information. Is there any way to bypass the computation that
>>   GroupHomomorphismByImages is doing?

However,  this is still not good enough,  because 'GroupHom..'
does not trust you.  You must set

    h.isMapping := true;
    h.isHomomorphism := true;
    h.isGroupHomomorphism := true;

in order to avoid unnecessary calculations.  'GL' and 'GroupHom...'
will be changed to be more user friendly,  but I am afraid that
this will happen *after* the release of 3.3.

best wishes
  Frank Celler



From L.H.Soicher@qmw.ac.uk Wed Aug 25 16:23:08 1993
From:        L.H.Soicher@qmw.ac.uk "Leonard Soicher"
Date:        Wed, 25 Aug 93 16:23:08 +0200
Subject:     Re: Calculating Invariants

My (old, PASCAL) programs for invariants are for linear groups over
finite fields, but the algorithms should work for linear groups over an
arbitrary field. To be more precise, given matrices generating a
subgroup G of GL(n,q), and a natural mnumber  k,  my programs calculate
a basis for the vector space of the n-variable degree  k  polynomials
invariant under  G.

Regards,        Leonard Soicher.



From Dave.Donaghy@bristol.ac.uk Thu Aug 26 13:41:54 1993
From:        Dave.Donaghy@bristol.ac.uk "Dave Donaghy"
Date:        Thu, 26 Aug 93 13:41:54 +0200
Subject:     Re: Calculating Invariants

Dear Leonard,
Many thanks for your reply. Unfortunately, my group action isn't linear.
Still, never mind, eh?

Dave Donaghy



From smith@pell.anu.edu.au Fri Aug 27 05:47:41 1993
From:        smith@pell.anu.edu.au "Michael Smith"
Date:        Fri, 27 Aug 93 05:47:41 +0200
Subject:     Compiling GAP under MiNT on 68040 Mac

Forum readers,
I am trying to get GAP running under a port of MiNT to the Mac. When
compiled with "make st-tos-gcc2", the resulting executable exits
immediately with memory allocation problems (I cannot remember the precise
message, something about corrupted workspace).

Anyway, my question is: has anyone compiled and run GAP under MiNT, and if
so, were any patches required to achieve this?

Thanks,
Michael.



From norai@ime.unicamp.br Mon Aug 30 21:20:17 1993
From:        norai@ime.unicamp.br "Norai Rocco - Prof. Visitante"
Date:        Mon, 30 Aug 93 21:20:17 +0200
Subject:     call a GAP session?

Dear Gap-forum,

A student here has been working with a (fortran) program to find out a kind 
of "first vector" in communication theory. One of its variables is to run 
certain iterations for a min-max problem, under a (matrix) group action, 
say X^T*g*X, g \in G, norm(X)=1. The first idea was to call GAP during 
this phase, not by simply storing a list "Elements(G)" and then using the 
list (this should take a lot of storage space), but to take advantage of GAP 
facilities to run things like an orbit algorithm. 

Could anuyone give me some hint concerning this "dynamical" use of GAP ?

Thanks in advance,
Norai Rocco.



From fceller@math.rwth-aachen.de Wed Sep  1 12:29:43 1993
From:        fceller@math.rwth-aachen.de "Frank Celler"
Date:        Wed, 1 Sep 93 12:29:43 +0200
Subject:     Re:  Calculating Invariants

Dear Forum,
some letter to the forum where rejected by our list-server, because
they were sent from different accounts than usual.

sorry for any delay
    Frank

-----------------------------------------------------------------------------
Date: Tue, 24 Aug 93 13:55:31 +0200
Comment: GAP Forum
Originator: gap-forum@samson.math.rwth-aachen.de
Errors-To: martin@samson
Reply-To: <gap-forum@samson>
Sender: gap-forum@samson
Version: 5.31 -- Copyright (c) 1991, Anastasios Kotsikonas
From: gap-forum@samson
To: martin@samson
Subject: Re:  Calculating Invariants

I might have two (!) answers for Mr Donaghy's request; both are programs
written in Maple. They calculate the ring of invariants of a finite
linear group defined over K=Q . In other words, the group acts on the
indeterminates of a purely transcendental extension of K by linear
transformations. "Calculate" means that they calculate a Cohen-Macaulay
basis for the ring of invariants.

    The first program has been written by Janet McShane together with
Larry Grove, whom Herr Neubueser already mentioned in his reply (email
grove@math.arizona.edu).

    The second one is by me. It has been published in the Maple Share
Library and can be obtained by anonymous ftp on
                    neptune.inf.ethz.ch    (129.132.101.33),
but also directly from me by email. In my program you can also take an
algebraic number field for K, and it can calculate syzygies between the
generating invariants.

Hope I won't get kicked out of the forum for advertising Maple programs!

Gregor Kemper



From fceller@math.rwth-aachen.de Wed Sep  1 12:41:48 1993
From:        fceller@math.rwth-aachen.de "Frank Celler"
Date:        Wed, 1 Sep 93 12:41:48 +0200
Subject:     Invariants

Rejected message sent to gap-forum@samson.math.rwth-aachen.de
-------------------------------------------------------------------------------
Date: Tue, 24 Aug 93 18:58:43 +0200
Comment: GAP Forum
Originator: gap-forum@samson.math.rwth-aachen.de
Errors-To: martin@samson
Reply-To: <gap-forum@samson>
Sender: gap-forum@samson
Version: 5.31 -- Copyright (c) 1991, Anastasios Kotsikonas
From: gap-forum@samson
To: martin@samson
Subject: Invariants

Having published a paper last year in Communications in Algebra
in which I computed the ring of invarinats of the simple group
of order 660 in a 5 dimensional complex representation, I
can point to some experience with such computations.

I am not aware of any package for doing them and if there was, I would
certainly want to use it. Based on my experience with the case I published
and some others, I have some ideas on how to attack such problems and
what kinds of software tools would be useful. Unfortunately, I am not
a very good programmer and I would need to work with someone who
is.

Actually, I did work with someone on this a couple of years ago, but
since I can't pay anyone to do this work and since programmers have a
tendency to be busy for long periods of time with things that they do get
paid to do, we didn't get very far. In addition, since the programmer in
question has asserted some of his rights over the code, I do not feel free
to distribute it, although I do tinker with it a little. I would actually
prefer to bury the package as it exists at the moment and start from scratch to
produce something that I can legally distribute freely to all who want to
use it or who want to help develop it further.

In addition, the programmer in question would have to know more mathematics
than most programmers that I have seen know. One of the reasons for the
painfully slow pace of development is that I could not take any
knowledge for granted on the part of the programmer and had to explain
even fairly routine computations in minute detail with examples that
I had to work out by hand. As the computations got more complicated, this
was more and more of a burden on me. It was also a burden that the
programmer had no idea whether the code was doing what it was supposed
to do at any level beyond conformity with the examples I had worked out by
hand.

I should add that I may not be as feeble a programmer as I thought.
The evidence is that after my collaborator left the project, I went
through the code he had written minutely and wrote detailed
comentary on exactly what was happening at each moment. In this way,
I found and corrected some of the outstanding bugs that caused performance
to deviate from the description of the manual. In the process, I learned a
certain amount about REDUCE symbolic mode programming conventions
and the resources lying around in the REDUCE source code. But I still have
a long way to go.

GAP has attractive features that lend itself to such computations,
namely the facility for working with groups, character tables,
representations, etc. But it is weak in more traditional computer
algebra such as polynomial manipulation. What is needed is an interface
between GAP and other packages.

If I am to be involved in a project like this, I would have to have
access to any computer algebra packages that would be used in
it. At the moment, the only computer algebra package I have
access to that is close to being adequate for my needs is REDUCE.
However, I am often frustrated by what I perceive as a "proprietary
mentality" when I try to learn about its inner workings. I think it
is something like the following at work: whereas I think of the programmer
as someone who is helping me develop a package and educating me an all that I
want to know in order to understand the final product (in particular,
that I am in charge of it and need to know minutely  what I am in charge of),
the corporate mentality instead views me as the individual whose
job it is to provide the programmer with algorithms in order to produce
proprietary software which it ultimately doesn't matter whether I
understand. In short, it is the point of view that I am part of a work
group in which my "need to know" is sharply curtailed by my perceived
function. Perhaps that is just what life is like when one works with
commercial packages. For that reason, I would much prefer to work with
a public domain algebra package. But a sufficiently powerful such package
doesn't seem to exist yet.

In fairness to the REDUCE people, I feel that they do a much better job of
documenting the inner workings of their product than the MACSYMA people
do. In both packages, there is a computer algebra package running over
a LISP substrate. In MACSYMA that substrate and the interface to it are
not documented while in REDUCE they are somewhat documented. Also,
there are now books available that discuss symbolic mode programming in
REDUCE. In addition, REDUCE comes with source code for REDUCE over
the LISP substrate and one can pay an extra $500 to get the source code
for the underlying LISP too. At any rate, I am more familiar with REDUCE
and although I am willing to learn other pacakges, my learning curve
would have to be taken into account, including the millions of naive and
apparently frivolous questions that I would have about it the
software and its inner workings, not to mention my insistence on having
access to complete source code. If one is willing to put up with that
and with my insistence of distributing the resulting code freely,
read on.

Actually, on second thought, I am probably making impossible demands
by insisting that in addition to having the program I also have a certain
working relationship to the programmers. So I will do the following:
(1) When I have a moment, I will make a revised copy of the manual
    available by anonymous ftp. It will be typeset in TeX (it already is).
    Anyone is then free to read the descriptions of the functions contained
    therein and write their own functions that duplicate the described
    behavior. If you do, please let me know. If it is in a package
    I don't have access to, I would appreciate it if you find a way to
    provide me access to the necessary packages.
(2) The manual only describes the work as far as we got with it. There are
    lot more functions that need to be included which are not described in the
    manual. I will be happy to collaborate with people in the development of
    those functions.


I would like to add that since I have been unemployed for 7 years and
have no income, I would not object if someone found a way to
compensate me for my efforts. However, that is not a condition for
the cooperation I have offered above.

Allan Adler
ara@altdorf.ai.mit.edu



From fceller@math.rwth-aachen.de Wed Sep  1 12:53:26 1993
From:        fceller@math.rwth-aachen.de "Frank Celler"
Date:        Wed, 1 Sep 93 12:53:26 +0200
Subject:     GAP for the Mac

Rejected message sent to gap-forum@samson.math.rwth-aachen.de follows.
-------------------------------------------------------------------------------
Is a port of GAP 3.2 (or 3.1) to the Macintosh available at
any FTP site? Thanks in advance.

Bob Rowley

 -------------------------------------------------------------------
|  Dept. of Computer Science |  email: rowley@research.cs.orst.edu  |
|  Oregon State University   |  phone: (503) 737-3371               |
|  Corvallis, OR 97331 USA   |                                      |
 -------------------------------------------------------------------



From neubuese@math.rwth-aachen.de Wed Sep  1 13:54:53 1993
From:        neubuese@math.rwth-aachen.de "Joachim Neubueser"
Date:        Wed, 1 Sep 93 13:54:53 +0200
Subject:     Re: Invariants

Alan Adler's   long  letter  to    the GAP-forum  of  August   24  was
unfortunately rejected by the mail server because the sender's address
was not  that of a member  of the GAP-forum.  It  was then sent to the
forum by Frank Celler. In order to avoid such  delays please make sure
that  you  write to  the GAP-forum  from   the address with which  you
originally registered with the forum.   When you change your  address,
please 'unsubscribe' and subscribe again with your new address.

As to Alan  Adler's letter: Yes,  GAP does not provide  all that a  CA
system like Reduce or Maple has. (For that reason  we do ourselves use
in particular Maple  in our work and  - to comment on Gregor  Kemper's
last remark - Maple or Reduce or some of the others are no no-no-words
in the GAP-forum  at all!) In  particular while  GAP  got a (hopefully
reasonable)   polynomial arithmetic for   univariate polynomials  with
version  3.2 it does   not  have (yet?!)   an efficient   multivariate
polynomial arithmetic. (Since polynomials can be formed over arbitrary
coefficient rings  you can mimic a   polynomial in two variables  by a
polynomial over the ring of univariate polynomials and so on, but that
is not suitable for  serious efficient computation).

However in answer to some of the problems, Alan Adler addresses: There
are systems for  handling  multivariate puolynomials  very efficiently
that are free of charge (although maybe  formally not public domain in
the same way that GAP is not public domain, namely in that a copyright
is  formulated that  forbids commercialisation  by  third parties).  I
particularly mention MACAULAY and CoCoA. 

By the way, if you  want rather comprehensive information on presently
available  CA systems (including CGT),   you may  want to consult  the
report   "Computeralgebra  in  Deutschland"  published  by "Fachgruppe
Computeralgebra  of   GI,  DMV,   and GAMM"  which   in  spite  of its
understating title gives  a fairly  broad  description on the  present
worldwide state of activities in algebraic and symbolic computation as
well as  good characterisations of  39  systems and  packages for such
computations  together  with   information  where  and   under   which
conditions to obtain them.

Joachim Neubueser



From neubuese@math.rwth-aachen.de Wed Sep  1 14:05:04 1993
From:        neubuese@math.rwth-aachen.de "Joachim Neubueser"
Date:        Wed, 1 Sep 93 14:05:04 +0200
Subject:     GAP 3.2 on the Mac (fwd)

In answer to Bob Rowley's question I reprint the message of Prof. 
Mendelsohn of July 19.       Joachim Neubueser
(Moral: Read the forum regularly, it has good news even at vacation time!)
==================================================================

Forwarded message:
> From gap-forum@samson.math.rwth-aachen.de Mon Jul 19 22:26:28 1993
> Date: Mon, 19 Jul 93 22:25:17 +0200
> Message-Id: <9307192022.AA07404@ccu.umanitoba.ca>
> Comment: GAP Forum
> Originator: gap-forum@samson.math.rwth-aachen.de
> Errors-To: martin@samson.math.rwth-aachen.de
> Reply-To: <gap-forum@samson.math.rwth-aachen.de>
> Sender: gap-forum@samson.math.rwth-aachen.de
> Version: 5.31 -- Copyright (c) 1991, Anastasios Kotsikonas
> From: mendel@ccu.umanitoba.ca (N. S. Mendelsohn)
> To: Multiple recipients of list <gap-forum@samson.math.rwth-aachen.de>
> Subject: GAP 3.2 on the Mac
> 
> For those not contacted by H. Lakser, Gap 3.2 on the Mac may be obtained
> from ftp anonymous at the address ccu.umanitoba.ca.  It is archived as
> /pub/mac/macgap32.
> The directory of macgap32 contains the following four files for
> downloading: MacGap32.sea.hqx; doc32.sea.hqx; lib32.sea.hqx; and
> macgap32.info.  These files are all self extracting. 
> 
> N. S. Mendelsohn
> 
> 
> 



From neubuese@math.rwth-aachen.de Wed Sep  1 15:16:10 1993
From:        neubuese@math.rwth-aachen.de "Joachim Neubueser"
Date:        Wed, 1 Sep 93 15:16:10 +0200
Subject:     Re: call a GAP session?

Norai Rocco asks for advice   how best to   call GAP functions from  a
FORTRAN program.   Nobody has answered to that   question in the forum
yet. Since I  try to make  sure that each question to  the forum is at
least acknowledged in  it, I have  asked people in our department, but
to my regret  must report that  nobody here  seems to have  experience
with such a situation. I hope that still somebody  else has some hint.
I know that  Leonard Soicher in GRAPE  has been using FORTRAN programs
together    with  GAP, but    as  I   understand   it  in  the   other
direction. Leonard is on  holidays at present,  perhaps he can comment
when he is back.

Joachim Neubueser



From hulpke@abacus.concordia.ca Wed Sep  1 17:14:26 1993
From:        hulpke@abacus.concordia.ca "Alexander Hulpke"
Date:        Wed, 1 Sep 93 17:14:26 +0200
Subject:     Re: Polynomials in GAP

Dear GAP-forum,
In his message of 24th of August, Allan Adler writes:

> GAP has attractive features that lend itself to such computations,
> namely the facility for working with groups, character tables,
> representations, etc. But it is weak in more traditional computer
> algebra such as polynomial manipulation.

Invariant computations (which were the initiator for this thread) surely
will need polynomial arithmetic in several variables, which is - at the
moment - not very feasible in GAP, as Joachim Neub"user already pointed
out.
However, if you need polynomial factorisations (over Q or an algebraic extension
Q(alpha)) and basic polynomial routines like resultant etc.; there will
be routines in a future version, that provide these functions. (They are
basically finished and just have to be incorporated.)
Probably this is of some use.

Alexander Hulpke



From greil@guug.de Fri Sep  3 11:50:09 1993
From:        greil@guug.de "Toni Greil"
Date:        Fri, 3 Sep 93 11:50:09 +0200
Subject:     GAP users in Muenchen ?

Hello GAP users,

are there any of you living/working in Muenchen (Germany) ?

I'd like to get an impression, what you undertake with GAP.

Toni Greil, Muenchen

Tel. 089-268562
greil@guug.de



From fceller@math.rwth-aachen.de Mon Sep  6 18:59:18 1993
From:        fceller@math.rwth-aachen.de "Frank Celler"
Date:        Mon, 6 Sep 93 18:59:18 +0200
Subject:     Missing Mail

Dear Forum,
due to a hard disk fault some mail to users on "math.rwth-aachen.de"
or "tiffy.math.rwth-aachen.de" might have been lost.  If you have sent
any mail to the above machines and didn't get an answer, please resent
the mail.  The gap-forum itself is not affected.

best wishes
  Frank Celler



From fceller@math.rwth-aachen.de Mon Sep  6 18:50:19 1993
From:        fceller@math.rwth-aachen.de "Frank Celler"
Date:        Mon, 6 Sep 93 18:50:19 +0200
Subject:     Re: GAP users in Muenchen ?

Dear Toni Greil,
>>   are there any of you living/working in Muenchen (Germany) ?
>>   I'd like to get an impression, what you undertake with GAP.

sending a message containing a single line "review gap-forum" to
"listserv@samson.math.rwth-aachen.de" will return a list of all
subscribers of the gap-forum.  Maybe you find someone from Muenchen
in this list.

best wishes
  Frank Celler



From RUTH@brunb Fri Sep 10 15:32:22 1993
From:        RUTH@brunb "Ruth Schwingel"
Date:        Fri, 10 Sep 93 15:32:22 +0200
Subject:     solvable factor group

Dear GAP-forum,
I'm studying Alexander Wegner's dissertation entitled
"Implementation eines Algorithmus zur Berechnung endlicher
aufl"osbarer Faktorgruppen einer endlich pr"asentierten
Gruppe im gruppentheoretischen Programmsystem GAP".

But apparently, this algorithm is not implemented in GAP-3.2.

I would like to know if there is such algorithm that computes
finite solvable factor groups of a finitely presented group
implemented in any other system.

Ruth Schwingel



From Johannes_Mueller@su.maus.de Mon Sep 13 18:48:34 1993
From:        Johannes_Mueller@su.maus.de "Johannes Mueller"
Date:        Mon, 13 Sep 93 18:48:34 +0200
Subject:     Running GAP under OS/2

-P54785@K
Dear Forum,

I have a problem with GAP running under OS/2:

When I start a DOS-Session from the desktop and call GAP386.EXE, I get the
following message:

CPU must be in REAL mode (not V86 mode) to run this program without VCPI. (If
you are using an EMS emulator, make sure that EMS isn't disabled)

Now I don't know how to react, the Online-Help and the very small OS/2-Manual
told me nothing, that led to a positive change.

Who can tell me in details, how to configure OS/2 to run GAP there?

Hope to get help, Johannes M|ller



From fceller@math.rwth-aachen.de Tue Sep 14 12:42:18 1993
From:        fceller@math.rwth-aachen.de "Frank Celler"
Date:        Tue, 14 Sep 93 12:42:18 +0200
Subject:     Re: Running GAP under OS/2

Dear Johannes Mueller
>>   CPU must be in REAL mode (not V86 mode) to run this program
>>   without VCPI. (If you are using an EMS emulator, make sure that
>>   EMS isn't disabled)
>>
>>   Now I don't know how to react, the Online-Help and the very small
>>   OS/2-Manual told me nothing, that led to a positive change.
>>
>>   Who can tell me in details, how to configure OS/2 to run GAP there?

Harald Boegeholz has done a port to OS/2.

best wishes
  Frank Celler

-----------------------------------------------------------------------------
Date: Thu, 4 Mar 93 17:23:31 +0100
Comment: GAP Forum
Originator: gap-forum@samson.math.rwth-aachen.de
Errors-To: martin@samson
Reply-To: <gap-forum@samson>
Sender: gap-forum@samson
Version: 5.31 -- Copyright (c) 1991, Anastasios Kotsikonas
From: hwblist@machnix.mathematik.uni-stuttgart.de (Harald Boegeholz)
To: Multiple recipients of list <gap-forum@samson>
Subject: A port of GAP to OS/2 2.0 and DOS

Hello!


I have started porting GAP 3.2 to emx, a free software development
system for OS/2 2.0 and DOS. I mainly did this because I wanted an
OS/2 version of GAP, but the resulting executable should run under
DOS, too.

This is my first try at porting GAP, and I have spent only very little
time on it. But if you need an OS/2 version or if you are curious
about another DOS version, give it a try!

I put the executable on

ftp.uni-stuttgart.de:/soft/os2/ProgLang/Languages/gapemx.zip

Please read the enclosed documentation.


Harald
--
Harald Boegeholz |Home:       hwb@texnix.stgt.sub.org (read daily)
                 |University: hwb@machnix.mathematik.uni-stuttgart.de
                 |please don't send large (>100k) mail to my home address.



From gurican@alpha.dcs.mff.uniba.cs Thu Sep 16 13:43:19 1993
From:        gurican@alpha.dcs.mff.uniba.cs "Jaroslav Gurican"
Date:        Thu, 16 Sep 93 13:43:19 +0200
Subject:     GAP for VAX/VMS and Alpha AXP/OpenVMS

Dear GAP Forum, 
I would like to notify you about the porting of gap to VAX/VMS and
ALPHA AXP/OpenVMS enviroments.
	This port has been done by me and my colleague/student Pavol Mederly.
	As far as the  ALPHA AXP/OpenVMS is concerned, we had only 1
day to make the port. The first thing we tried was translate VAX/VMS
image (gap.exe) using VEST (translator from VAX/VMS images to ALPHA
AXP/OpenVMS images). This is not good job, of course, but it could
serve as as the last possibility (this is not what is  ALPHA AXP meant
for). The program was running well. (Combinat.tst gave approximately
11000 GAPStones -  ALPHA AXP/OpenVMS running on 150 MHz, 64MBytes of memory, O.K.)
	Then we tried to compile it from the sources. 
The compiler and linker were succesful, there was one linker warning.
	I run combinat.tst, no problems, it gave at about 71000
GAPStones at the first run, 73500 at the second run. Even if it was not
new world record, ALPHA seemd to be extermely fast gay.)
	After it I made all examples from About Group Chapter of GAP
manual without problems. There were some (many) garbage collections
during the session.
	Finally I tried some big arithmetic and I haven't find any mistake. 
	So, I hope we produced fully functional version of GAP also for
 ALPHA AXP/OpenVMS environment (we used patch level 3).
	This version would be distributed on DEMO CD ROM by DEC
(together with Announcement). You can get  gap.exe (image file for 
ALPHA AXP/OpenVMS) from ftp.eunet.sk via anounymous ftp, it resides in
the directory itr/techreports/incoming together with sysvax.c file.
(This is the only file necessary to compile GAP on both VAX/VMS (we did
it on 5.5) and Alpha AXP/OpenVMS and which is not included in usual
distribution.) If you want to run GAP on VAX/Alpha, you have to unpack
*.tar.Z or *.tar.zoo files in UNIX environement and send it to your
VAX/Alpha (e.g. via ftp), BUT AS ASCII files. If you would use binary
transfer, you will have problems with line-feets - you will get
approximately 5 compilation errors. These errors can be fixed easily -
simply remove LF sign from the ends of apropriate lines. (The gap.exe
should be send as binary file.) 

	I would like to mention one point which could explain
differences (problems) with  ALPHA AXP/OSF-1 environment:
	The cc on  ALPHA AXP/OpenVMS knows only about 16 and 32 bits
integers, there are no 64 bits integers.  

				Jaroslav Gurican
				Dept. Of Algebra & Number Theory
				Mlynska dolina
				Bratislava
				SK- 842 15

P.S.: I would like to express my congratulations (and thanks, as well)
for such clean design of GAP.

P.S.1: GAPStones on some VMS machines
---------------------------------------------------------------------------

First column = first run of GAPu
Second column  = another run of GAPu
first raw = first run of  the test
second raw = second run of the test

Alpha AXP 3000-500S	(118 SPECmark89  (DECchip 21064/150 MHz))

	71000 (less than 10 seconds)   71000
	73500                          72992  

MicroVAX 3100/90	(24 VUP - Vax Unit Performance)

	25510 (28s)		26099 (27s)
	26505 (27s)		27100 (26s)

VAXstation 4000/60	(12 VUP)

	12660 (58s)		12697 (57s)
	13069 (55s)             13118 (55s)

VAX 6000/420		(2 proccesors 7 VUP each)

	 9350 (80s)		 9422 (77s)
	 9727 (76s)		 9652 (76s)
	
VAX 4000/200		(4.8 VUP)

	 5006 (140s)		 4976 (143s)
	 5128 (140s)             5173 (137s)



From neubuese@math.rwth-aachen.de Thu Sep 16 19:44:57 1993
From:        neubuese@math.rwth-aachen.de "Joachim Neubueser"
Date:        Thu, 16 Sep 93 19:44:57 +0200
Subject:     Re: solvable factor group

In a letter of last Friday Ruth Schwingel asked:
> I'm studying Alexander Wegner's dissertation entitled
> "Implementation eines Algorithmus zur Berechnung endlicher
> aufl"osbarer Faktorgruppen einer endlich pr"asentierten
> Gruppe im gruppentheoretischen Programmsystem GAP".
> 
> But apparently, this algorithm is not implemented in GAP-3.2.
> 
> I would like to know if there is such algorithm that computes
> finite solvable factor groups of a finitely presented group
> implemented in any other system.

Alexander Wegner's  Soluble Quotient program,  following W.  Plesken's
proposal, was implemented  for GAP 2.4,  it did not  get included into
this and the later versions so far, however right now work is going on
to modify  it slightly and  to make it  available with the then latest
version of GAP. Prior to full integration and  soon we hope to provide
a separate file with this program for extensive testing.

Another  Soluble   Quotient using   completely   different methods and
involving Steve Linton's  Module Enumerator has  been written by Alice
Niemeyer in Canberra.   She  plans  to  make it  available both  as  a
standalone and as a share library with GAP also in the near future.

No dates promised for both,  but near future is  hoped to mean what it
says in  both cases!!  Availability of both  will be  announced in the
GAP-forum.

Charles  Sims has  written  an experimental   version of a  Metabelian
Quotient  in connection with his  paper  on implementing the Baumslag-
Cannonito-Miller algorithm, however this is not publicly available.

I do not know of a Soluble Quotient in any other system, sorry.

Joachim Neubueser



From hwblist@machnix.mathematik.uni-stuttgart.de Thu Sep 23 16:34:53 1993
From:        hwblist@machnix.mathematik.uni-stuttgart.de "Harald Boegeholz"
Date:        Thu, 23 Sep 93 16:34:53 +0200
Subject:     new port of GAP for OS/2 2.x and DOS

Hello!
I have completed a new version of my port of GAP 3.2 to OS/2 2.x and
DOS. The executable is now at patchlevel 3, and I made some more minor
emx-specific improvements. You can download it from

ftp.uni-stuttgart.de:/soft/os2/ProgLang/Languages/gapemx.zip

This file contains an executable of GAP compiled for OS/2 2.x and DOS
as well as all those files of the GAP library that were updated by the
three patches to GAP. That way you can conveniently upgrade to
patchlevel 3 without using PATCH and the diffs.

For running GAP under OS/2 2.x, you also need the emx runtime. It is
available from

ftp.uni-stuttgart.de:/soft/os2/emx-0.8g/emxrt.zip.

Please refer to the file gap/emx/README in gapemx.zip for more
information.

New features of this port:

 * works correctly under GNU Emacs under OS/2 (identifier completion etc.)

 * signal handling (Ctrl-Break) now works under DOS, too


There is also a hypertext version of the GAP documentation for OS/2.
It can be found at

ftp.uni-stuttgart.de:/soft/os2/ProgLang/Languages/gapinf.zip


Since I have had practically no feedback from people using GAP under
OS/2, I would like to hear from anybody who is using this port. I
would also like to hear from people who have tested this version of
GAP under DOS. I don't use DOS myself, but I have briefly tested this
port under DOS and it seems to work pretty well. It even seems to be a
little faster than gap386.exe.


Enjoy!

Harald Boegeholz
--
Harald Boegeholz |   hwb@mathematik.uni-stuttgart.de
                 |   please note that I will discontinue using my home
                 |   address hwb@texnix... in the near future.



From L.H.Soicher@qmw.ac.uk Thu Sep 30 12:26:46 1993
From:        L.H.Soicher@qmw.ac.uk "Leonard Soicher"
Date:        Thu, 30 Sep 93 12:26:46 +0100
Subject:     GRAPE reference

The reference to quote if you use GRAPE has now appeared in print.  
It is:

L.H. Soicher, GRAPE: a system for computing with graphs and groups, in
"Groups and Computation" (L. Finkelstein and W.M. Kantor, eds.), DIMACS
Series in Discrete Mathematics and Theoretical Computer Science 11,
American Mathematical Society, 1993, pp. 287-291.


