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Date: Wed, 03 Sep 2003 14:05:00 +0200
From: Marc Conrad
Organization: University of Luton
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Subject: [Axiom-mail] Citing axiom
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I want to cite Axiom in a scientific paper, for that I thought to use as
reference:
Tim Daly et. al.
{\em Axiom Computer Algebra System},
\newblock http://savannah.nongnu.org/projects/axiom.
Any better ideas?
Marc
--
Marc Conrad - Luton, Southampton, Merzig, Podstrana.
http://www.perisic.com/marc
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Cc: axiom@tenkan.org, axiom-developer@nongnu.org, gcl-devel@gnu.org,
axiom-mail@nongnu.org
Subject: [Axiom-mail] Re: [Axiom-developer] Axiom Availability Announcement
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Greetings all!
Just a quick note to say that I've put together a preliminary
axiom.deb and uploaded it last night into unstable. It will likely
take a few days before being approved, but after that point the
autobuilders should let us know how portable we are! Doubtless many
changes will be needed to the package that now exists, so comments
most appreciated.
A few notes:
1) I made several changes to GCL. At a users request, GCL is now
following the linux release naming conventions -- x.y.z where y is
*even* denotes stable releases, and y odd refers to development/cvs
snapshot releases. So the latest stable GCL we're working on is
2.6.1, which can be obtained via CVS with the flag -r
Version_2_6_1. ftp.gnu.org is *still* down, so this isn't an
"official" release. Nevertheless, I've uploaded a 2.6.1 gcl deb to
the unstable Debian distribution last night to see where we stand.
So the sources/binary can also be retrieved from
incoming.debian.org.
Among the changes were modifications designed to enable axiom to be
built with gcl installed externally. This now works, at least for
me, with the following two minor patches to the axiom source
(currently in the Debian .diff:)
=============================================================================
--- axiom-0.0.0cvs.orig/lsp/Makefile.pamphlet
+++ axiom-0.0.0cvs/lsp/Makefile.pamphlet
@@ -152,17 +152,7 @@
@echo 1 building ${LSP} ${GCLVERSION}
gcldir:
- @echo 2 building ${GCLVERSION}
- @tar -zxf ${ZIPS}/${GCLVERSION}.tgz
-<>
-<>
-<>
-<>
-<>
-<>
-<>
-<>
-<>
+ echo "(compiler::link nil \"${OUT}/lisp\" \"\" \"${OBJ}/${SYS}/lib/cfuns-c.o ${OBJ}/${SYS}/lib/sockio-c.o ${OBJ}/${SYS}/lib/libspad.a\")" | gcl
@echo 13 finished system build on `date` | tee >gcldir
ccldir: ${LSP}/ccl/Makefile
--- axiom-0.0.0cvs.orig/src/interp/util.lisp.pamphlet
+++ axiom-0.0.0cvs/src/interp/util.lisp.pamphlet
@@ -68,7 +68,7 @@
;; perform system initializations for building a starter system
(init-memory-config)
#+:AKCL
- (let ((collectfn (concatenate 'string (string lsp) "/cmpnew/collectfn")))
+ (let ((collectfn (concatenate 'string si::*system-directory* "../cmpnew/collectfn")))
(unless (probe-file (concatenate 'string collectfn ".o"))
(compile-file collectfn))
(load collectfn)
=============================================================================
More on (compiler::link ...) below.
2) The current axiom .deb, also available at incoming.debian.org,
basically consists of the mnt/linux and obj/linux trees copied
wholesale (with a few minor exceptions), and a shell script
wrapper called 'axiom' to set the path and execute interpsys. I
added a placeholder manpage to conform to Debian policy, but this
brought to my attention the question of (user) documentation -- is
there any?
3) Unfortunately, there are still 5 Debian platforms on which GCL can
not natively relocate objects (mips(el), alpha, ia64, hppa). On
these boxes, one must use (compiler::link...) to build images.
This can also be used on the other platforms, but save-system is
easier to use, and we hope to make it available everywhere in the
future.
So if we want axiom on these machines, we need to add a little
code following the example in the patch above at the image dumping
point, i.e. bootsys, depsys, and interpsys. The arguments to link
are:
a list of compiled lisp object file pathnames, preferably
complete.
a pathname for the output image
(optional) a string of lisp code to be run at the end of the
normal lisp initialization.
(optional) a string of non-lisp objects and libraries to be
placed on the command line
(optional) a flag indicating if the user module initialization
code should be run (defaults to 't)
Lisp modules used in this call must be compiled with the :system-p
flag to compile file set to 't. This is most easily done with
(setq compiler::*default-system-p* t) before compiling.
I can look into making some patches, but as these should be arch
specific, I wanted to consult how this could best be done in
axiom's build system. I.e. axiom has no 'configure' script.
Take care,
root writes:
> *,
>
> Axiom exists as free and open source software.
>
> The first version of the Axiom sources has been uploaded to the CVS at
> http://savannah.gnu.org/projects/axiom. Congrats to all involved.
> Many thanks to the Numerical Algorithms Group, the CAISS Institute at
> City College of New York and to the people of these mailing lists.
>
> This version contains (almost) all of the algebra, the interpreter,
> and the spad compiler. This is the heart of Axiom. The graphics,
> hyperdoc, documentation, numerical code, Axiom Journal papers,
> openmath, and CATS test suite are in my source tree but are not ready
> for distribution yet. I'll announce these parts as they become
> available.
>
> A gzipped-tar file of the sources will be available soon.
> Debian apt and Redhat rpm files are under discussion.
>
> The CVS version can be downloaded by anonymous CVS:
>
> cvs -d:pserver:anoncvs@subversions.gnu.org:/cvsroot/savannah login
> cvs -z3 -d:pserver:anoncvs@subversions.gnu.org:/cvsroot/savannah co axiom
>
> NOTE: when prompted for a password for anoncvs simply press the Enter key
>
> The primary documentation is in the Makefile.dvi file.
>
> To build the system in a directory (e.g. /SPAD) you do:
>
> cd /SPAD
> export AXIOM=/SPAD/mnt/linux
> make
>
> The executable is (currently) found by doing:
>
> export PATH=/SPAD/obj/linux/bin:/SPAD/mnt/linux/bin:$PATH
> interpsys
>
> The build takes about 2 hours and 15 minutes on a 2Ghz/1Gb machine.
> You might want to do the build in an emacs shell buffer so you can
> save the console output in case of trouble.
>
> So far the build works properly on Redhat GNU/Linux 9. If you build it
> on another system please let us know. A port to Windows is in process.
>
> This is an alpha version of the system so expect (and report) bugs.
> The savannah website has a bug reporting tool.
>
> The algebra runs but has not yet been tested. This version has been
> uploaded so we can all test from the same base. When reporting bugs
> please use this version number printed at the top of your Axiom session.
> It will look something like:
> Thursday, August 28, 2003, 2:31am
>
> This version is a complete rebuild of Axiom. Many changes have been made.
>
> First, the system has been rewritten using literate programming.
> Each file is in "pamphlet" format (which is basically Latex with
> two extra tags). The reason for this is explained in the top-level
> Makefile.dvi file.
>
> Second, the system has been ported to GCL. This is the first of many
> common lisp ports where Axiom will exist.
>
> Third, the makefile tree has been rewritten. Most of the documentation
> that exists at the moment is in the various Makefile.dvi files.
>
> Fourth, the algebra is built from scratch rather than pre-existing files.
>
> The tenkan.org website and CVS is now obsolete and will be removed.
> Please use savannah for future development.
>
> Much work needs to be done. Click on the homepage link to see some of
> the future tasks.
>
> Questions, comments, and snide remarks can be sent to me at:
>
> Tim Daly
> axiom@tenkan.org
> daly@idsi.net
>
>
>
>
> _______________________________________________
> Axiom-developer mailing list
> Axiom-developer@nongnu.org
> http://mail.nongnu.org/mailman/listinfo/axiom-developer
>
>
--
Camm Maguire camm@enhanced.com
==========================================================================
"The earth is but one country, and mankind its citizens." -- Baha'u'llah
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From: root
To: marc@pension-perisic.de
Subject: Re: [Axiom-mail] Citing axiom
Cc: axiom-mail@nongnu.org
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Marc,
The only other citation is the book :
Jenks, Richard D. and Sutor, Robert S. "Axiom The Scientific Computation
System" Springer-Verlag 1992 New York ISBN 0-387-97855-0
The website is newer.
Tim
axiom@tenkan.org
daly@idsi.net
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From: root
To: axiom-developer@nongnu.org, axiom-mail@nongnu.org
Cc:
Subject: [Axiom-mail] TeX help
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*,
I have a very long equation that I need to break up. I can't seem to get
LaTex to break a line in math mode. Clearly this is possible but every attempt
so far has failed. The equation reads:
\begin{displaymath}
\left(
{-{2 \ {b \sp 2} \ {x \sp 2} \ {\sqrt {3}} \ {\log
\left(
{{{{\root {3} \of {a}} \ {{\root {3} \of {{{b \ x}+a}}} \sp 2}}+{{{\root
{3} \of {a}} \sp 2} \ {\root {3} \of {{{b \ x}+a}}}}+a}}
\right)}}+
{4 \ {b \sp 2} \ {x \sp 2} \ {\sqrt {3}} \ {\log
\left(
{{{{{\root {3} \of {a}} \sp 2} \ {\root {3} \of {{{b \ x}+a}}}} -a}}
\right)}}+{{12}
\ {b \sp 2} \ {x \sp 2} \ {\arctan
\left(
{{{{2 \ {\sqrt {3}} \ {{\root {3} \of {a}} \sp 2} \ {\root {3} \of {{{b \
x}+a}}}}+{a \ {\sqrt {3}}}} \over {3 \ a}}}
\right)}}+{{\left(
{{12} \ b \ x} -{9 \ a}
\right)}
\ {\sqrt {3}} \ {\root {3} \of {a}} \ {{\root {3} \of {{{b \ x}+a}}} \sp
2}}}
\right)
\over {{18} \ {a \sp 2} \ {x \sp 2} \ {\sqrt {3}} \ {\root {3} \of
{a}}}
\end{displaymath}
Suggestions are welcome.
Tim
axiom@tenkan.org
daly@idsi.net
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Cc: axiom-developer@nongnu.org, axiom-mail@nongnu.org
Subject: [Axiom-mail] Re: [Axiom-developer] TeX help
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Tim,
An eqnarray or eqnarrry* environment is what you want (Lamport,
_LaTeX_, 2d ed. p. 48.).
Use & to separate items in a line and \\ to break lines.
Greg
On Friday, September 5, 2003, at 12:56 AM, root wrote:
> *,
>
> I have a very long equation that I need to break up. I can't seem to
> get
> LaTex to break a line in math mode. Clearly this is possible but every
> attempt
> so far has failed. The equation reads:
>
> \begin{displaymath}
> \left(
> {-{2 \ {b \sp 2} \ {x \sp 2} \ {\sqrt {3}} \ {\log
> \left(
> {{{{\root {3} \of {a}} \ {{\root {3} \of {{{b \ x}+a}}} \sp
> 2}}+{{{\root
> {3} \of {a}} \sp 2} \ {\root {3} \of {{{b \ x}+a}}}}+a}}
> \right)}}+
> {4 \ {b \sp 2} \ {x \sp 2} \ {\sqrt {3}} \ {\log
> \left(
> {{{{{\root {3} \of {a}} \sp 2} \ {\root {3} \of {{{b \ x}+a}}}} -a}}
> \right)}}+{{12}
> \ {b \sp 2} \ {x \sp 2} \ {\arctan
> \left(
> {{{{2 \ {\sqrt {3}} \ {{\root {3} \of {a}} \sp 2} \ {\root {3} \of
> {{{b \
> x}+a}}}}+{a \ {\sqrt {3}}}} \over {3 \ a}}}
> \right)}}+{{\left(
> {{12} \ b \ x} -{9 \ a}
> \right)}
> \ {\sqrt {3}} \ {\root {3} \of {a}} \ {{\root {3} \of {{{b \
> x}+a}}} \sp
> 2}}}
> \right)
> \over {{18} \ {a \sp 2} \ {x \sp 2} \ {\sqrt {3}} \ {\root {3} \of
> {a}}}
> \end{displaymath}
>
> Suggestions are welcome.
>
> Tim
> axiom@tenkan.org
> daly@idsi.net
>
>
> _______________________________________________
> Axiom-developer mailing list
> Axiom-developer@nongnu.org
> http://mail.nongnu.org/mailman/listinfo/axiom-developer
>
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From: Tim Daly
To: A.G.Grozin@inp.nsk.su
Cc: axiom-developer@nongnu.org, daly@idsi.net, axiom-mail@nongnu.org
Subject: [Axiom-mail] TeX help
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Andrey,
I tried re-arranging the equation by hand but clearly my skills
are lacking. I was not expecting automated equation breaking as
I know that's an unsolved problem.
The equation is automatically TeX formatted by Axiom.
Tim
axiom@tenkan.org
daly@idsi.net
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From: Tim Daly
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Ralf,
I'll look into \multiline. Thanks.
Tim
axiom@tenkan.org
daly@idsi.net
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From: Tim Daly
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Greg,
I couldn't get eqnarray to work and eventually gave up.
I'll revisit it.
Thanks.
Tim
axiom@tenkan.org
daly@idsi.net
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From: Tim Daly
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Subject: [Axiom-mail] GCL sockets and sockio-c.o
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Camm,
Yes, I'm considering removing the sockio-c.o code in the future.
Most Common Lisps support sockets now although the support is
not standardized.
Tim
axiom@tenkan.org
daly@idsi.net
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From: Tim Daly
To: camm@enhanced.com
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Subject: [Axiom-mail] interpsys vs axiom
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Camm,
Mea Culpa. I copied the wrong version of the final Makefile.pamphlet.
I broke the build. I'll fix it when I get home from work.
CVS doesn't seem to work from here.
Tim
axiom@tenkan.org
daly@idsi.net
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To: Gregory Wright
Subject: Re: [Axiom-mail] Re: [Axiom-developer] TeX help
References:
From: David MENTRE
Organization: none
Date: Fri, 05 Sep 2003 21:04:06 +0200
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Tim,
Gregory Wright writes:
> An eqnarray or eqnarrry* environment is what you want (Lamport, _LaTeX_,
> 2d ed. p. 48.).
> Use & to separate items in a line and \\ to break lines.
To add to Gregory comment, you'll find additional tips for long
equations on following web page:
http://www.math.uiuc.edu/~hildebr/tex/displays.html
# How to break up long formulas. Breaking up overlong lines in displays
can be very tricky, and requires a good knowledge of the underlying
mathematics as well as a feel for good mathematical typesetting. For
that reason, TeX doesn't break formulas, as it does with ordinary
text. However, there are some general guidelines. Here are possible
breaking points, in decreasing order of desirability:
* Right before an equal sign or equivalent (e.g., a "less than"
sign). In this case, place the alignment symbol (ampersand) placed
before the equal sign, i.e., ... + x \\ &= . The equal signs (or
equivalent) should be aligned.
* Before a plus or minus sign. In that case, the continuation line
should be shifted to the right by a \qquad. If the continuation
line is very short, two \qquad's might be better.
* Between two large "chunks" that are multiplied. The chunks could
be large parenthesized expression, sums or integrals. This should
be used only as a last resort, and in that case the preceding line
should end with an explicit multiplication symbol (\times), the
continuation line should begin with \times symbol and be shifted
as far to the right (by preceding it with a few \qquad's after the
alignment symbol).
Yours,
d.
--
david.mentre@wanadoo.fr
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Subject: [Axiom-mail] src/interp/Makefile.pamphlet
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The file has been corrected (and tested).
Sorry about that.
You should now be able to build the system using on mnt.
Tim
axiom@tenkan.org
daly@idsi.net
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Great! Am building now .... Thanks!
root writes:
> The file has been corrected (and tested).
> Sorry about that.
> You should now be able to build the system using on mnt.
>
> Tim
> axiom@tenkan.org
> daly@idsi.net
>
>
>
--
Camm Maguire camm@enhanced.com
==========================================================================
"The earth is but one country, and mankind its citizens." -- Baha'u'llah
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From: Daniel Duparc
To: daly@idsi.net
Subject: Re: [Axiom-mail] TeX help
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On Fri, 5 Sep 2003 10:10:16 -0400
Tim Daly wrote:
> I tried re-arranging the equation by hand but clearly my skills
> are lacking. I was not expecting automated equation breaking as
> I know that's an unsolved problem.
>
Here is an example of solution _by hand_:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\documentclass[english]{article}
\usepackage[T1]{fontenc}
\usepackage[latin1]{inputenc}
\makeatletter
\usepackage{babel}
\makeatother
\begin{document}
\section{for Tim}
$
{
\displaystyle
\Biggl(
{-{2 \ {b \sp 2} \ {x \sp 2} \ {\sqrt {3}} \ {\log
\left(
{{{{\root {3} \of {a}} \ {{\root {3} \of {{{b \ x}+a}}} \sp 2}}+{{{\root
{3} \of {a}} \sp 2} \ {\root {3} \of {{{b \ x}+a}}}}+a}}
\right)}}+
% fin du premier log
{4 \ {b \sp 2} \ {x \sp 2} \ {\sqrt {3}} \ {\log
\left(
{{{{{\root {3} \of {a}} \sp 2} \ {\root {3} \of {{{b \ x}+a}}}} -a}}
\right)}}+}}$\hfill
% fin du deuxieme log
${{{12}
\ {b \sp 2} \ {x \sp 2} \ {\arctan
\left(
{{{{2 \ {\sqrt {3}} \ {{\root {3} \of {a}} \sp 2} \ {\root {3} \of {{{b \
x}+a}}}}+{a \ {\sqrt {3}}}} \over {3 \ a}}}
\right)}}+{{\left(
{{12} \ b \ x} -{9 \ a}
\right)}
\ {\sqrt {3}} \ {\root {3} \of {a}} \ {{\root {3} \of {{{b \ x}+a}}} \sp
2}}}
\Biggr)
\times {\displaystyle 1
\over \displaystyle {
{18} \ {a \sp 2} \ {x \sp 2} \ {\sqrt {3}} \ {\root {3} \of {a}}
}
}
$
\end{document}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Best regards
--
Daniel Duparc
29 av. de la Commune de Paris
94400 Vitry sur Seine (France)
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In-reply-to: <20030906112132.2591588e.daniel.duparc@free.fr> (message from
Daniel Duparc on Sat, 6 Sep 2003 11:21:32 +0200)
Subject: Re: [Axiom-mail] TeX help
References: <200309051410.h85EAGU20207@rio.sci.ccny.cuny.edu>
<20030906112132.2591588e.daniel.duparc@free.fr>
Cc: daly@idsi.net, Axiom-mail@nongnu.org
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Daniel, Cool. Thanks. -- t
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Date: Mon, 8 Sep 2003 10:13:48 +0100
From: Mike Dewar
To: daly@idsi.net
Message-ID: <20030908101348.B19200@nag.co.uk>
References: <200309051410.h85EAGU20207@rio.sci.ccny.cuny.edu>
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from daly@rio.sci.ccny.cuny.edu on Fri, Sep 05, 2003 at
10:10:16AM -0400
Cc: axiom-developer@nongnu.org, A.G.Grozin@inp.nsk.su, axiom-mail@nongnu.org
Subject: [Axiom-mail] Re: [Axiom-developer] TeX help
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Hi Tim,
Since the formula came from Axiom you could always try using Bob Sutor's
texbreak program (written to make sure that all the formulae in the
Axiom book fitted onto a page). Its probably not as good as breaking
the expression by hand but a lot less work :-) You should find it in
the src/htex directory.
Cheers, Mike.
On Fri, Sep 05, 2003 at 10:10:16AM -0400, Tim Daly wrote:
> Andrey,
>
> I tried re-arranging the equation by hand but clearly my skills
> are lacking. I was not expecting automated equation breaking as
> I know that's an unsolved problem.
>
> The equation is automatically TeX formatted by Axiom.
>
> Tim
> axiom@tenkan.org
> daly@idsi.net
>
>
> _______________________________________________
> Axiom-developer mailing list
> Axiom-developer@nongnu.org
> http://mail.nongnu.org/mailman/listinfo/axiom-developer
>
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Subject: [Axiom-mail] feedback
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*,
MIT has a lot of courses online. In particular, it has a fair number
of math and science courses online. (http://ocw.mit.edu)
The discussion at work today (I'm at City College of NY) is a proposal
to develop a common-format targeted front-end to Axiom which would
match and support the MIT math and science online courses. Of course
we don't have the man-power or expertise to develop such a large range
of courses in-house. Nevertheless, I think the idea has a lot of merit
for the education community and, in particular, the Axiom community.
Clearly the MIT math courses are reasonable for implementation in
Axiom (for example, Strang's Linear Algebra). And the Linear Algebra
course is clearly the basis for the Mechanical Engineering
course. Both of these are probably well addressed by the 3 Ms
(Mathematica, Maple, Matlab). I don't believe, however, that there is
a coordinated body of code for the range of available courses in any
of these systems although pieces exist for some of them. Axiom is in
a "come from behind" position at the moment.
I believe that Axiom's new open source nature gives it a major
advantage over the 3Ms since both professors and students can read,
modify, and create new algebra which could be freely shared worldwide.
Since we're trying to get Axiom shipped with all of the available
operating systems (Linux, Windows, Macs, etc.) it will be available on
all university and student desktops worldwide. This will give Axiom a
common foothold in the education market. A common front-end approach
would lower the learning curve for students so less class time would
be spent teaching students to use a computer algebra system. A
connection to the online courseware would make it very useful. And it
would give widely available tutorials for Axiom so everyone benefits.
Is it reasonable for an amorphous, worldwide community to try to do
coordinated development of software around a single MIT target? Would it
be reasonable to convince, or hope to convince, MIT to host the same
courses in multiple languages? Could we figure out a way to develop a
grant/subgrant structure that would attract developers for particular
courses? Is it possible that any granting organization would fund
developers worldwide? Is it politically possible within Universities
to expect that MIT's presentation of Linear Algebra would supercede
locally developed courses? If not, is it reasonable to design the
software to allow selective order of topic introduction? Can we design
courseware that would handle, say, the top 10 selling Linear Algebra
books? Will professors allow students to use Axiom on tests (my math
professors would not let us bring calculators to class, including my
Advanced Calculus class :-) ). Can we arrange the issues and try to
address each of them in some coordinated fashion?
It is clear that free and open source development can have as large
an impact on education as Linux has had on the operating system area
if we can build a community around the effort. One of the major issues
is that building software gets little or no academic credit and even
less grant funding. Perhaps a coordinated effort can change both of
these mindsets.
If you have a few minutes I'd like some feedback on this idea.
Please reply on the axiom-math@nongnu.org mailing list.
Tim Daly
axiom@tenkan.org
daly@idsi.net
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From: root
To: Daniel AUGOT
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Subject: [Axiom-mail] (no subject)
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Subject: Axiom and the scientific commnunauty]
Reply-to: daly@idsi.net
--text follows this line--
------- Start of forwarded message -------
Daniel,
Thanks for your note.
I have had both face-to-face and direct email discussions that the
issues you raise are real and need to be addressed. I'll try to give
you my current thinking on the subject.
> Dear Axiom developpers,
>
> I think there is an issue for the future life of Axiom, which involves
> researchers in computer algebra. From some email exchanges with
> friends, I do not feel that the revival of Axiom as free software will
> motivate them to go back to Axiom.
I don't expect that Axiom will gain a great deal of use simply because
it is free. I have collected about 100 free "computer algebra" systems
which I distribute on my Rosetta CD collection. Free CA systems are
"a dime a dozen" quite literally. Indeed many of these systems were
built by researchers as part of their research work.
My experience shows that most of these free systems start with the insight
that math "types" and programming "types" are similar. Starting with this
idea it becomes clear that you can build a nice, clean system from scratch.
It takes about a semester to build up a full, general purpose, polynomial
manipulation library in C++ and, indeed, you find that the math and computer
types interact very well. Then the insight occurs that the library isn't
useful to anyone but the researcher so the second semester of work involves
writing a front-end interpreter on the library. Subsequent effort involves
trying to convince others that this could be a very useful system given
sufficient effort.
This is very seductive since it looks like great progress. It has several
problems.
First, a local problem is that the research work that is "reduced to
practice" using a newly implemented system cannot be effectively used by
others (e.g. library systems rarely do simplification and almost never
document their algorithms).
Second, a local problem is that reduction to practice, that is, "programming"
is generally not "valorized". The research is recognized but the year or
two spent building a working system is either ignored or considered to
be of little worth during tenure discussions.
Third, a global problem is that the algorithmic work, while free, is
generally useless to others. Either the system is so specialized that
it only does one thing well which makes it into a single-purpose, once-only
use tool or it tries to be general purpose and has such a limited range of
algorithms that it quickly reaches a point of frustration for the user.
Thus the one great algorithm at the center of the system is buried and lost.
Fourth is the "rule of 3". It takes 1 unit of work to get something for
yourself. It takes 3x1 units of work to make is so your office neighbor
can use it. It takes 3x3x1 units of work so you can use it "in the
department" and in courses. It takes 3x3x3x1 units of work to give it
to the world for free without support. It takes 3x3x3x3x1 units of work
to make it into a commercial product with support, a hotline, lawyers, etc.
Most "computer algebra" systems stop at the 3x1 level as there is no
interesting new research work beyond the first unit and the 3x1 units
are expended as a matter of trying to get the work out to the world.
Building your research on top of Axiom or the 3Ms (Mathematica, Maple,
Matlab) immediately gives you the benefit of the 81 units of work already
done.
Systems like the 3Ms get purchased because they are general purpose
enough to do virtually anything and hold out the hope that research
done with these systems will be picked up and made useful to others.
However you tend to lose control of your work. If it is badly implemented
in the 3M world and has your name attached to it you have little choice
but to suffer the hit on your reputation. In a free system like Axiom
your reputation is yours to make or break.
Detailed discussions with researchers highlights another subtle fact.
The 3Ms are built on weak theory ground. Practically speaking this has
the effect of "limits of scale". You'll find that the more complex the
package you build the more difficult these systems become, for reasons
not related to your package. The difficulty is compounded if you need
to use other "non-core" packages. In some sense, these systems are like
Perl which is easy to use, fast to write, hard to scale to large projects,
and impossible to maintain (yes, I know this is a religious debate).
>
> In the French commnunauty, which I know a bit, because I was involved
> during my PHD thesis, 10 years ago, many people got very involved with
> Axiom. Many wrote domains, packages etc... for implementing the
> algorithms they were introducing in their research work.
Axiom started out like any other home-grown system, called Scratchpad.
However it was started at a time that major funding was available
(computer algebra was considered to be a branch of artificial intelligence).
It was heavily funded by both the U.S. government and IBM Research for about
23 years. Many researchers came to visit, many people worked on the system,
many algorithms were created in a broad range of areas. This is the
"dream realized" for the authors of the many free "library" systems.
Fortunately Axiom started out as a "theory" system and not a "library".
(See the footnote).
IBM ran into financial trouble and sold Scratchpad (as Axiom) to raise cash.
As a business decision this made sense but as a global decisions it was
pointless. Scratchpad is a great system for doing research work and had
the support and attention of about 400 researchers worldwide. If you're
going to do real math research Scratchpad was definitely the place to work.
It required at least a master's degree to learn but was easy to extend if
you understood the underlying math. Your work could be integrated and used
by the research community. As a "product" (Axiom) it had a very limited
market with cash-poor clients who could not support Axiom as a commercial
product. Axiom could never generate sufficient cash flow to cover the cost
of a development team in the commercial, closed source world. And open-source
generates no cash. So Axiom is the best place to do research and the worst
place to make money.
>
> But at his time, Axiom was a very closed software, and the French
> communauty was on its own, for documentation, help, contacting gurus,
> etc... Axiom also had its load of defaults~: a cumbersome system of
> categories, poor speed of code, compiler and interpreter bizareness,
> no way to use Unix pipes and redirection etc. Furthermore NAG did not
> show any clear sign about the future of Axiom. Even more, there was
> the promising A#/axiomxl/aldor project, with Basicmath, but it was
> immature, so the choice between Axiom and aldor was unclear.
Scratchpad was "open source" before the term existed. People who asked me
(while I was at IBM) could get a free copy of the source code. Axiom
when it was released followed the standard commercial path of closed
source software. This depends on a staff of people to maintain, which
depends on a good cash flow, and clearly Axiom couldn't generate the
cash flow. So Axiom was cut off from the customers who made it useful
and could never survive in a closed source model.
Scratchpad was ported onto AKCL, a compiled, hand-optimized version of
common lisp specifically developed under contract. I worked closely
with Bill Schelter on several detailed features like second-compile
optimization of function calling, tail recursive optimizations, memory
management, etc. to make Scratchpad perform well. When Axiom became a
commercial product it was ported to run on CCL, a byte-code interpreted
partial common lisp. This solved the portability problem (AKCL was
very hard to port as it compiles to optimized machine code) but
basically broke Scratchpad. Function calling and garbage collection
optimizations disappeared. Axiom is now back to running on GCL, the
open-source version of AKCL. Camm, the GCL lead developer, is on the
Axiom maintainer list.
As to contacting gurus we on the scratchpad team were told to "circle
our chairs" until we came up with something other than computer algebra
to work on (they even brought in an industrial psych. to "reprogram" us
which I found to be a very painful experience both professionally and
emotionally). NAG was in a very difficult situation guru-wise as they
lost the help of the guys who wrote it.
Aldor has great promise but people insist on trying to build the world
"from scratch". It may be several years and several failed experiments
before it becomes clear that the "library" approach is flawed. In the
mean time Axiom and Aldor have committed to supporting cross-compiled
compatibility.
As to the other issues like "cumbersome categories", hey, it's now
open-source and I'm open to ways of improving it. Scratchpad/Axiom
evolved to the system it is now because hundreds of people worked on
it and improved it. Someone needs to "unify" the Axiom type tree with
the mathematics in a much more systematic way. This is about a whole
Ph.D-thesis level of effort. The benefits of such thesis work would
be enormous as it would clarify how to correctly build these systems.
Axiom's types grew with knowledge of the theory but without benefit
of the detailed analysis.
>
> As a consequence many were confused and discouraged, and switched to
> other computer algebra systems, for instance Magma, which offers a
> large library and is very fast (although it does not offer the rich
> mechanism of Axiom for contructing domains and categories).
Now Axiom is back as open source. That is a necessary condition but not
sufficient. We need two things to survive. We need a community and we
need a funding model.
>
> Consequently, I think there must be a thinking about the state of
> Axiom, and clear signs concerning its future, beyond the point of
> making it publicly available. Will the compiler will be fixed ? Will
> it be documented ? Will compiled code be faster ? Will researchers in
> computer algebra be able to incorporate easily their software ? Will
> they be able to redesign the system of categories ? Will it be
> possible to link against efficient C code ? etc, etc...
For signs about its future visit savannah.nongnu.org/projects/axiom and
click on the "homepage" link. There are long range plans to unify with
theorem proving (ACL2 or MetaPRL), group theory (GAP and Magnus),
numerical work (Octave, etc). These are evolving as discussions proceed
and the webpage has not kept pace. In addition there is the CATS (computer
algebra test suite) effort to unify the test cases from the many systems
and put them on a better mathematical footing.
The documentation is in process. Virtually all of Axiom is now written
in a literate programming style and examples of literate programs which
combine a Ph.D thesis (Richard Paul's Robotics work) with a domain
(DHMATRIX) exist in the distribution. More work needs to be done both
on this domain and on recovering the research papers behind the other
domains. I've contacted several researchers and gotten their permission
to use their research papers and integrate them into the documentation.
This work continues but it is tedious because I need to find the research
and secure the permissions.
In addition I'm rewriting the Axiom book as we speak. The current work
is rebuilding the book but the later steps involve much rewriting
as well as exploiting the power of Active DVI. The online book will
likely be the "next announcement" so documentation is being given a
priority.
Community can only occur if people feel there efforts will bring reward.
In most cases, especially open source, this involves recognition. This
is a particularly thorny problem as computer algebra systems tend to be
the child of mathematicians. Math departments seems to feel that the
reduction to practice of math theory is uninteresting. Until the cross
breeding of the Computer Science and the Mathematics department yields
a "Computational Mathematics" department I suspect the problem will
continue. In the long run, of course, this has to occur as some of the
mathematics can no longer be done without a computer and some of the
mathematics only exists BECAUSE computers exist.
Beyond University issues Axiom needs to build a wider community of
users who are not researchers. This involves reaching out to the teaching
community. It involves finding ways to make Axiom easier to use and reducing
the learning curve. It involves developing a focusing agenda for coordinating
and developing teaching materials for the sciences (see footnote2). The MIT
suggestion is motivated by the question of who is the Axiom community and
how to reach/motivate/support it.
As to the funding issue I believe that this will also be a struggle. I've
been mulling the idea of creating an Axiom company which would be chartered
to work with schools to construct grant requests and administer grants for
researchers. This is an outgrowth of the way Scratchpad worked during the
IBM days. Researchers would come and spend time on site writing new domains,
learning Axiom, and returning back to their schools. Unfortunately I'm not
sufficiently skilled at grant writing to figure out how to make this work.
The Axiom company wouldn't own anything and would only be a paper agency
with a grant number and financial tracking.
An alternative approach is to "side-effect" the grants. That is, encourage
and support researchers who are applying for grants that involve Axiom
(such as classroom development of courses) in their efforts. This is much
harder as the researcher has to decide to make it part of the grant.
Clearly I have no creative new ideas about how to get money. However
if you take the "30 year view" of computer algebra it is clear that
we need to build on the current systems rather than start from scratch.
For one thing there is already 30 years of funding investment in Axiom
which shows just how expensive it can be to develop a "real" system.
For another it is clear that no-one is going to support another 30
years of funding just to achieve the same level as Axiom has reached.
So either we expend a great deal of energy creating small, special purpose
library systems or we contribute to the larger systems like the 3Ms and
Axiom. I would argue that Axiom is better designed to scale to higher
mathematics and also better able to support the amplification of the
teaching and research work because of the "open source" effect (that is,
freely downloadable packages widely available with multiple authors
as with Linux).
>
> May be the benefits of the free software will show up, but, after
> discussion with friends, it will not be enough for switching back to
> Axiom.
I don't expect people to switch back to Axiom because it is free. I
hope they will switch back because it is better, both technically and
socially, than the alternatives.
In addition I believe that "Computational Mathematics" will eventually
arrive as a discipline in its own right just as the Computer Science
departments eventually arose. As an undergrad 35 years ago I had to
convince my math profs to create courses in "computer science" as it
was "just a fad". We need to begin to collect the widespread
research (enshrined in libraries and journals) and use it to document
the algorithms. There needs to be a whole tower of computer algebra
theory that can be taught as a field of research combining work in
math, computer science, complexity, types, simplification, etc.
There needs to be support work for the sciences that need computer algebra.
Switching to Axiom isn't really the point (pretend I never said that)
but Axiom provides a kernel for the field of developing theory. In 30 years
this will be perfectly obvious. Computer algebra both stimulates fields
of research and provides answers that can't be arrived at by any non-computer
means.
>
> Kind regards, and felicitations for the work done. I have been able to
> download and compile all Axiom, and I am very glad for that.
Anyway, that's my current thinking on the subject.
There is more to come as work on Axiom continues.
Tim Daly
axiom@tenkan.org
daly@idsi.net
Footnote: My survey of the computer algebra field shows that systems can
be classified in one of three ways.
"Library systems" start out with the realization that math types and
computer types are similar. A C++ (usually but not always) library
gets created. An interpreter is grafted on top of the library. The
focus of these systems is "speed".
"Engineering systems", like Mathematica, Maple, and Matlab, are systems
that try to get "an answer". They seem to ignore math types and sometimes
specialize in one general purpose programming type (e.g. lists). You can
recognize these systems because operations like subtracting two equal
matricies will yield the zero integer. They are general purpose, easy to
use, and hard to scale (i.e. build on the work of other non-core packages).
"Theory systems" like Axiom or Docon. These systems start with the math
types and build up a language based on them. The programming representations
are flexible. Subtracting two matricies yields the zero matrix. They are
general purpose, hard to learn, but scale very cleanly.
Footnote2: There is a game called Pontifex which simulates bridge building.
It includes a construction set. Bridges are built and simulated loads (such
as trains) are applied to the bridges. Learning occurs. See
(http://www.bridgebuilder-game.com)
Axiom could be very useful when packaged with games of this type in a
classroom setting. Consider a mechanical engineering course where you
have software that can compute virtual work loads on beam members (which
are basically delta-displacements). You could explain the theory, show
how to compute loads of 2 and 3 dimensional lattices, how to apply them
to bridges, how to predict bridge successes and failures, and use the
game to build the simulated bridges. Game playing and mathematics in the
same course.
You could do the same in other sciences such as biology. If you look
at the forces involved in protein folding you could create models
using Axiom, define the forces, and compute results. The challenge
would be to create a game that accurately simulates the models. Perhaps
in chemistry you could model glue-binding forces for various types of
glues (like post-it notes) and construct things with glue. Game playing
is a fast growing (and profitable) field. We should bring games into the
classroom along with the theory.
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*,
A correction on the footnote in the last reply...
I used the example of matrix subtraction and made the claim that
engineering systems would give an integer zero as the result.
This is not correct. The point of the incorrect example was
that type information is not carried in these system.
Please ignore the example.
Tim Daly
axiom@tenkan.org
daly@idsi.net
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Organization: City College of New York
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root wrote:
>
> *,
>
> A correction on the footnote in the last reply...
> I used the example of matrix subtraction and made the claim that
> engineering systems would give an integer zero as the result.
> This is not correct. The point of the incorrect example was
> that type information is not carried in these system.
> Please ignore the example.
>
> Tim Daly
> axiom@tenkan.org
> daly@idsi.net
>
In the 3M's, the difference of two equal matrices is the zero matrix. However,
a brief investigation seems to indicate that type information in Maple or
Mathematica is carried only to a limited extent, and not as formally or robustly
as in Axiom. Matlab has types (classes), apparently based on C++ or Java
constructs.
In Mathematica: Head[ ] does not always give types; and there are only a few
specific routines to test types.
In[1]:=
a := x^2 + 1
In[2]:=
b := x^2
In[3]:=
c := a - b
In[4]:=
PolynomialQ[c]
Out[4]=
True
In[5]:=
IntegerQ[c]
Out[5]=
True
In[6]:=
Head[c]
Out[6]=
Integer
Maple has a type function with two arguments to test the type of a variable, but
only if you already know what type to test against. Similar to Mathematica, the
difference of two similarly typed objects may have multiple other types and need
not have the type of the operands.
> a:=x^2+1;
2
a := x + 1
> b:=x^2;
2
b := x
> c:=a-b;
1
> type(c,integer);
true
> type(c,polynom);
true
> a:=1/2;
a := 1/2
> type(a,fraction);
true
> b:=1/2;
b := 1/2
> c:=a-b;
c := 0
> type(c,fraction);
false
> type(c,integer);
true
In Matlab, the type is called class and seems to be retained.
>> sym x
ans =
x
>> a = x^2 + 1
a =
x^2+1
>> b = x^2+1
b =
x^2
>> c = a-b
c =
1
>> class(c)
ans =
sym
William
--
William Sit
Department of Mathematics..............Email: wyscc@cunyvm.cuny.edu
City College of New York..........................Tel: 212-650-5179
Convent Ave at West 138th Street..................Fax: 212-862-0004
New York, NY 10031.....Asian Symposium on Computer Mathematics 2003
USA..........................http://www.mmrc.iss.ac.cn/~ascm/ascm03
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Hi,
I have a problem running axiom (latest version) under texmacs (version
1.0.2), both installed on a pc running RH8. Inserting an axiom session
in a first buffer only gives me the "(AXIOM Sockets) The AXIOM server
number is undefined." warning. Inserting a session in a next buffer
gives me a prompt that does not seem to respond.
Do I need to configure anything ?
Thanks in advance,
Koen
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Koen,
There is a known problem running the latest version of Axiom under TeXmacs.
There is a posted fix but I was not involved in it and don't know how to
apply it to TeXmacs.
Joris, David, Bill,
Could you help this person with the details of the TeXmacs fix?
Tim
axiom@tenkan.org
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From: "Page, Bill"
To: "'Koen Hillewaert'"
Subject: RE: [Axiom-mail] problem using axiom in texmacs
Date: Tue, 30 Sep 2003 08:42:21 -0400
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Koen,
The new open source version of Axiom is a little
different than the older commercial (NAG) version.
As a result, you must install an updated version
of the TeXmacs - Axiom interface program. Go to
http://savannah.nongnu.org/files/?group=axiom
and take a look at
Axiom_Texmacs 1.0.2
Simple instructions are included in the README.txt
file.
and also the files under
Axiom_Book
So far, this new interface for TeXmacs has not been
tested very much. Also TeXmacs 1.0.2 is a new version
of TeXmacs. I am beginning to think that this combination
shows a lot of promise, but I would have to say that the
behaviour is still a little "fagile". I was however able
to get through almost all of the computations in the
introduction section of the Axiom book and some initial
formatting of the contents in just a few hours last
night.
If you have any problems, I would be glad to try
to help.
Cheers,
Bill Page.
> -----Original Message-----
> From: Koen Hillewaert [mailto:koenhillewaert@tiscali.be]
> Sent: Tuesday, September 30, 2003 6:20 AM
> To: axiom-mail@nongnu.org
> Subject: [Axiom-mail] problem using axiom in texmacs
>
>
> Hi,
>
> I have a problem running axiom (latest version) under texmacs
> (version
> 1.0.2), both installed on a pc running RH8. Inserting an
> axiom session
> in a first buffer only gives me the "(AXIOM Sockets) The AXIOM server
> number is undefined." warning. Inserting a session in a next buffer
> gives me a prompt that does not seem to respond.
>
> Do I need to configure anything ?
>
> Thanks in advance,
>
> Koen
>
>
>
>
> _______________________________________________
> Axiom-mail mailing list
> Axiom-mail@nongnu.org
> http://mail.nongnu.org/mailman/listinfo/axiom-mail
>
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To: Koen Hillewaert
Subject: Re: [Axiom-mail] problem using axiom in texmacs
References: <3F7958E9.4070903@tiscali.be>
From: David MENTRE
Organization: none
Date: Tue, 30 Sep 2003 19:36:11 +0200
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Hello Koen,
Koen Hillewaert writes:
> Do I need to configure anything ?
Yes. You need to upgrade the tm_axiom program provided by TeXmacs.
You'll find updated tm_axiom.c and instructions on to compile and
install it at (Axiom_texmacs section):
http://savannah.nongnu.org/files/?group=axiom
If you have other issues, let us know.
Yours,
d.
--
david.mentre@wanadoo.fr
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From: "Page, Bill"
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Subject: RE: [Axiom-mail] problem using axiom in texmacs
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