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<feed xmlns="http://www.w3.org/2005/Atom">
	<id>tag:old.nabble.com,2006:forum-6885</id>
	<title>Nabble - Axiom</title>
	<updated>2009-12-04T01:20:54Z</updated>
	<link rel="self" type="application/atom+xml" href="http://old.nabble.com/Axiom-f6885.xml" />
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	<subtitle type="html">nongnu - axiom home is &lt;a href=&quot;http://savannah.nongnu.org/projects/axiom&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;here&lt;/a&gt;.</subtitle>
	
<entry>
	<id>tag:old.nabble.com,2006:post-26639741</id>
	<title>Re: Literate programming and how it scales</title>
	<published>2009-12-04T01:20:54Z</published>
	<updated>2009-12-04T01:20:54Z</updated>
	<author>
		<name>Tim Daly-3</name>
	</author>
	<content type="html">&lt;br&gt;(actual text is snipped out since this was not public but I want to record
&lt;br&gt;the reply on axiom-developer)
&lt;br&gt;&lt;br&gt;...[snip]...comments about scale...
&lt;br&gt;&lt;br&gt;What kind of scaling are you thinking about? Axiom currently has about 
&lt;br&gt;20 books
&lt;br&gt;that will eventually have all of the source code in literate form. Some 
&lt;br&gt;of the books
&lt;br&gt;are several thousand pages long. There is hyperlinking within the files. 
&lt;br&gt;Axiom is
&lt;br&gt;about 1 million &amp;quot;things of code&amp;quot; and it will all reside in literate 
&lt;br&gt;files so I think the
&lt;br&gt;technology scales to really large systems.
&lt;br&gt;&lt;br&gt;If you are talking about scaling in terms of humans I think the problem 
&lt;br&gt;is not one of
&lt;br&gt;technology. The problem is that you really can't do a literate work with 
&lt;br&gt;dozens of
&lt;br&gt;authors. Literature requires one, or at most a few, authors in order to 
&lt;br&gt;make sure that
&lt;br&gt;the &amp;quot;style&amp;quot; and &amp;quot;voice&amp;quot; of the documentation is coherent. So I think 
&lt;br&gt;that many people
&lt;br&gt;can work on the system but only a very few are the &amp;quot;editors/primary 
&lt;br&gt;authors&amp;quot;. I don't
&lt;br&gt;think there is a good label for this historically, except perhaps the 
&lt;br&gt;&amp;quot;Chief Programmer&amp;quot;
&lt;br&gt;from Harlan Mills &amp;quot;Chief Programmer Teams&amp;quot;. I don't care for that label.
&lt;br&gt;&lt;br&gt;Ultimately literate programming requires a complete understanding of the 
&lt;br&gt;system.
&lt;br&gt;The point of literate programming is to convey this understanding to the 
&lt;br&gt;reader
&lt;br&gt;in a smooth, consistent way. Since programming is involved it is also 
&lt;br&gt;important
&lt;br&gt;that all of the details are explained, but also important that they are 
&lt;br&gt;introduced
&lt;br&gt;in some &amp;quot;motivated&amp;quot; fashion. It is the &amp;quot;motivation&amp;quot; for code snippets 
&lt;br&gt;that is usually
&lt;br&gt;left out of other documentation forms (e.g. doxygen, javadoc, etc.).
&lt;br&gt;&lt;br&gt;...[snip]...comments about TeX and multiple languages
&lt;br&gt;&lt;br&gt;I see TeX as a major strength since most technical papers are written in 
&lt;br&gt;Latex.
&lt;br&gt;TeX is also a strength for Axiom because it handles mathematical typesetting
&lt;br&gt;very well and Axiom is a mathematical system.
&lt;br&gt;&lt;br&gt;Every literate system will have at least 2 languages, one for 
&lt;br&gt;programming and one
&lt;br&gt;for writing. I find that TeX does everything I need or can be extended 
&lt;br&gt;with macros
&lt;br&gt;to do what I need. I don't know how to add macros to an HTML system (without
&lt;br&gt;writing in Perl as you do, which is yet a third language)
&lt;br&gt;&lt;br&gt;... [snip] ...comments about noweb
&lt;br&gt;&lt;br&gt;Axiom is moving away from noweb, although we have used it for years and 
&lt;br&gt;I can
&lt;br&gt;highly recommend it. Some of Axiom's literate files now have &amp;quot;straight 
&lt;br&gt;latex&amp;quot; macros
&lt;br&gt;for chunks so where you would write
&lt;br&gt;&amp;lt;&amp;lt;noweb chunk name&amp;gt;&amp;gt;=
&lt;br&gt;&amp;nbsp; &amp;nbsp;your code
&lt;br&gt;@
&lt;br&gt;&lt;br&gt;now Axiom allows you to write
&lt;br&gt;&lt;br&gt;\begin{chunk}{Axiom chunk name}
&lt;br&gt;&amp;nbsp; your code
&lt;br&gt;\end{chunk}
&lt;br&gt;&lt;br&gt;This uses straight latex macros which means that your file is pure Latex.
&lt;br&gt;Since the file is pure Latex you no longer need &amp;quot;weave&amp;quot; so half of noweb 
&lt;br&gt;is gone.
&lt;br&gt;&lt;br&gt;The only other remaining function is &amp;quot;tangle&amp;quot;. Axiom is being rewritten
&lt;br&gt;to understand Latex files directly so it can &amp;quot;tangle&amp;quot; the file without 
&lt;br&gt;using noweb.
&lt;br&gt;The underlying lisp system (GCL) has been modified to include a &amp;quot;tangle&amp;quot;
&lt;br&gt;function directly so Axiom is not needed to extract code.
&lt;br&gt;&lt;br&gt;Thus we will no longer need noweb in the future.
&lt;br&gt;&lt;br&gt;...[snip]...comments about new tool features for code organization
&lt;br&gt;&lt;br&gt;Programmers have been conditioned to believe that they should work on small
&lt;br&gt;files with &amp;quot;include files&amp;quot; to carry information that is shared.
&lt;br&gt;&lt;br&gt;If you look where this idea comes from historically you'll find there 
&lt;br&gt;was a memory
&lt;br&gt;limitation on the PDP 11/40 (I worked on one so I know) that limited a 
&lt;br&gt;file to
&lt;br&gt;about 4K characters. In order to make larger files you needed to invent 
&lt;br&gt;&amp;quot;include files&amp;quot;.
&lt;br&gt;So C programs started the idea that files should be really small.
&lt;br&gt;&lt;br&gt;Then you needed to invent directories since groups of files in a 
&lt;br&gt;directory made
&lt;br&gt;up a single larger idea.
&lt;br&gt;&lt;br&gt;Then you needed to invent &amp;quot;make&amp;quot; because it becomes impossible to figure 
&lt;br&gt;out
&lt;br&gt;how to compile all the files in all the directories and get all the 
&lt;br&gt;parts right.
&lt;br&gt;&lt;br&gt;Then you needed to invent &amp;quot;grep&amp;quot; to find functions.
&lt;br&gt;&lt;br&gt;Then you needed to invent IDEs so you could work with the whole project.
&lt;br&gt;&lt;br&gt;&lt;br&gt;Today I have 4G of memory and a 1T of disk space. I can trivially handle
&lt;br&gt;multi-megabyte files, my functions are all in one file, &amp;quot;make&amp;quot; is 
&lt;br&gt;trivial, &amp;quot;grep&amp;quot;
&lt;br&gt;is an editor &amp;quot;find&amp;quot; command and I don't need an IDE. Latex provides an
&lt;br&gt;automatic cross-reference mechanism that allows me to find all of the places
&lt;br&gt;where a function is called.
&lt;br&gt;&lt;br&gt;Once we stop pretending we work on a PDP 11/40 life gets so much easier
&lt;br&gt;&lt;br&gt;...[snip]... tool description using HTML, Perl, Javascript
&lt;br&gt;&lt;br&gt;So instead of Latex and Lisp, I now need Lisp, HTML, Perl,
&lt;br&gt;and Javascript?
&lt;br&gt;&lt;br&gt;Is adding new languages an improvement? Are HTML files &amp;quot;documents&amp;quot;, i.e.,
&lt;br&gt;are they designed to be read as books? Can you control the layout and fonts
&lt;br&gt;that are so necessary to convey certain information?
&lt;br&gt;&lt;br&gt;...[snip]... features of the new tool
&lt;br&gt;&lt;br&gt;Like any author, I keep my ongoing work in the manuscript, which is the 
&lt;br&gt;literate file itself.
&lt;br&gt;There are no auxillary files, no project files, no directory structure, 
&lt;br&gt;no includes, nothing.
&lt;br&gt;&lt;br&gt;...[snip]...
&lt;br&gt;&lt;br&gt;I'm sure you have a good tool set that most people would find useful.
&lt;br&gt;Unfortunately, the Axiom project is working to &amp;quot;remove the tools&amp;quot; that
&lt;br&gt;are not absolutely required by making Axiom aware of its own file format
&lt;br&gt;(pamphlet, also known as .tex, files)
&lt;br&gt;&lt;br&gt;Tim
&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
&lt;br&gt;Axiom-developer mailing list
&lt;br&gt;&lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26639741&amp;i=0&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;Axiom-developer@...&lt;/a&gt;
&lt;br&gt;&lt;a href=&quot;http://lists.nongnu.org/mailman/listinfo/axiom-developer&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://lists.nongnu.org/mailman/listinfo/axiom-developer&lt;/a&gt;&lt;br&gt;&lt;p&gt;From forum: &lt;a href=&quot;http://old.nabble.com/axiom-developer-f6886.html&quot; embed=&quot;fixTarget[6886]&quot; target=&quot;_top&quot; &gt;axiom-developer&lt;/a&gt;&lt;/p&gt;</content>
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</entry>

<entry>
	<id>tag:old.nabble.com,2006:post-26601114</id>
	<title>Re: my axiom is broken</title>
	<published>2009-12-01T15:41:57Z</published>
	<updated>2009-12-01T15:41:57Z</updated>
	<author>
		<name>Tim Daly-3</name>
	</author>
	<content type="html">Cap wrote:
&lt;div class='shrinkable-quote'&gt;&lt;br&gt;&amp;gt; Hi again,
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; I installed axiom using the Synaptic packet manager. Here is the complete output of the axiom command:
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; cap@miles:~$ axiom
&lt;br&gt;&amp;gt; GCL (GNU Common Lisp) &amp;nbsp;2.6.7 CLtL1 &amp;nbsp; &amp;nbsp;Nov 10 2006 14:25:02
&lt;br&gt;&amp;gt; Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
&lt;br&gt;&amp;gt; Binary License: &amp;nbsp;GPL due to GPL'ed components: (XGCL READLINE BFD UNEXEC)
&lt;br&gt;&amp;gt; Modifications of this banner must retain notice of a compatible license
&lt;br&gt;&amp;gt; Dedicated to the memory of W. Schelter
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Use (help) to get some basic information on how to use GCL.
&lt;br&gt;&amp;gt; Temporary directory for compiler files set to /tmp/
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; AXIOM Computer Algebra System 
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;Version: Axiom 3.9 (September 2005)
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Timestamp: Saturday December 2, 2006 at 09:30:31 
&lt;br&gt;&amp;gt; -----------------------------------------------------------------------------
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;Issue )copyright to view copyright notices.
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;Issue )summary for a summary of useful system commands.
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;Issue )quit to leave AXIOM and return to shell.
&lt;br&gt;&amp;gt; -----------------------------------------------------------------------------
&lt;br&gt;&amp;gt; &amp;nbsp;
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;Re-reading compress.daase &amp;nbsp; Re-reading interp.daase
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;Re-reading operation.daase
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;Re-reading category.daase 
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;&amp;gt;&amp;gt; System error:
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;Couldn't protect
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Error: The tag |top_level| is undefined.
&lt;br&gt;&amp;gt; Fast links are on: do (si::use-fast-links nil) for debugging
&lt;br&gt;&amp;gt; Error signalled by RETURN.
&lt;br&gt;&amp;gt; Broken at APPLY. &amp;nbsp;Type :H for Help.
&lt;br&gt;&amp;gt; BOOT&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Cappy
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; --- On Mon, 11/30/09, Tim Daly &amp;lt;&lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26601114&amp;i=0&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;daly@...&lt;/a&gt;&amp;gt; wrote:
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; &amp;nbsp; 
&lt;br&gt;&amp;gt;&amp;gt; From: Tim Daly &amp;lt;&lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26601114&amp;i=1&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;daly@...&lt;/a&gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt; Subject: Re: [Axiom-mail] my axiom is broken
&lt;br&gt;&amp;gt;&amp;gt; To: &amp;quot;Cap&amp;quot; &amp;lt;&lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26601114&amp;i=2&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;daCaptain@...&lt;/a&gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt; Cc: &lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26601114&amp;i=3&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;axiom-mail@...&lt;/a&gt;
&lt;br&gt;&amp;gt;&amp;gt; Date: Monday, November 30, 2009, 2:53 PM
&lt;br&gt;&amp;gt;&amp;gt; Cap wrote:
&lt;br&gt;&amp;gt;&amp;gt; &amp;nbsp; &amp;nbsp; 
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; Hello,
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; I get an error message when I try to start axiom.
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; Re-reading compress.daase &amp;nbsp; Re-reading
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; &amp;nbsp; &amp;nbsp; &amp;nbsp; 
&lt;br&gt;&amp;gt;&amp;gt; interp.daase
&lt;br&gt;&amp;gt;&amp;gt; &amp;nbsp; &amp;nbsp; 
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; &amp;nbsp; &amp;nbsp; Re-reading operation.daase
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; &amp;nbsp; &amp;nbsp; Re-reading category.daase 
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; &amp;nbsp; &amp;nbsp; &amp;gt;&amp;gt; System error:
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; &amp;nbsp; &amp;nbsp; Couldn't protect
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; Error: The tag |top_level| is undefined.
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; Fast links are on: do (si::use-fast-links nil) for
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; &amp;nbsp; &amp;nbsp; &amp;nbsp; 
&lt;br&gt;&amp;gt;&amp;gt; debugging
&lt;br&gt;&amp;gt;&amp;gt; &amp;nbsp; &amp;nbsp; 
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; Error signalled by RETURN.
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; Broken at APPLY. &amp;nbsp;Type :H for Help.
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; BOOT&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; I tried reinstalling the package (Ubuntu 9.04 64), but
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; &amp;nbsp; &amp;nbsp; &amp;nbsp; 
&lt;br&gt;&amp;gt;&amp;gt; it didn't help. I don't know what else to try. Can anyone
&lt;br&gt;&amp;gt;&amp;gt; please help?
&lt;br&gt;&amp;gt;&amp;gt; &amp;nbsp; &amp;nbsp; 
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; thanks
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; Cappy
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; _______________________________________________
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; Axiom-mail mailing list
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; &lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26601114&amp;i=4&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;Axiom-mail@...&lt;/a&gt;
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; &lt;a href=&quot;http://lists.nongnu.org/mailman/listinfo/axiom-mail&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://lists.nongnu.org/mailman/listinfo/axiom-mail&lt;/a&gt;&lt;br&gt;&amp;gt;&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; &amp;nbsp; &amp;nbsp;
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; &amp;nbsp; &amp;nbsp; &amp;nbsp; 
&lt;br&gt;&amp;gt;&amp;gt; Axiom prints out a banner that contains the date.
&lt;br&gt;&amp;gt;&amp;gt; What is the build date in the banner?
&lt;br&gt;&amp;gt;&amp;gt; Where did you get Axiom?
&lt;br&gt;&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt; Tim
&lt;br&gt;&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt; &amp;nbsp; &amp;nbsp; 
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp; &amp;nbsp; 
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; _______________________________________________
&lt;br&gt;&amp;gt; Axiom-mail mailing list
&lt;br&gt;&amp;gt; &lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26601114&amp;i=5&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;Axiom-mail@...&lt;/a&gt;
&lt;br&gt;&amp;gt; &lt;a href=&quot;http://lists.nongnu.org/mailman/listinfo/axiom-mail&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://lists.nongnu.org/mailman/listinfo/axiom-mail&lt;/a&gt;&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; &amp;nbsp; 
&lt;/div&gt;This package is broken. I am unable to convince Debian to
&lt;br&gt;fix it or to let me fix it. Please visit
&lt;br&gt;&lt;a href=&quot;http://axiom-developer.org/axiom-website/download.html&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://axiom-developer.org/axiom-website/download.html&lt;/a&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
&lt;br&gt;Axiom-mail mailing list
&lt;br&gt;&lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26601114&amp;i=6&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;Axiom-mail@...&lt;/a&gt;
&lt;br&gt;&lt;a href=&quot;http://lists.nongnu.org/mailman/listinfo/axiom-mail&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://lists.nongnu.org/mailman/listinfo/axiom-mail&lt;/a&gt;&lt;br&gt;&lt;p&gt;From forum: &lt;a href=&quot;http://old.nabble.com/axiom-mail-f6888.html&quot; embed=&quot;fixTarget[6888]&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;axiom-mail&lt;/a&gt;&lt;/p&gt;</content>
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</entry>

<entry>
	<id>tag:old.nabble.com,2006:post-26597271</id>
	<title>Re: my axiom is broken</title>
	<published>2009-12-01T11:03:33Z</published>
	<updated>2009-12-01T11:03:33Z</updated>
	<author>
		<name>Cappy</name>
	</author>
	<content type="html">Hi again,
&lt;br&gt;&lt;br&gt;I installed axiom using the Synaptic packet manager. Here is the complete output of the axiom command:
&lt;br&gt;&lt;br&gt;cap@miles:~$ axiom
&lt;br&gt;GCL (GNU Common Lisp) &amp;nbsp;2.6.7 CLtL1 &amp;nbsp; &amp;nbsp;Nov 10 2006 14:25:02
&lt;br&gt;Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
&lt;br&gt;Binary License: &amp;nbsp;GPL due to GPL'ed components: (XGCL READLINE BFD UNEXEC)
&lt;br&gt;Modifications of this banner must retain notice of a compatible license
&lt;br&gt;Dedicated to the memory of W. Schelter
&lt;br&gt;&lt;br&gt;Use (help) to get some basic information on how to use GCL.
&lt;br&gt;Temporary directory for compiler files set to /tmp/
&lt;br&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; AXIOM Computer Algebra System 
&lt;br&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;Version: Axiom 3.9 (September 2005)
&lt;br&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Timestamp: Saturday December 2, 2006 at 09:30:31 
&lt;br&gt;-----------------------------------------------------------------------------
&lt;br&gt;&amp;nbsp; &amp;nbsp;Issue )copyright to view copyright notices.
&lt;br&gt;&amp;nbsp; &amp;nbsp;Issue )summary for a summary of useful system commands.
&lt;br&gt;&amp;nbsp; &amp;nbsp;Issue )quit to leave AXIOM and return to shell.
&lt;br&gt;-----------------------------------------------------------------------------
&lt;br&gt;&amp;nbsp;
&lt;br&gt;&amp;nbsp; &amp;nbsp;Re-reading compress.daase &amp;nbsp; Re-reading interp.daase
&lt;br&gt;&amp;nbsp; &amp;nbsp;Re-reading operation.daase
&lt;br&gt;&amp;nbsp; &amp;nbsp;Re-reading category.daase 
&lt;br&gt;&amp;nbsp; &amp;nbsp;&amp;gt;&amp;gt; System error:
&lt;br&gt;&amp;nbsp; &amp;nbsp;Couldn't protect
&lt;br&gt;&lt;br&gt;&lt;br&gt;Error: The tag |top_level| is undefined.
&lt;br&gt;Fast links are on: do (si::use-fast-links nil) for debugging
&lt;br&gt;Error signalled by RETURN.
&lt;br&gt;Broken at APPLY. &amp;nbsp;Type :H for Help.
&lt;br&gt;BOOT&amp;gt;&amp;gt;
&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;Cappy
&lt;br&gt;&lt;br&gt;&lt;br&gt;--- On Mon, 11/30/09, Tim Daly &amp;lt;&lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26597271&amp;i=0&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;daly@...&lt;/a&gt;&amp;gt; wrote:
&lt;br&gt;&lt;div class='shrinkable-quote'&gt;&lt;br&gt;&amp;gt; From: Tim Daly &amp;lt;&lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26597271&amp;i=1&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;daly@...&lt;/a&gt;&amp;gt;
&lt;br&gt;&amp;gt; Subject: Re: [Axiom-mail] my axiom is broken
&lt;br&gt;&amp;gt; To: &amp;quot;Cap&amp;quot; &amp;lt;&lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26597271&amp;i=2&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;daCaptain@...&lt;/a&gt;&amp;gt;
&lt;br&gt;&amp;gt; Cc: &lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26597271&amp;i=3&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;axiom-mail@...&lt;/a&gt;
&lt;br&gt;&amp;gt; Date: Monday, November 30, 2009, 2:53 PM
&lt;br&gt;&amp;gt; Cap wrote:
&lt;br&gt;&amp;gt; &amp;gt; Hello,
&lt;br&gt;&amp;gt; &amp;gt;
&lt;br&gt;&amp;gt; &amp;gt; I get an error message when I try to start axiom.
&lt;br&gt;&amp;gt; &amp;gt;
&lt;br&gt;&amp;gt; &amp;gt; Re-reading compress.daase   Re-reading
&lt;br&gt;&amp;gt; interp.daase
&lt;br&gt;&amp;gt; &amp;gt;    Re-reading operation.daase
&lt;br&gt;&amp;gt; &amp;gt;    Re-reading category.daase 
&lt;br&gt;&amp;gt; &amp;gt;    &amp;gt;&amp;gt; System error:
&lt;br&gt;&amp;gt; &amp;gt;    Couldn't protect
&lt;br&gt;&amp;gt; &amp;gt;
&lt;br&gt;&amp;gt; &amp;gt;
&lt;br&gt;&amp;gt; &amp;gt; Error: The tag |top_level| is undefined.
&lt;br&gt;&amp;gt; &amp;gt; Fast links are on: do (si::use-fast-links nil) for
&lt;br&gt;&amp;gt; debugging
&lt;br&gt;&amp;gt; &amp;gt; Error signalled by RETURN.
&lt;br&gt;&amp;gt; &amp;gt; Broken at APPLY.  Type :H for Help.
&lt;br&gt;&amp;gt; &amp;gt; BOOT&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt; &amp;gt;
&lt;br&gt;&amp;gt; &amp;gt; I tried reinstalling the package (Ubuntu 9.04 64), but
&lt;br&gt;&amp;gt; it didn't help. I don't know what else to try. Can anyone
&lt;br&gt;&amp;gt; please help?
&lt;br&gt;&amp;gt; &amp;gt;
&lt;br&gt;&amp;gt; &amp;gt;
&lt;br&gt;&amp;gt; &amp;gt; thanks
&lt;br&gt;&amp;gt; &amp;gt; Cappy
&lt;br&gt;&amp;gt; &amp;gt;
&lt;br&gt;&amp;gt; &amp;gt;
&lt;br&gt;&amp;gt; &amp;gt;
&lt;br&gt;&amp;gt; &amp;gt;       
&lt;br&gt;&amp;gt; &amp;gt;
&lt;br&gt;&amp;gt; &amp;gt;
&lt;br&gt;&amp;gt; &amp;gt; _______________________________________________
&lt;br&gt;&amp;gt; &amp;gt; Axiom-mail mailing list
&lt;br&gt;&amp;gt; &amp;gt; &lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26597271&amp;i=4&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;Axiom-mail@...&lt;/a&gt;
&lt;br&gt;&amp;gt; &amp;gt; &lt;a href=&quot;http://lists.nongnu.org/mailman/listinfo/axiom-mail&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://lists.nongnu.org/mailman/listinfo/axiom-mail&lt;/a&gt;&lt;br&gt;&amp;gt; &amp;gt;
&lt;br&gt;&amp;gt; &amp;gt;   
&lt;br&gt;&amp;gt; Axiom prints out a banner that contains the date.
&lt;br&gt;&amp;gt; What is the build date in the banner?
&lt;br&gt;&amp;gt; Where did you get Axiom?
&lt;br&gt;&amp;gt; 
&lt;br&gt;&amp;gt; Tim
&lt;br&gt;&amp;gt; 
&lt;br&gt;&amp;gt; 
&lt;/div&gt;&lt;br&gt;&lt;br&gt;&amp;nbsp;
&lt;br&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
&lt;br&gt;Axiom-mail mailing list
&lt;br&gt;&lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26597271&amp;i=5&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;Axiom-mail@...&lt;/a&gt;
&lt;br&gt;&lt;a href=&quot;http://lists.nongnu.org/mailman/listinfo/axiom-mail&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://lists.nongnu.org/mailman/listinfo/axiom-mail&lt;/a&gt;&lt;br&gt;&lt;p&gt;From forum: &lt;a href=&quot;http://old.nabble.com/axiom-mail-f6888.html&quot; embed=&quot;fixTarget[6888]&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;axiom-mail&lt;/a&gt;&lt;/p&gt;</content>
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</entry>

<entry>
	<id>tag:old.nabble.com,2006:post-26592972</id>
	<title>Re: [Aldor-l] License for FriCAS-Aldor interface files</title>
	<published>2009-12-01T06:44:32Z</published>
	<updated>2009-12-01T06:44:32Z</updated>
	<author>
		<name>Tim Daly-3</name>
	</author>
	<content type="html">Ralf Hemmecke wrote:
&lt;div class='shrinkable-quote'&gt;&lt;br&gt;&amp;gt; Dear Mike, dear Stephen,
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; may I ask you again to consider the attached request.
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Thank you
&lt;br&gt;&amp;gt; Ralf
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; On 09/24/2009 11:38 PM, Ralf HEMMECKE wrote:
&lt;br&gt;&amp;gt;&amp;gt; Dear Stephen, dear Mike
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt; as you might know, I have built some scripts in FriCAS (a fork of 
&lt;br&gt;&amp;gt;&amp;gt; Axiom) (&lt;a href=&quot;http://fricas.sourceforge.net/&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://fricas.sourceforge.net/&lt;/a&gt;) in order to build libaxiom.al 
&lt;br&gt;&amp;gt;&amp;gt; from scratch. Unfortunately, I can neither distribute libaxiom.al nor 
&lt;br&gt;&amp;gt;&amp;gt; some necessary .as files under the same license as FriCAS (mBSD), 
&lt;br&gt;&amp;gt;&amp;gt; since this code is only available under the Aldor Public License 2.0.
&lt;br&gt;&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt; I hereby kindly ask you to release the following files under a BSD 
&lt;br&gt;&amp;gt;&amp;gt; license (same as for the Axiom code).
&lt;br&gt;&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt; &amp;nbsp; &lt;a href=&quot;https://svn.origo.ethz.ch/algebraist/trunk/aldor/lib/libax0/axiom.as&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;https://svn.origo.ethz.ch/algebraist/trunk/aldor/lib/libax0/axiom.as&lt;/a&gt;&lt;br&gt;&amp;gt;&amp;gt; &amp;nbsp; 
&lt;br&gt;&amp;gt;&amp;gt; &lt;a href=&quot;https://svn.origo.ethz.ch/algebraist/trunk/aldor/lib/libax0/axextend.as&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;https://svn.origo.ethz.ch/algebraist/trunk/aldor/lib/libax0/axextend.as&lt;/a&gt;&lt;br&gt;&amp;gt;&amp;gt; &amp;nbsp; &lt;a href=&quot;https://svn.origo.ethz.ch/algebraist/trunk/aldor/lib/libax0/axlit.as&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;https://svn.origo.ethz.ch/algebraist/trunk/aldor/lib/libax0/axlit.as&lt;/a&gt;&lt;br&gt;&amp;gt;&amp;gt; &amp;nbsp; &lt;a href=&quot;https://svn.origo.ethz.ch/algebraist/trunk/aldor/lib/libax0/stub.as&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;https://svn.origo.ethz.ch/algebraist/trunk/aldor/lib/libax0/stub.as&lt;/a&gt;&lt;br&gt;&amp;gt;&amp;gt; &amp;nbsp; 
&lt;br&gt;&amp;gt;&amp;gt; &lt;a href=&quot;https://svn.origo.ethz.ch/algebraist/trunk/aldor/lib/libax0/minimach.as&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;https://svn.origo.ethz.ch/algebraist/trunk/aldor/lib/libax0/minimach.as&lt;/a&gt;&lt;br&gt;&amp;gt;&amp;gt; &amp;nbsp; 
&lt;br&gt;&amp;gt;&amp;gt; &lt;a href=&quot;https://svn.origo.ethz.ch/algebraist/trunk/aldor/lib/axllib/src/lang.as&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;https://svn.origo.ethz.ch/algebraist/trunk/aldor/lib/axllib/src/lang.as&lt;/a&gt;&lt;br&gt;&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt; Furthermore, in order to distribute a precompiled libaxiom.al 
&lt;br&gt;&amp;gt;&amp;gt; together with FriCAS, it would be helpful to also release
&lt;br&gt;&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt; $(ALDORROOT)/lib/libfoam.al(runtime.ao)
&lt;br&gt;&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt; under a BSD license. For 'runtime.ao', also releasing the sources 
&lt;br&gt;&amp;gt;&amp;gt; under a BSD license would be good, but I explicitly ask for the 
&lt;br&gt;&amp;gt;&amp;gt; release of the .ao format.
&lt;br&gt;&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt; Please help the FriCAS project and don't let Aldor die.
&lt;br&gt;&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt; Has meanwhile anything been done to release all of the Aldor 
&lt;br&gt;&amp;gt;&amp;gt; compiler+library sources under a GPL-compatible license?
&lt;br&gt;&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt; Thank you for your time.
&lt;br&gt;&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt; Yours sincerely
&lt;br&gt;&amp;gt;&amp;gt; Ralf Hemmecke
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; _______________________________________________
&lt;br&gt;&amp;gt; Aldor-l mailing list
&lt;br&gt;&amp;gt; &lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26592972&amp;i=0&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;Aldor-l@...&lt;/a&gt;
&lt;br&gt;&amp;gt; &lt;a href=&quot;http://aldor.org/mailman/listinfo/aldor-l_aldor.org&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://aldor.org/mailman/listinfo/aldor-l_aldor.org&lt;/a&gt;&lt;br&gt;&amp;gt;
&lt;/div&gt;Mike, Stephen,
&lt;br&gt;&lt;br&gt;I have recently decided after two years that Aldor was
&lt;br&gt;never going to become free enough to be integrated back
&lt;br&gt;into Axiom. The FriCAS project has been trying to keep
&lt;br&gt;the connection alive.
&lt;br&gt;&lt;br&gt;It would seem that changing the license on the FriCAS
&lt;br&gt;related files would at least help them in their efforts
&lt;br&gt;to keep the connection alive. Thus, I'm adding my voice
&lt;br&gt;to the request to make this change.
&lt;br&gt;&lt;br&gt;I realize that such changes involve your legal department
&lt;br&gt;and come at a non-trivial cost. I also realize that you
&lt;br&gt;may have prior agreements that prevent it. In any case,
&lt;br&gt;I think that the sense of frustration in FriCAS appears
&lt;br&gt;to be reaching a critical tipping point and this is likely
&lt;br&gt;to end with Aldor being deleted.
&lt;br&gt;&lt;br&gt;Tim Daly
&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
&lt;br&gt;Axiom-developer mailing list
&lt;br&gt;&lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26592972&amp;i=1&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;Axiom-developer@...&lt;/a&gt;
&lt;br&gt;&lt;a href=&quot;http://lists.nongnu.org/mailman/listinfo/axiom-developer&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://lists.nongnu.org/mailman/listinfo/axiom-developer&lt;/a&gt;&lt;br&gt;&lt;p&gt;From forum: &lt;a href=&quot;http://old.nabble.com/axiom-developer-f6886.html&quot; embed=&quot;fixTarget[6886]&quot; target=&quot;_top&quot; &gt;axiom-developer&lt;/a&gt;&lt;/p&gt;</content>
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</entry>

<entry>
	<id>tag:old.nabble.com,2006:post-26583530</id>
	<title>Re: my axiom is broken</title>
	<published>2009-11-30T14:51:41Z</published>
	<updated>2009-11-30T14:51:41Z</updated>
	<author>
		<name>Tim Daly-3</name>
	</author>
	<content type="html">Cap wrote:
&lt;div class='shrinkable-quote'&gt;&lt;br&gt;&amp;gt; Hello,
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; I get an error message when I try to start axiom.
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Re-reading compress.daase &amp;nbsp; Re-reading interp.daase
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;Re-reading operation.daase
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;Re-reading category.daase 
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;&amp;gt;&amp;gt; System error:
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;Couldn't protect
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Error: The tag |top_level| is undefined.
&lt;br&gt;&amp;gt; Fast links are on: do (si::use-fast-links nil) for debugging
&lt;br&gt;&amp;gt; Error signalled by RETURN.
&lt;br&gt;&amp;gt; Broken at APPLY. &amp;nbsp;Type :H for Help.
&lt;br&gt;&amp;gt; BOOT&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; I tried reinstalling the package (Ubuntu 9.04 64), but it didn't help. I don't know what else to try. Can anyone please help?
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; thanks
&lt;br&gt;&amp;gt; Cappy
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp; &amp;nbsp; 
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; _______________________________________________
&lt;br&gt;&amp;gt; Axiom-mail mailing list
&lt;br&gt;&amp;gt; &lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26583530&amp;i=0&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;Axiom-mail@...&lt;/a&gt;
&lt;br&gt;&amp;gt; &lt;a href=&quot;http://lists.nongnu.org/mailman/listinfo/axiom-mail&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://lists.nongnu.org/mailman/listinfo/axiom-mail&lt;/a&gt;&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; &amp;nbsp; 
&lt;/div&gt;Axiom prints out a banner that contains the date.
&lt;br&gt;What is the build date in the banner?
&lt;br&gt;Where did you get Axiom?
&lt;br&gt;&lt;br&gt;Tim
&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
&lt;br&gt;Axiom-mail mailing list
&lt;br&gt;&lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26583530&amp;i=1&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;Axiom-mail@...&lt;/a&gt;
&lt;br&gt;&lt;a href=&quot;http://lists.nongnu.org/mailman/listinfo/axiom-mail&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://lists.nongnu.org/mailman/listinfo/axiom-mail&lt;/a&gt;&lt;br&gt;&lt;p&gt;From forum: &lt;a href=&quot;http://old.nabble.com/axiom-mail-f6888.html&quot; embed=&quot;fixTarget[6888]&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;axiom-mail&lt;/a&gt;&lt;/p&gt;</content>
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</entry>

<entry>
	<id>tag:old.nabble.com,2006:post-26581521</id>
	<title>my axiom is broken</title>
	<published>2009-11-30T12:42:55Z</published>
	<updated>2009-11-30T12:42:55Z</updated>
	<author>
		<name>Cappy</name>
	</author>
	<content type="html">Hello,
&lt;br&gt;&lt;br&gt;I get an error message when I try to start axiom.
&lt;br&gt;&lt;br&gt;Re-reading compress.daase &amp;nbsp; Re-reading interp.daase
&lt;br&gt;&amp;nbsp; &amp;nbsp;Re-reading operation.daase
&lt;br&gt;&amp;nbsp; &amp;nbsp;Re-reading category.daase 
&lt;br&gt;&amp;nbsp; &amp;nbsp;&amp;gt;&amp;gt; System error:
&lt;br&gt;&amp;nbsp; &amp;nbsp;Couldn't protect
&lt;br&gt;&lt;br&gt;&lt;br&gt;Error: The tag |top_level| is undefined.
&lt;br&gt;Fast links are on: do (si::use-fast-links nil) for debugging
&lt;br&gt;Error signalled by RETURN.
&lt;br&gt;Broken at APPLY. &amp;nbsp;Type :H for Help.
&lt;br&gt;BOOT&amp;gt;&amp;gt;
&lt;br&gt;&lt;br&gt;I tried reinstalling the package (Ubuntu 9.04 64), but it didn't help. I don't know what else to try. Can anyone please help?
&lt;br&gt;&lt;br&gt;&lt;br&gt;thanks
&lt;br&gt;Cappy
&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; 
&lt;br&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
&lt;br&gt;Axiom-mail mailing list
&lt;br&gt;&lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26581521&amp;i=0&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;Axiom-mail@...&lt;/a&gt;
&lt;br&gt;&lt;a href=&quot;http://lists.nongnu.org/mailman/listinfo/axiom-mail&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://lists.nongnu.org/mailman/listinfo/axiom-mail&lt;/a&gt;&lt;br&gt;&lt;p&gt;From forum: &lt;a href=&quot;http://old.nabble.com/axiom-mail-f6888.html&quot; embed=&quot;fixTarget[6888]&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;axiom-mail&lt;/a&gt;&lt;/p&gt;</content>
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</entry>

<entry>
	<id>tag:old.nabble.com,2006:post-26573759</id>
	<title>Embedding Axiom</title>
	<published>2009-11-30T04:12:26Z</published>
	<updated>2009-11-30T04:12:26Z</updated>
	<author>
		<name>Tim Daly-3</name>
	</author>
	<content type="html">Another trend that is important is the development of parallelism.
&lt;br&gt;Berkeley has a group dedicated to this it seems[1]. Assuming that
&lt;br&gt;today's uniprocessor power is the peak speed for the future we
&lt;br&gt;need to architect the system to take advantage of parallelism.
&lt;br&gt;&lt;br&gt;My view of the natural embedding of parallelism in Axiom is
&lt;br&gt;tightly coupled to provisos. The proviso mechanism holds, manages,
&lt;br&gt;and carries the assumptions that each branch of a computation will
&lt;br&gt;use to constrain the answer. Thus if you have
&lt;br&gt;&amp;nbsp; &amp;nbsp;f(x) | x &amp;gt; 0
&lt;br&gt;&amp;nbsp; &amp;nbsp;f(x) | x = 0
&lt;br&gt;&amp;nbsp; &amp;nbsp;f(x) | x &amp;lt; 0
&lt;br&gt;then you have the ability to perform all three computations in
&lt;br&gt;parallel. I am assuming functional programming and immutable
&lt;br&gt;data structures. These three computations can be forked into their
&lt;br&gt;own images and then the results can be joined. This is a &amp;quot;natural&amp;quot;
&lt;br&gt;parallelism for mathematics computation.
&lt;br&gt;&lt;br&gt;Thus some thought needs to be given to re-architecting the system
&lt;br&gt;to support provisos in a natural way.
&lt;br&gt;&lt;br&gt;Tim
&lt;br&gt;&lt;br&gt;[1] &lt;a href=&quot;http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-183.pdf&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-183.pdf&lt;/a&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
&lt;br&gt;Axiom-developer mailing list
&lt;br&gt;&lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26573759&amp;i=0&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;Axiom-developer@...&lt;/a&gt;
&lt;br&gt;&lt;a href=&quot;http://lists.nongnu.org/mailman/listinfo/axiom-developer&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://lists.nongnu.org/mailman/listinfo/axiom-developer&lt;/a&gt;&lt;br&gt;&lt;p&gt;From forum: &lt;a href=&quot;http://old.nabble.com/axiom-developer-f6886.html&quot; embed=&quot;fixTarget[6886]&quot; target=&quot;_top&quot; &gt;axiom-developer&lt;/a&gt;&lt;/p&gt;</content>
	<link rel="alternate" type="text/html" href="http://old.nabble.com/Embedding-Axiom-tp26366779p26573759.html" />
</entry>

<entry>
	<id>tag:old.nabble.com,2006:post-26567912</id>
	<title>Knuth talks about Literate Programming</title>
	<published>2009-11-29T16:20:22Z</published>
	<updated>2009-11-29T16:20:22Z</updated>
	<author>
		<name>Tim Daly-3</name>
	</author>
	<content type="html">&lt;a href=&quot;http://stanford-online.stanford.edu/seminars/knuth/871021-knuth-100.asx&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://stanford-online.stanford.edu/seminars/knuth/871021-knuth-100.asx&lt;/a&gt;&lt;br&gt;&lt;a href=&quot;http://stanford-online.stanford.edu/seminars/knuth/871023-knuth-100.asx&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://stanford-online.stanford.edu/seminars/knuth/871023-knuth-100.asx&lt;/a&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
&lt;br&gt;Axiom-developer mailing list
&lt;br&gt;&lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26567912&amp;i=0&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;Axiom-developer@...&lt;/a&gt;
&lt;br&gt;&lt;a href=&quot;http://lists.nongnu.org/mailman/listinfo/axiom-developer&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://lists.nongnu.org/mailman/listinfo/axiom-developer&lt;/a&gt;&lt;br&gt;&lt;p&gt;From forum: &lt;a href=&quot;http://old.nabble.com/axiom-developer-f6886.html&quot; embed=&quot;fixTarget[6886]&quot; target=&quot;_top&quot; &gt;axiom-developer&lt;/a&gt;&lt;/p&gt;</content>
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</entry>

<entry>
	<id>tag:old.nabble.com,2006:post-26559238</id>
	<title>Re: recent versions</title>
	<published>2009-11-28T20:13:03Z</published>
	<updated>2009-11-28T20:13:03Z</updated>
	<author>
		<name>Tim Daly-3</name>
	</author>
	<content type="html">Alejandro:
&lt;br&gt;&lt;br&gt;&lt;a href=&quot;http://daly.axiom-developer.org:/axiom-ubuntu-nov2009-bin.tgz&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://daly.axiom-developer.org:/axiom-ubuntu-nov2009-bin.tgz&lt;/a&gt;&lt;br&gt;&lt;br&gt;Let me know if it works.
&lt;br&gt;&lt;br&gt;Tim
&lt;br&gt;&lt;br&gt;Alejandro Jakubi wrote:
&lt;div class='shrinkable-quote'&gt;&lt;br&gt;&amp;gt; I find the recent improvements in the documentation of Axiom of paramount
&lt;br&gt;&amp;gt; importance in trying to understand this complex system. In this 
&lt;br&gt;&amp;gt; regards, I
&lt;br&gt;&amp;gt; have just read about the new )describe command and found it quite 
&lt;br&gt;&amp;gt; interesting.
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Anyways, I have found in another of your posts a link to a Debian 
&lt;br&gt;&amp;gt; binary for
&lt;br&gt;&amp;gt; the November 2009 version. I have downloaded it already but not 
&lt;br&gt;&amp;gt; installed yet.
&lt;br&gt;&amp;gt; Hopefully it will work in Debian Etch. Will be there an Ubuntu binary 
&lt;br&gt;&amp;gt; for this
&lt;br&gt;&amp;gt; (or latter) version? (if it were an issue of priorities, I would 
&lt;br&gt;&amp;gt; prefer it to
&lt;br&gt;&amp;gt; an updated download page).
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Of course, it would be wonderful if the maintainer of the Axiom 
&lt;br&gt;&amp;gt; package in
&lt;br&gt;&amp;gt; Debian and Ubuntu distributions could keep it updated, ideally in sync
&lt;br&gt;&amp;gt; with the 2-month (or whatever) period source releases. See e.g.:
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; &lt;a href=&quot;http://packages.debian.org/etch/math/axiom&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://packages.debian.org/etch/math/axiom&lt;/a&gt;&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; &lt;a href=&quot;http://packages.ubuntu.com/hardy/math/axiom&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://packages.ubuntu.com/hardy/math/axiom&lt;/a&gt;&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; This package seems stuck because of bugs and other issues.
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Alejandro
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; On Sat, 28 Nov 2009, Tim Daly wrote:
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt; Alejandro Jakubi wrote:
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; The download page 
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; (&lt;a href=&quot;http://axiom-developer.org/axiom-website/download.html&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://axiom-developer.org/axiom-website/download.html&lt;/a&gt;) has links 
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; for downloading Axiom versions up to May 2009. Where are the more 
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; recent versions?
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; Regards, Alejandro Jakubi
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; _______________________________________________
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; Axiom-mail mailing list
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; &lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26559238&amp;i=0&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;Axiom-mail@...&lt;/a&gt;
&lt;br&gt;&amp;gt;&amp;gt;&amp;gt; &lt;a href=&quot;http://lists.nongnu.org/mailman/listinfo/axiom-mail&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://lists.nongnu.org/mailman/listinfo/axiom-mail&lt;/a&gt;&lt;br&gt;&amp;gt;&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt; I did not create them. I will put it on the list to do.
&lt;br&gt;&amp;gt;&amp;gt; You would be amazed how little time there is between releases
&lt;br&gt;&amp;gt;&amp;gt; if you do them every 2 months.
&lt;br&gt;&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt; The effort has been mostly removing boot and converging the
&lt;br&gt;&amp;gt;&amp;gt; interpreter into book volume 5. This doesn't change the user
&lt;br&gt;&amp;gt;&amp;gt; functionality (although I've introduced )debug and )describe).
&lt;br&gt;&amp;gt;&amp;gt; From my point of view the effort is continuous but I have
&lt;br&gt;&amp;gt;&amp;gt; committed to time-boxed Axiom releases every 2 months.
&lt;br&gt;&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt; There is a long thread (pre-fork) about the importance of doing
&lt;br&gt;&amp;gt;&amp;gt; time-boxed releases every 2 months.
&lt;br&gt;&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;&amp;gt; Tim
&lt;br&gt;&amp;gt;&amp;gt;
&lt;br&gt;&amp;gt;
&lt;/div&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
&lt;br&gt;Axiom-mail mailing list
&lt;br&gt;&lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26559238&amp;i=1&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;Axiom-mail@...&lt;/a&gt;
&lt;br&gt;&lt;a href=&quot;http://lists.nongnu.org/mailman/listinfo/axiom-mail&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://lists.nongnu.org/mailman/listinfo/axiom-mail&lt;/a&gt;&lt;br&gt;&lt;p&gt;From forum: &lt;a href=&quot;http://old.nabble.com/axiom-mail-f6888.html&quot; embed=&quot;fixTarget[6888]&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;axiom-mail&lt;/a&gt;&lt;/p&gt;</content>
	<link rel="alternate" type="text/html" href="http://old.nabble.com/recent-versions-tp26558462p26559238.html" />
</entry>

<entry>
	<id>tag:old.nabble.com,2006:post-26559165</id>
	<title>Re: recent versions</title>
	<published>2009-11-28T19:49:41Z</published>
	<updated>2009-11-28T19:49:41Z</updated>
	<author>
		<name>Alejandro Jakubi</name>
	</author>
	<content type="html">I find the recent improvements in the documentation of Axiom of paramount
&lt;br&gt;importance in trying to understand this complex system. In this regards, I
&lt;br&gt;have just read about the new )describe command and found it quite interesting.
&lt;br&gt;&lt;br&gt;Anyways, I have found in another of your posts a link to a Debian binary for
&lt;br&gt;the November 2009 version. I have downloaded it already but not installed yet.
&lt;br&gt;Hopefully it will work in Debian Etch. Will be there an Ubuntu binary for this
&lt;br&gt;(or latter) version? (if it were an issue of priorities, I would prefer it to
&lt;br&gt;an updated download page).
&lt;br&gt;&lt;br&gt;Of course, it would be wonderful if the maintainer of the Axiom package in
&lt;br&gt;Debian and Ubuntu distributions could keep it updated, ideally in sync
&lt;br&gt;with the 2-month (or whatever) period source releases. See e.g.:
&lt;br&gt;&lt;br&gt;&lt;a href=&quot;http://packages.debian.org/etch/math/axiom&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://packages.debian.org/etch/math/axiom&lt;/a&gt;&lt;br&gt;&lt;br&gt;&lt;a href=&quot;http://packages.ubuntu.com/hardy/math/axiom&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://packages.ubuntu.com/hardy/math/axiom&lt;/a&gt;&lt;br&gt;&lt;br&gt;This package seems stuck because of bugs and other issues.
&lt;br&gt;&lt;br&gt;Alejandro
&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;On Sat, 28 Nov 2009, Tim Daly wrote:
&lt;br&gt;&lt;div class='shrinkable-quote'&gt;&lt;br&gt;&amp;gt; Alejandro Jakubi wrote:
&lt;br&gt;&amp;gt;&amp;gt; The download page (&lt;a href=&quot;http://axiom-developer.org/axiom-website/download.html&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://axiom-developer.org/axiom-website/download.html&lt;/a&gt;) 
&lt;br&gt;&amp;gt;&amp;gt; has links for downloading Axiom versions up to May 2009. Where are the more 
&lt;br&gt;&amp;gt;&amp;gt; recent versions?
&lt;br&gt;&amp;gt;&amp;gt; 
&lt;br&gt;&amp;gt;&amp;gt; Regards, Alejandro Jakubi
&lt;br&gt;&amp;gt;&amp;gt; 
&lt;br&gt;&amp;gt;&amp;gt; 
&lt;br&gt;&amp;gt;&amp;gt; 
&lt;br&gt;&amp;gt;&amp;gt; _______________________________________________
&lt;br&gt;&amp;gt;&amp;gt; Axiom-mail mailing list
&lt;br&gt;&amp;gt;&amp;gt; &lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26559165&amp;i=0&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;Axiom-mail@...&lt;/a&gt;
&lt;br&gt;&amp;gt;&amp;gt; &lt;a href=&quot;http://lists.nongnu.org/mailman/listinfo/axiom-mail&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://lists.nongnu.org/mailman/listinfo/axiom-mail&lt;/a&gt;&lt;br&gt;&amp;gt;&amp;gt; 
&lt;br&gt;&amp;gt; I did not create them. I will put it on the list to do.
&lt;br&gt;&amp;gt; You would be amazed how little time there is between releases
&lt;br&gt;&amp;gt; if you do them every 2 months.
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; The effort has been mostly removing boot and converging the
&lt;br&gt;&amp;gt; interpreter into book volume 5. This doesn't change the user
&lt;br&gt;&amp;gt; functionality (although I've introduced )debug and )describe).
&lt;br&gt;&amp;gt; From my point of view the effort is continuous but I have
&lt;br&gt;&amp;gt; committed to time-boxed Axiom releases every 2 months.
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; There is a long thread (pre-fork) about the importance of doing
&lt;br&gt;&amp;gt; time-boxed releases every 2 months.
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Tim
&lt;br&gt;&amp;gt;
&lt;/div&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
&lt;br&gt;Axiom-mail mailing list
&lt;br&gt;&lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26559165&amp;i=1&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;Axiom-mail@...&lt;/a&gt;
&lt;br&gt;&lt;a href=&quot;http://lists.nongnu.org/mailman/listinfo/axiom-mail&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://lists.nongnu.org/mailman/listinfo/axiom-mail&lt;/a&gt;&lt;br&gt;&lt;p&gt;From forum: &lt;a href=&quot;http://old.nabble.com/axiom-mail-f6888.html&quot; embed=&quot;fixTarget[6888]&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;axiom-mail&lt;/a&gt;&lt;/p&gt;</content>
	<link rel="alternate" type="text/html" href="http://old.nabble.com/recent-versions-tp26558462p26559165.html" />
</entry>

<entry>
	<id>tag:old.nabble.com,2006:post-26558689</id>
	<title>Re: recent versions</title>
	<published>2009-11-28T17:38:27Z</published>
	<updated>2009-11-28T17:38:27Z</updated>
	<author>
		<name>Tim Daly-3</name>
	</author>
	<content type="html">Alejandro Jakubi wrote:
&lt;div class='shrinkable-quote'&gt;&lt;br&gt;&amp;gt; The download page 
&lt;br&gt;&amp;gt; (&lt;a href=&quot;http://axiom-developer.org/axiom-website/download.html&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://axiom-developer.org/axiom-website/download.html&lt;/a&gt;) has links for 
&lt;br&gt;&amp;gt; downloading Axiom versions up to May 2009. Where are the more recent 
&lt;br&gt;&amp;gt; versions?
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Regards, Alejandro Jakubi
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; _______________________________________________
&lt;br&gt;&amp;gt; Axiom-mail mailing list
&lt;br&gt;&amp;gt; &lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26558689&amp;i=0&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;Axiom-mail@...&lt;/a&gt;
&lt;br&gt;&amp;gt; &lt;a href=&quot;http://lists.nongnu.org/mailman/listinfo/axiom-mail&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://lists.nongnu.org/mailman/listinfo/axiom-mail&lt;/a&gt;&lt;br&gt;&amp;gt;
&lt;/div&gt;I did not create them. I will put it on the list to do.
&lt;br&gt;You would be amazed how little time there is between releases
&lt;br&gt;if you do them every 2 months.
&lt;br&gt;&lt;br&gt;The effort has been mostly removing boot and converging the
&lt;br&gt;interpreter into book volume 5. This doesn't change the user
&lt;br&gt;functionality (although I've introduced )debug and )describe).
&lt;br&gt;&amp;nbsp;From my point of view the effort is continuous but I have
&lt;br&gt;committed to time-boxed Axiom releases every 2 months.
&lt;br&gt;&lt;br&gt;There is a long thread (pre-fork) about the importance of doing
&lt;br&gt;time-boxed releases every 2 months.
&lt;br&gt;&lt;br&gt;Tim
&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
&lt;br&gt;Axiom-mail mailing list
&lt;br&gt;&lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26558689&amp;i=1&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;Axiom-mail@...&lt;/a&gt;
&lt;br&gt;&lt;a href=&quot;http://lists.nongnu.org/mailman/listinfo/axiom-mail&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://lists.nongnu.org/mailman/listinfo/axiom-mail&lt;/a&gt;&lt;br&gt;&lt;p&gt;From forum: &lt;a href=&quot;http://old.nabble.com/axiom-mail-f6888.html&quot; embed=&quot;fixTarget[6888]&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;axiom-mail&lt;/a&gt;&lt;/p&gt;</content>
	<link rel="alternate" type="text/html" href="http://old.nabble.com/recent-versions-tp26558462p26558689.html" />
</entry>

<entry>
	<id>tag:old.nabble.com,2006:post-26558462</id>
	<title>recent versions</title>
	<published>2009-11-28T16:51:00Z</published>
	<updated>2009-11-28T16:51:00Z</updated>
	<author>
		<name>Alejandro Jakubi</name>
	</author>
	<content type="html">The download page (&lt;a href=&quot;http://axiom-developer.org/axiom-website/download.html&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://axiom-developer.org/axiom-website/download.html&lt;/a&gt;) 
&lt;br&gt;has links for downloading Axiom versions up to May 2009. Where are the 
&lt;br&gt;more recent versions?
&lt;br&gt;&lt;br&gt;Regards, Alejandro Jakubi
&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
&lt;br&gt;Axiom-mail mailing list
&lt;br&gt;&lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26558462&amp;i=0&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;Axiom-mail@...&lt;/a&gt;
&lt;br&gt;&lt;a href=&quot;http://lists.nongnu.org/mailman/listinfo/axiom-mail&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://lists.nongnu.org/mailman/listinfo/axiom-mail&lt;/a&gt;&lt;br&gt;&lt;p&gt;From forum: &lt;a href=&quot;http://old.nabble.com/axiom-mail-f6888.html&quot; embed=&quot;fixTarget[6888]&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;axiom-mail&lt;/a&gt;&lt;/p&gt;</content>
	<link rel="alternate" type="text/html" href="http://old.nabble.com/recent-versions-tp26558462p26558462.html" />
</entry>

<entry>
	<id>tag:old.nabble.com,2006:post-26550880</id>
	<title>Re: [Bug 387255] Axiom in Debian</title>
	<published>2009-11-27T22:46:44Z</published>
	<updated>2009-11-27T22:46:44Z</updated>
	<author>
		<name>Tim Daly-3</name>
	</author>
	<content type="html">Christoph,
&lt;br&gt;&lt;br&gt;I would like to replace the Debian version (from 2005)
&lt;br&gt;to be a later version. How do I go about doing this?
&lt;br&gt;&lt;br&gt;Tim Daly
&lt;br&gt;Axiom Lead Developer
&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
&lt;br&gt;Axiom-developer mailing list
&lt;br&gt;&lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26550880&amp;i=0&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;Axiom-developer@...&lt;/a&gt;
&lt;br&gt;&lt;a href=&quot;http://lists.nongnu.org/mailman/listinfo/axiom-developer&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://lists.nongnu.org/mailman/listinfo/axiom-developer&lt;/a&gt;&lt;br&gt;&lt;p&gt;From forum: &lt;a href=&quot;http://old.nabble.com/axiom-developer-f6886.html&quot; embed=&quot;fixTarget[6886]&quot; target=&quot;_top&quot; &gt;axiom-developer&lt;/a&gt;&lt;/p&gt;</content>
	<link rel="alternate" type="text/html" href="http://old.nabble.com/Re%3A--Bug-387255--Axiom-in-Debian-tp26550710p26550880.html" />
</entry>

<entry>
	<id>tag:old.nabble.com,2006:post-26550710</id>
	<title>Re: [Bug 387255] Axiom in Debian</title>
	<published>2009-11-27T21:51:02Z</published>
	<updated>2009-11-27T21:51:02Z</updated>
	<author>
		<name>Tim Daly-3</name>
	</author>
	<content type="html">Christoph Egger wrote:
&lt;div class='shrinkable-quote'&gt;&lt;br&gt;&amp;gt; Hi!
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; 	I'm currently having a look at this open RC Bug in Debian and
&lt;br&gt;&amp;gt; Ubuntu. You said you know how this is to be solved, can you provide a
&lt;br&gt;&amp;gt; patch or instructions on how to fix it?
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Thanks
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Christoph
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; &amp;nbsp; 
&lt;/div&gt;Christoph,
&lt;br&gt;&lt;br&gt;I downloaded debian-503-i386-netinst.iso and used it to build a clean
&lt;br&gt;version of debian.
&lt;br&gt;&lt;br&gt;I set up the prerequired packages (not all are required but....) and
&lt;br&gt;then built the latest release (November 2009)
&lt;br&gt;&lt;br&gt;I did the following steps:
&lt;br&gt;&lt;br&gt;apt-get -y install gcc build-essential debhelper gcl gettext gs-gpl 
&lt;br&gt;html2text
&lt;br&gt;apt-get -y install intltool-debian libgmp3-dev libice-dev libxau-dev 
&lt;br&gt;libxaw7-dev
&lt;br&gt;apt-get -y install po-debconf x-dev x11proto-input-dev x11proto-kb-dev
&lt;br&gt;apt-get -y install libncurses5-dev libreadline5-dev libstdc++6-4.1-dev gawk
&lt;br&gt;apt-get -y install texlive-pstricks git-core texlive
&lt;br&gt;git clone git://axiom.git.sourceforge.net/gitroot/axiom/axiom
&lt;br&gt;cd axiom
&lt;br&gt;export AXIOM=`pwd`/mnt/debian
&lt;br&gt;export PATH=$AXIOM/bin:$PATH
&lt;br&gt;make
&lt;br&gt;&lt;br&gt;I uploaded the binary as
&lt;br&gt;&lt;a href=&quot;http://daly.axiom-developer.org/axiom-debian-nov2009-bin.tgz&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://daly.axiom-developer.org/axiom-debian-nov2009-bin.tgz&lt;/a&gt;&lt;br&gt;&lt;br&gt;To run it do:
&lt;br&gt;wget &lt;a href=&quot;http://daly.axiom-developer.org/axiom-debian-nov2009-bin.tgz&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://daly.axiom-developer.org/axiom-debian-nov2009-bin.tgz&lt;/a&gt;&lt;br&gt;tar -zxf axiom-debian-nov2009-bin.tgz
&lt;br&gt;cd axiom
&lt;br&gt;export AXIOM=`pwd`/mnt/debian
&lt;br&gt;export PATH=$AXIOM/bin:$PATH
&lt;br&gt;axiom
&lt;br&gt;&lt;br&gt;In the hyperdoc window you can click on
&lt;br&gt;&lt;br&gt;Basic Commands -&amp;gt; Draw -&amp;gt; A function of two variables -&amp;gt; Continue -&amp;gt; Do It
&lt;br&gt;&lt;br&gt;and you should see a 3D graphics
&lt;br&gt;&lt;br&gt;At the Axiom comand line you can type:
&lt;br&gt;&lt;br&gt;integrate(sin(x),x)
&lt;br&gt;&lt;br&gt;and get back &amp;quot;- cos(x)&amp;quot;
&lt;br&gt;&lt;br&gt;Let me know if it works for you.
&lt;br&gt;&lt;br&gt;Tim Daly
&lt;br&gt;Axiom Lead Developer
&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
&lt;br&gt;Axiom-developer mailing list
&lt;br&gt;&lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26550710&amp;i=0&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;Axiom-developer@...&lt;/a&gt;
&lt;br&gt;&lt;a href=&quot;http://lists.nongnu.org/mailman/listinfo/axiom-developer&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://lists.nongnu.org/mailman/listinfo/axiom-developer&lt;/a&gt;&lt;br&gt;&lt;p&gt;From forum: &lt;a href=&quot;http://old.nabble.com/axiom-developer-f6886.html&quot; embed=&quot;fixTarget[6886]&quot; target=&quot;_top&quot; &gt;axiom-developer&lt;/a&gt;&lt;/p&gt;</content>
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</entry>

<entry>
	<id>tag:old.nabble.com,2006:post-26533714</id>
	<title>Re: Re: Clifford Algebra examples:</title>
	<published>2009-11-26T10:52:43Z</published>
	<updated>2009-11-26T10:52:43Z</updated>
	<author>
		<name>Tim Daly-3</name>
	</author>
	<content type="html">&lt;br&gt;&amp;nbsp;From an Axiom point of view this is stunningly good documentation.
&lt;br&gt;I've downloaded the paper and added it to the reading queue.
&lt;br&gt;I thought I had a grip on the Clifford Algebra stuff but clearly I do not.
&lt;br&gt;Thanks.
&lt;br&gt;&lt;br&gt;Tim
&lt;br&gt;&lt;br&gt;There is no such thing as a simple job.
&lt;br&gt;&lt;div class='shrinkable-quote'&gt;&lt;br&gt;&amp;gt; Dear Martin,
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; &amp;nbsp; 
&lt;br&gt;&amp;gt;&amp;gt; Can I ask about the definitions of the involutions:
&lt;br&gt;&amp;gt;&amp;gt; &amp;nbsp; &amp;nbsp; 
&lt;br&gt;&amp;gt; Yes, please ask, I'll answer if I know and time permits.
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; &amp;nbsp; 
&lt;br&gt;&amp;gt;&amp;gt; gradeInvolution == reversion? sign=(-1)^(d(d-1)/2) symbol= ~
&lt;br&gt;&amp;gt;&amp;gt; Cliplus clirev == ? symbol=multiply by pseudoscalar? symbol=
&lt;br&gt;&amp;gt;&amp;gt; Clifford conjugation: scalar part minus non-scalar part? symbol=
&lt;br&gt;&amp;gt;&amp;gt; &amp;nbsp; &amp;nbsp; 
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; The involutions you give are again assuming a diagonal (orthonormal)
&lt;br&gt;&amp;gt; basis for the quadratic (bilinear) form. Since this is bad for applications,
&lt;br&gt;&amp;gt; it has to be avoided. Of course if you know you are in a diagonal basis
&lt;br&gt;&amp;gt; you can use faster algorithms (like defining a cmulDiag)
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Grade involution:
&lt;br&gt;&amp;gt; Any (Grassmann-) Clifford algebra is built up from a base space V (of dimension
&lt;br&gt;&amp;gt; dim V = n) You have two natural transformations on V which generalize
&lt;br&gt;&amp;gt; to the whole space W=/\V of dim W = 2^n.
&lt;br&gt;&amp;gt; a) The identity map (does nothing on W)
&lt;br&gt;&amp;gt; b) The map sending every vector v \in V to its additiove inverse (negative)
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp; barV : V -&amp;gt; V :: v |--&amp;gt; -v
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp; This will send any basis vector to its negative (regardless of the bilinear
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp; form). So iff your basis is like the grBasis :=[Id, e1, e2, e1we2, e3,...]
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp; barW will send all elements eiw..wej to (-)^number of basis
&lt;br&gt;&amp;gt; elements eiw..wej
&lt;br&gt;&amp;gt; c) Iff the basis is more general (like in the case with an antisymmetric part in
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp; the bilinear form, you always fing a new basis (inhomgeous in the old
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp; generators) such that the involution does the trick for the new
&lt;br&gt;&amp;gt; basis elements.
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp; Eg: B:= matrix [[1,q],[-q ,1]] you would liek tto define a new
&lt;br&gt;&amp;gt; Grassmann basis
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;grBasWf = [Id, f1(=e1),f2(=e2), f1wf2 ( f1wf2-q*Id), f3 (=e3),...] etc
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;In this case you will see that the new basis is graded (only even or odd
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;elements appear) so the involution still works as expected.
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Whta you technically do is the following:
&lt;br&gt;&amp;gt; * Take a vector space V
&lt;br&gt;&amp;gt; * build the free algebra over it, that is the tensor algebra TV, its product is
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;concatenation it is noncommutative
&lt;br&gt;&amp;gt; * You are only intersted in antisymmetric tensors, hence factor out
&lt;br&gt;&amp;gt; all symmetric
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;ones. That is you identify all terms of the form
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;(v1 (x)... (x) vi (x) vi (x) ... (x) vd) = 0
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;[One can check that this is a graded ideal I_gr and one can therefor factor
&lt;br&gt;&amp;gt; &amp;nbsp; the tensor algebra TV/I_gr = /\V
&lt;br&gt;&amp;gt; &amp;nbsp; (for the generators this means you impose ei^2=0. From that you conclude that
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;0=(ei+ej)^(x)2 = ei^2+ei (x) ej + ej (x) ei + ej^2
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp; &amp;nbsp;= ei (x) ej + ej (x) ej
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;calling the projectet tensor /\ you get
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;ei /\ ej = - &amp;nbsp;ej /\ ei )
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Reversion:
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;This is quite different. The reversion needs to know about the Clifford
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;multiplication, so its actually defined in the Clifford basis
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;cliBas:= [Id, e(1), e(2), e(12):=e(1)*e(2), e(3),... ]
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;and it reverses the order of the Clifford multiplication (which depends on
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;the quadratic (bilinear) form. Hence you have (eij) Grassmann ,
&lt;br&gt;&amp;gt; e(ij) Clifford
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;basis elements)
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;reversion e12 = reversion (e(12)-B(e1,e2)*Id) = e(21)-B(e1,e2)*Id
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;= e2/\e1 +(B(e2,e1)-B(e1,e2))*Id
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;= -e12 - 2F(e1,e2)
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;where F(e1,e2) is the antisymmetric part of B, hence this difficulty will
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;_only_ appear when there is an antisymmetric part. Since not many people
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;have looked at that, its rarely described in literature, but see my
&lt;br&gt;&amp;gt; joint papers
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;with Rafal Ablamowicz:
&lt;br&gt;&amp;gt; #
&lt;br&gt;&amp;gt; Mathematics of CLIFFORD - A Maple package for Clifford and Grassmann algebras
&lt;br&gt;&amp;gt; Rafal Ablamowicz, B. Fauser: Adv. in Appl. Clifford Alg. 15 No. 2, 2005:157-181
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; #
&lt;br&gt;&amp;gt; arXiv:math-ph/0212032
&lt;br&gt;&amp;gt; Clifford and Grassmann Hopf algebras via the BIGEBRA package for Maple
&lt;br&gt;&amp;gt; Rafal Ablamowicz, B. Fauser: Comp. Physics Comm. 170, 2005:115--130
&lt;br&gt;&amp;gt; &amp;nbsp; available from the arXiv (or I can send you pdf's).
&lt;br&gt;&amp;gt; &amp;nbsp; 
&lt;br&gt;&amp;gt; Technically the reversion comes from the dualising the vector space V -&amp;gt; V*
&lt;br&gt;&amp;gt; and building the tensor algebra over the dualised vector space V* and
&lt;br&gt;&amp;gt; identifying
&lt;br&gt;&amp;gt; V* ~= V canonically. The project onto antisymmetric tensors. You see
&lt;br&gt;&amp;gt; that the symmetric group acts on tensors by permuting the 'list' ov
&lt;br&gt;&amp;gt; vectors a tensor is forms of. The reverison is the unique larget
&lt;br&gt;&amp;gt; permutation (usually called w)
&lt;br&gt;&amp;gt; with the most inversions (in reduced notation). So reversion is not
&lt;br&gt;&amp;gt; just adding a sign, its really reversing the list of all vectors
&lt;br&gt;&amp;gt; (generators) and then reorder them using the antisymmetry and collect
&lt;br&gt;&amp;gt; the minus signs.
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; conjugation is just the composition of recerion and grade involution:
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; conjugation x == reversion gradeinvolution x
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; (== gradeinvolution reversion x) -- oder does not matter
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; So first thing is to implement:
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Grassmann wedge
&lt;br&gt;&amp;gt; Grassmann meet (note that the meet is a sort of wedge but with the roles
&lt;br&gt;&amp;gt; &amp;nbsp; of the grades inverted)
&lt;br&gt;&amp;gt; Clifford product for a bilinear form (this is not hard, its the same routine
&lt;br&gt;&amp;gt; which calculates the Clifford product for a symmetric bilinear form or an
&lt;br&gt;&amp;gt; arbitrary bilinear form)
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; &amp;nbsp; 
&lt;br&gt;&amp;gt;&amp;gt; I expect I had better ignore the Spinors for now although I am curious about
&lt;br&gt;&amp;gt;&amp;gt; how they should be added on later.
&lt;br&gt;&amp;gt;&amp;gt; &amp;nbsp; &amp;nbsp; 
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Indeed, forget about them for now. I just added the spinor things to
&lt;br&gt;&amp;gt; make sure there are matrix analogs which show that the algebra
&lt;br&gt;&amp;gt; computes correctly. It is
&lt;br&gt;&amp;gt; just a way to convince yourself that everything works right. It was not meant
&lt;br&gt;&amp;gt; (yet) as a feature request. (Spinors come in handy when describing
&lt;br&gt;&amp;gt; linear complexes in projective space)
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; &amp;nbsp; 
&lt;br&gt;&amp;gt;&amp;gt; Upto now I have thought of spinors as an even subalgebra of Clifford
&lt;br&gt;&amp;gt;&amp;gt; algebras?
&lt;br&gt;&amp;gt;&amp;gt; &amp;nbsp; &amp;nbsp; 
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; There are many ways to look at spinors. Every way has its own benefit.
&lt;br&gt;&amp;gt; Indeed the weakest is to go for matrix representations and confuse
&lt;br&gt;&amp;gt; those with the abstract algebra. In the examples you see that all
&lt;br&gt;&amp;gt; three Clifford algebras Cl(2,0), CL(1,1)
&lt;br&gt;&amp;gt; and CL(0,2) finally can be modelled by 2x2 matrices, but how to
&lt;br&gt;&amp;gt; identify them if only the matrices are given?
&lt;br&gt;&amp;gt; &amp;nbsp; The spinors in the examples are (left) idela spinors, that is they
&lt;br&gt;&amp;gt; are elements of a minimal left ideal of the Clifford algebra and
&lt;br&gt;&amp;gt; therefore them self representable as Clifford numbers (as clearly can
&lt;br&gt;&amp;gt; be seen by inspecting the lists calld spinorSpace). If represented in
&lt;br&gt;&amp;gt; the (same) spinor basis, these elements make up a matrix with a single
&lt;br&gt;&amp;gt; non-zero column, forgetting about the zero columns gives what you see
&lt;br&gt;&amp;gt; usually (but it gets more complicated if the ring is no longer the
&lt;br&gt;&amp;gt; reals, even complex conjugation is then a differently presented
&lt;br&gt;&amp;gt; operation).
&lt;br&gt;&amp;gt; &amp;nbsp; Some of the matrix concepts are difficult to translate back into the
&lt;br&gt;&amp;gt; algebra, eg transposition if the bilinear form is not
&lt;br&gt;&amp;gt; diagonal/symmetric... this is a reseach
&lt;br&gt;&amp;gt; subject (and I hope there will be soon a paper comming out clarifying
&lt;br&gt;&amp;gt; this partly).
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; &amp;nbsp; 
&lt;br&gt;&amp;gt;&amp;gt; (rotation by 2*pi multiplies by -1) but
&lt;br&gt;&amp;gt;&amp;gt; this does not seem to be the case here? Would spinors require a new type of
&lt;br&gt;&amp;gt;&amp;gt; multiplication or a new domain?
&lt;br&gt;&amp;gt;&amp;gt; &amp;nbsp; &amp;nbsp; 
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; If a spinor is represented _inside_ of the Clifford algebra, no new
&lt;br&gt;&amp;gt; multiplications are needed. That's the nice feature of unifying these
&lt;br&gt;&amp;gt; things. Interpreting spinors as rotations can be done by constructing
&lt;br&gt;&amp;gt; so called operator spinors, well described eg in Perrti Lounesto's
&lt;br&gt;&amp;gt; boon Clifford algebras and spinors. Also this is not yet important.
&lt;br&gt;&amp;gt; (And will not need new algebra).
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; What you need to implement at the moment is:
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; a) A Grassmann basis (module over some (commutative) ring, field)
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;[Clifford has some undocumented features which allow a q-deformation here
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp; but I guess you should ignore that too]
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; b) the wedge and meet products, and some helper functions, like
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;extraction of the coefficient of the identiy, the volume elemenet etc
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;gradeinvolution, Grassmann reversion (that is the above reversion where
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;all terms comming from the bilinear form are absent), so this is
&lt;br&gt;&amp;gt; just the sign
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;factor (or better (-1)^{number of involutions of the permutatiosn which
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;reorders the rerm} this would allow to replace -1 by generic q).
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; a) and b) make up a GrassmannAlgebra (and with very little effort could be
&lt;br&gt;&amp;gt; turned into a Grassmann Hopf algebra by adding a wedge corproduct, and
&lt;br&gt;&amp;gt; an antipode)
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; c) The Clifford product, based on a correctly implemented
&lt;br&gt;&amp;gt; leftContraction and rightContraction. This is done easily by a
&lt;br&gt;&amp;gt; recursion, as I tried to explain in a previous mail.
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; With x,y in V u,v,w in W=/\V you have
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; i) x * y = &amp;nbsp;lc(x,y) + x/\y &amp;nbsp;and 1*1=1
&lt;br&gt;&amp;gt; ii) x * (u /\ v) = x /\ u /\ v + lc(x, u/\v)
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;= x/\u/\v + lc(x,u)/\v + gradeinvolution(u) /\ lc(x, v)
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;(same for (u/\v) * y using right contraction)
&lt;br&gt;&amp;gt; iii) Since every term u can be recursively be decomposed as a Clifford product
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;you can finally evaluate u * v by
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;u = w*x &amp;nbsp;(where the grade of w is strictly less than that of u
&lt;br&gt;&amp;gt; &amp;nbsp; &amp;nbsp;u * v = (w*x)*v = w*(x*v) &amp;nbsp;and use the above recursion with 1*1=1
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; I am sorry to have to less time currently to sit down and just provide the code,
&lt;br&gt;&amp;gt; I have some other things on my table which are urgent.
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Hope this helps, otherwise feel free to ask.
&lt;br&gt;&amp;gt; Ciao
&lt;br&gt;&amp;gt; BF.
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; &amp;nbsp; 
&lt;/div&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
&lt;br&gt;Axiom-developer mailing list
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</entry>

<entry>
	<id>tag:old.nabble.com,2006:post-26533437</id>
	<title>Re: Clifford Algebra examples:</title>
	<published>2009-11-26T10:29:16Z</published>
	<updated>2009-11-26T10:29:16Z</updated>
	<author>
		<name>Bertfried Fauser-2</name>
	</author>
	<content type="html">Dear Martin,
&lt;br&gt;&lt;br&gt;&amp;gt; Can I ask about the definitions of the involutions:
&lt;br&gt;Yes, please ask, I'll answer if I know and time permits.
&lt;br&gt;&lt;br&gt;&amp;gt; gradeInvolution == reversion? sign=(-1)^(d(d-1)/2) symbol= ~
&lt;br&gt;&amp;gt; Cliplus clirev == ? symbol=multiply by pseudoscalar? symbol=
&lt;br&gt;&amp;gt; Clifford conjugation: scalar part minus non-scalar part? symbol=
&lt;br&gt;&lt;br&gt;The involutions you give are again assuming a diagonal (orthonormal)
&lt;br&gt;basis for the quadratic (bilinear) form. Since this is bad for applications,
&lt;br&gt;it has to be avoided. Of course if you know you are in a diagonal basis
&lt;br&gt;you can use faster algorithms (like defining a cmulDiag)
&lt;br&gt;&lt;br&gt;Grade involution:
&lt;br&gt;Any (Grassmann-) Clifford algebra is built up from a base space V (of dimension
&lt;br&gt;dim V = n) You have two natural transformations on V which generalize
&lt;br&gt;to the whole space W=/\V of dim W = 2^n.
&lt;br&gt;a) The identity map (does nothing on W)
&lt;br&gt;b) The map sending every vector v \in V to its additiove inverse (negative)
&lt;br&gt;&amp;nbsp; &amp;nbsp; barV : V -&amp;gt; V :: v |--&amp;gt; -v
&lt;br&gt;&amp;nbsp; &amp;nbsp; This will send any basis vector to its negative (regardless of the bilinear
&lt;br&gt;&amp;nbsp; &amp;nbsp; form). So iff your basis is like the grBasis :=[Id, e1, e2, e1we2, e3,...]
&lt;br&gt;&amp;nbsp; &amp;nbsp; barW will send all elements eiw..wej to (-)^number of basis
&lt;br&gt;elements eiw..wej
&lt;br&gt;c) Iff the basis is more general (like in the case with an antisymmetric part in
&lt;br&gt;&amp;nbsp; &amp;nbsp; the bilinear form, you always fing a new basis (inhomgeous in the old
&lt;br&gt;&amp;nbsp; &amp;nbsp; generators) such that the involution does the trick for the new
&lt;br&gt;basis elements.
&lt;br&gt;&amp;nbsp; &amp;nbsp; Eg: B:= matrix [[1,q],[-q ,1]] you would liek tto define a new
&lt;br&gt;Grassmann basis
&lt;br&gt;&amp;nbsp; &amp;nbsp;grBasWf = [Id, f1(=e1),f2(=e2), f1wf2 ( f1wf2-q*Id), f3 (=e3),...] etc
&lt;br&gt;&amp;nbsp; &amp;nbsp;In this case you will see that the new basis is graded (only even or odd
&lt;br&gt;&amp;nbsp; &amp;nbsp;elements appear) so the involution still works as expected.
&lt;br&gt;&lt;br&gt;Whta you technically do is the following:
&lt;br&gt;* Take a vector space V
&lt;br&gt;* build the free algebra over it, that is the tensor algebra TV, its product is
&lt;br&gt;&amp;nbsp; &amp;nbsp;concatenation it is noncommutative
&lt;br&gt;* You are only intersted in antisymmetric tensors, hence factor out
&lt;br&gt;all symmetric
&lt;br&gt;&amp;nbsp; &amp;nbsp;ones. That is you identify all terms of the form
&lt;br&gt;&amp;nbsp; &amp;nbsp;(v1 (x)... (x) vi (x) vi (x) ... (x) vd) = 0
&lt;br&gt;&amp;nbsp; &amp;nbsp;[One can check that this is a graded ideal I_gr and one can therefor factor
&lt;br&gt;&amp;nbsp; the tensor algebra TV/I_gr = /\V
&lt;br&gt;&amp;nbsp; (for the generators this means you impose ei^2=0. From that you conclude that
&lt;br&gt;&amp;nbsp; &amp;nbsp;0=(ei+ej)^(x)2 = ei^2+ei (x) ej + ej (x) ei + ej^2
&lt;br&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp;= ei (x) ej + ej (x) ej
&lt;br&gt;&amp;nbsp; &amp;nbsp;calling the projectet tensor /\ you get
&lt;br&gt;&amp;nbsp; &amp;nbsp;ei /\ ej = - &amp;nbsp;ej /\ ei )
&lt;br&gt;&lt;br&gt;Reversion:
&lt;br&gt;&amp;nbsp; &amp;nbsp;This is quite different. The reversion needs to know about the Clifford
&lt;br&gt;&amp;nbsp; &amp;nbsp;multiplication, so its actually defined in the Clifford basis
&lt;br&gt;&amp;nbsp; &amp;nbsp;cliBas:= [Id, e(1), e(2), e(12):=e(1)*e(2), e(3),... ]
&lt;br&gt;&amp;nbsp; &amp;nbsp;and it reverses the order of the Clifford multiplication (which depends on
&lt;br&gt;&amp;nbsp; &amp;nbsp;the quadratic (bilinear) form. Hence you have (eij) Grassmann ,
&lt;br&gt;e(ij) Clifford
&lt;br&gt;&amp;nbsp; &amp;nbsp;basis elements)
&lt;br&gt;&amp;nbsp; &amp;nbsp;reversion e12 = reversion (e(12)-B(e1,e2)*Id) = e(21)-B(e1,e2)*Id
&lt;br&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;= e2/\e1 +(B(e2,e1)-B(e1,e2))*Id
&lt;br&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;= -e12 - 2F(e1,e2)
&lt;br&gt;&amp;nbsp; &amp;nbsp;where F(e1,e2) is the antisymmetric part of B, hence this difficulty will
&lt;br&gt;&amp;nbsp; &amp;nbsp;_only_ appear when there is an antisymmetric part. Since not many people
&lt;br&gt;&amp;nbsp; &amp;nbsp;have looked at that, its rarely described in literature, but see my
&lt;br&gt;joint papers
&lt;br&gt;&amp;nbsp; &amp;nbsp;with Rafal Ablamowicz:
&lt;br&gt;#
&lt;br&gt;Mathematics of CLIFFORD - A Maple package for Clifford and Grassmann algebras
&lt;br&gt;Rafal Ablamowicz, B. Fauser: Adv. in Appl. Clifford Alg. 15 No. 2, 2005:157-181
&lt;br&gt;&lt;br&gt;#
&lt;br&gt;arXiv:math-ph/0212032
&lt;br&gt;Clifford and Grassmann Hopf algebras via the BIGEBRA package for Maple
&lt;br&gt;Rafal Ablamowicz, B. Fauser: Comp. Physics Comm. 170, 2005:115--130
&lt;br&gt;&amp;nbsp; available from the arXiv (or I can send you pdf's).
&lt;br&gt;&lt;br&gt;Technically the reversion comes from the dualising the vector space V -&amp;gt; V*
&lt;br&gt;and building the tensor algebra over the dualised vector space V* and
&lt;br&gt;identifying
&lt;br&gt;V* ~= V canonically. The project onto antisymmetric tensors. You see
&lt;br&gt;that the symmetric group acts on tensors by permuting the 'list' ov
&lt;br&gt;vectors a tensor is forms of. The reverison is the unique larget
&lt;br&gt;permutation (usually called w)
&lt;br&gt;with the most inversions (in reduced notation). So reversion is not
&lt;br&gt;just adding a sign, its really reversing the list of all vectors
&lt;br&gt;(generators) and then reorder them using the antisymmetry and collect
&lt;br&gt;the minus signs.
&lt;br&gt;&lt;br&gt;conjugation is just the composition of recerion and grade involution:
&lt;br&gt;&lt;br&gt;conjugation x == reversion gradeinvolution x
&lt;br&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; (== gradeinvolution reversion x) -- oder does not matter
&lt;br&gt;&lt;br&gt;So first thing is to implement:
&lt;br&gt;&lt;br&gt;Grassmann wedge
&lt;br&gt;Grassmann meet (note that the meet is a sort of wedge but with the roles
&lt;br&gt;&amp;nbsp; of the grades inverted)
&lt;br&gt;Clifford product for a bilinear form (this is not hard, its the same routine
&lt;br&gt;which calculates the Clifford product for a symmetric bilinear form or an
&lt;br&gt;arbitrary bilinear form)
&lt;br&gt;&lt;br&gt;&amp;gt; I expect I had better ignore the Spinors for now although I am curious about
&lt;br&gt;&amp;gt; how they should be added on later.
&lt;br&gt;&lt;br&gt;Indeed, forget about them for now. I just added the spinor things to
&lt;br&gt;make sure there are matrix analogs which show that the algebra
&lt;br&gt;computes correctly. It is
&lt;br&gt;just a way to convince yourself that everything works right. It was not meant
&lt;br&gt;(yet) as a feature request. (Spinors come in handy when describing
&lt;br&gt;linear complexes in projective space)
&lt;br&gt;&lt;br&gt;&amp;gt; Upto now I have thought of spinors as an even subalgebra of Clifford
&lt;br&gt;&amp;gt; algebras?
&lt;br&gt;&lt;br&gt;There are many ways to look at spinors. Every way has its own benefit.
&lt;br&gt;Indeed the weakest is to go for matrix representations and confuse
&lt;br&gt;those with the abstract algebra. In the examples you see that all
&lt;br&gt;three Clifford algebras Cl(2,0), CL(1,1)
&lt;br&gt;and CL(0,2) finally can be modelled by 2x2 matrices, but how to
&lt;br&gt;identify them if only the matrices are given?
&lt;br&gt;&amp;nbsp; The spinors in the examples are (left) idela spinors, that is they
&lt;br&gt;are elements of a minimal left ideal of the Clifford algebra and
&lt;br&gt;therefore them self representable as Clifford numbers (as clearly can
&lt;br&gt;be seen by inspecting the lists calld spinorSpace). If represented in
&lt;br&gt;the (same) spinor basis, these elements make up a matrix with a single
&lt;br&gt;non-zero column, forgetting about the zero columns gives what you see
&lt;br&gt;usually (but it gets more complicated if the ring is no longer the
&lt;br&gt;reals, even complex conjugation is then a differently presented
&lt;br&gt;operation).
&lt;br&gt;&amp;nbsp; Some of the matrix concepts are difficult to translate back into the
&lt;br&gt;algebra, eg transposition if the bilinear form is not
&lt;br&gt;diagonal/symmetric... this is a reseach
&lt;br&gt;subject (and I hope there will be soon a paper comming out clarifying
&lt;br&gt;this partly).
&lt;br&gt;&lt;br&gt;&amp;gt; (rotation by 2*pi multiplies by -1) but
&lt;br&gt;&amp;gt; this does not seem to be the case here? Would spinors require a new type of
&lt;br&gt;&amp;gt; multiplication or a new domain?
&lt;br&gt;&lt;br&gt;If a spinor is represented _inside_ of the Clifford algebra, no new
&lt;br&gt;multiplications are needed. That's the nice feature of unifying these
&lt;br&gt;things. Interpreting spinors as rotations can be done by constructing
&lt;br&gt;so called operator spinors, well described eg in Perrti Lounesto's
&lt;br&gt;boon Clifford algebras and spinors. Also this is not yet important.
&lt;br&gt;(And will not need new algebra).
&lt;br&gt;&lt;br&gt;What you need to implement at the moment is:
&lt;br&gt;&lt;br&gt;a) A Grassmann basis (module over some (commutative) ring, field)
&lt;br&gt;&amp;nbsp; &amp;nbsp;[Clifford has some undocumented features which allow a q-deformation here
&lt;br&gt;&amp;nbsp; &amp;nbsp; but I guess you should ignore that too]
&lt;br&gt;&lt;br&gt;b) the wedge and meet products, and some helper functions, like
&lt;br&gt;&amp;nbsp; &amp;nbsp;extraction of the coefficient of the identiy, the volume elemenet etc
&lt;br&gt;&amp;nbsp; &amp;nbsp;gradeinvolution, Grassmann reversion (that is the above reversion where
&lt;br&gt;&amp;nbsp; &amp;nbsp;all terms comming from the bilinear form are absent), so this is
&lt;br&gt;just the sign
&lt;br&gt;&amp;nbsp; &amp;nbsp;factor (or better (-1)^{number of involutions of the permutatiosn which
&lt;br&gt;&amp;nbsp; &amp;nbsp;reorders the rerm} this would allow to replace -1 by generic q).
&lt;br&gt;&lt;br&gt;a) and b) make up a GrassmannAlgebra (and with very little effort could be
&lt;br&gt;turned into a Grassmann Hopf algebra by adding a wedge corproduct, and
&lt;br&gt;an antipode)
&lt;br&gt;&lt;br&gt;c) The Clifford product, based on a correctly implemented
&lt;br&gt;leftContraction and rightContraction. This is done easily by a
&lt;br&gt;recursion, as I tried to explain in a previous mail.
&lt;br&gt;&lt;br&gt;With x,y in V u,v,w in W=/\V you have
&lt;br&gt;&lt;br&gt;i) x * y = &amp;nbsp;lc(x,y) + x/\y &amp;nbsp;and 1*1=1
&lt;br&gt;ii) x * (u /\ v) = x /\ u /\ v + lc(x, u/\v)
&lt;br&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;= x/\u/\v + lc(x,u)/\v + gradeinvolution(u) /\ lc(x, v)
&lt;br&gt;&amp;nbsp; &amp;nbsp;(same for (u/\v) * y using right contraction)
&lt;br&gt;iii) Since every term u can be recursively be decomposed as a Clifford product
&lt;br&gt;&amp;nbsp; &amp;nbsp;you can finally evaluate u * v by
&lt;br&gt;&amp;nbsp; &amp;nbsp;u = w*x &amp;nbsp;(where the grade of w is strictly less than that of u
&lt;br&gt;&amp;nbsp; &amp;nbsp;u * v = (w*x)*v = w*(x*v) &amp;nbsp;and use the above recursion with 1*1=1
&lt;br&gt;&lt;br&gt;I am sorry to have to less time currently to sit down and just provide the code,
&lt;br&gt;I have some other things on my table which are urgent.
&lt;br&gt;&lt;br&gt;Hope this helps, otherwise feel free to ask.
&lt;br&gt;Ciao
&lt;br&gt;BF.
&lt;br&gt;&lt;br&gt;-- 
&lt;br&gt;% PD Dr Bertfried Fauser
&lt;br&gt;% &amp;nbsp; &amp;nbsp; &amp;nbsp; Research Fellow, School of Computer Science, Univ. of Birmingham
&lt;br&gt;% &amp;nbsp; &amp;nbsp; &amp;nbsp; Honorary Associate, University of Tasmania
&lt;br&gt;% &amp;nbsp; &amp;nbsp; &amp;nbsp; Privat Docent: University of Konstanz, Physics Dept
&lt;br&gt;&amp;lt;&lt;a href=&quot;http://www.uni-konstanz.de&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://www.uni-konstanz.de&lt;/a&gt;&amp;gt;
&lt;br&gt;% contact |-&amp;gt; &amp;nbsp; &amp;nbsp;URL : &lt;a href=&quot;http://www.cs.bham.ac.uk/~fauserb/&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://www.cs.bham.ac.uk/~fauserb/&lt;/a&gt;&lt;br&gt;% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;Phone : &amp;nbsp;+44-121-41-42795 and +49 1520 9874517
&lt;br&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
&lt;br&gt;Axiom-developer mailing list
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</entry>

<entry>
	<id>tag:old.nabble.com,2006:post-26532872</id>
	<title>Re: Clifford Algebra examples:</title>
	<published>2009-11-26T09:11:17Z</published>
	<updated>2009-11-26T09:11:17Z</updated>
	<author>
		<name>Martin Baker-3</name>
	</author>
	<content type="html">Bertfried,
&lt;br&gt;&lt;br&gt;Thanks this looks very useful.
&lt;br&gt;&lt;br&gt;Can I ask about the definitions of the involutions:
&lt;br&gt;&lt;br&gt;gradeInvolution == reversion? sign=(-1)^(d(d-1)/2) symbol= ~
&lt;br&gt;Cliplus clirev == ? symbol=multiply by pseudoscalar? symbol=
&lt;br&gt;Clifford conjugation: scalar part minus non-scalar part? symbol=
&lt;br&gt;&lt;br&gt;I know these are wrong but I just made a guess!
&lt;br&gt;&lt;br&gt;I expect I had better ignore the Spinors for now although I am curious about 
&lt;br&gt;how they should be added on later. Upto now I have thought of spinors as an 
&lt;br&gt;even subalgebra of Clifford algebras? (rotation by 2*pi multiplies by -1) but 
&lt;br&gt;this does not seem to be the case here? Would spinors require a new type of 
&lt;br&gt;multiplication or a new domain?
&lt;br&gt;&lt;br&gt;Martin
&lt;br&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
&lt;br&gt;Axiom-developer mailing list
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&lt;br&gt;&lt;a href=&quot;http://lists.nongnu.org/mailman/listinfo/axiom-developer&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://lists.nongnu.org/mailman/listinfo/axiom-developer&lt;/a&gt;&lt;br&gt;&lt;p&gt;From forum: &lt;a href=&quot;http://old.nabble.com/axiom-developer-f6886.html&quot; embed=&quot;fixTarget[6886]&quot; target=&quot;_top&quot; &gt;axiom-developer&lt;/a&gt;&lt;/p&gt;</content>
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</entry>

<entry>
	<id>tag:old.nabble.com,2006:post-26524656</id>
	<title>large PDFs</title>
	<published>2009-11-25T21:49:31Z</published>
	<updated>2009-11-25T21:49:31Z</updated>
	<author>
		<name>Tim Daly-3</name>
	</author>
	<content type="html">You might be pleasantly surprised that the Axiom PDFs
&lt;br&gt;actually are heavily cross-referenced. If you have a
&lt;br&gt;recent version of any pdf viewer you'll see that there
&lt;br&gt;are hyperlinks in the pdf. The index is also hyperlinked
&lt;br&gt;so you can look things up in the index and jump to the
&lt;br&gt;most interesting point.
&lt;br&gt;&lt;br&gt;The algebra PDFs (volume 10.2, 10.3, and 10.4) are all
&lt;br&gt;hyperlinked. This makes it easy to find algebra. In
&lt;br&gt;addition, the two algebra graphs on the webpage are
&lt;br&gt;hyperlinked into the correct pdfs so you can walk the
&lt;br&gt;algebra graph and see the corresponding code.
&lt;br&gt;&lt;br&gt;The Interpreter (volume 5) even includes both forward
&lt;br&gt;(calls) and backward hyperlinks (called by) so you can
&lt;br&gt;find callers and callees making it very easy to walk
&lt;br&gt;the lisp code. The compiler (volume 9) will be the same.
&lt;br&gt;&lt;br&gt;The hypertex pages (volume 7.1) has pictures of the pages
&lt;br&gt;that the code describes so you can &amp;quot;hyperdoc browse&amp;quot; in
&lt;br&gt;the pdf viewer.
&lt;br&gt;&lt;br&gt;Eventually all of the volumes will be fully hyperlinked.
&lt;br&gt;The Jenks book (volume 0) and the tutorial (volume 1) are
&lt;br&gt;&amp;quot;in the queue&amp;quot;.
&lt;br&gt;&lt;br&gt;Yes, the PDFs are large but they are easy to navigate.
&lt;br&gt;&lt;br&gt;Tim
&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
&lt;br&gt;Axiom-developer mailing list
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<entry>
	<id>tag:old.nabble.com,2006:post-26511569</id>
	<title>Spad for OO Programmers</title>
	<published>2009-11-25T03:54:37Z</published>
	<updated>2009-11-25T03:54:37Z</updated>
	<author>
		<name>Martin Baker-3</name>
	</author>
	<content type="html">I am still trying to properly understand the Spad language properly, what I 
&lt;br&gt;would like is a introduction for people who have object oriented experience. 
&lt;br&gt;In other words to point out the differences that may confuse and also a crib 
&lt;br&gt;sheet for the syntax.
&lt;br&gt;&lt;br&gt;I have not yet found such a document (by the way, the link to st-andrews 
&lt;br&gt;website on Axiom documentation page is broken).
&lt;br&gt;&lt;br&gt;Since I have not found this I have been making some notes for my own benefit:
&lt;br&gt;&lt;a href=&quot;http://www.euclideanspace.com/maths/standards/program/spad/&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://www.euclideanspace.com/maths/standards/program/spad/&lt;/a&gt;&lt;br&gt;Any corrections welcome.
&lt;br&gt;&lt;br&gt;Martin Baker
&lt;br&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
&lt;br&gt;Axiom-developer mailing list
&lt;br&gt;&lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26511569&amp;i=0&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;Axiom-developer@...&lt;/a&gt;
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<entry>
	<id>tag:old.nabble.com,2006:post-26507849</id>
	<title>Axiom release for November 2009</title>
	<published>2009-11-24T21:43:22Z</published>
	<updated>2009-11-24T21:43:22Z</updated>
	<author>
		<name>Tim Daly-3</name>
	</author>
	<content type="html">Summary: November 2009 release
&lt;br&gt;&lt;br&gt;The major changes are:
&lt;br&gt;&amp;nbsp; &amp;nbsp;A new )describe command, boot language removal, and more motion
&lt;br&gt;&amp;nbsp; &amp;nbsp;toward a fully literate system.
&lt;br&gt;&lt;br&gt;The )describe command was added.
&lt;br&gt;&lt;br&gt;&amp;nbsp; &amp;nbsp;The )describe function was added to Volume 5 (Interpreter)
&lt;br&gt;&amp;nbsp; &amp;nbsp;The )describe function was documented in Volume 2 (Users Guide)
&lt;br&gt;&amp;nbsp; &amp;nbsp;The Description field for the Categories, Domains, and Packages
&lt;br&gt;&amp;nbsp; &amp;nbsp;were cleanup up and reformatted in Volumes 10.2 (Categories)
&lt;br&gt;&amp;nbsp; &amp;nbsp;10.3 (Domains) and 10.4 (Packages)
&lt;br&gt;&amp;nbsp;
&lt;br&gt;&lt;br&gt;Boot Language removal
&lt;br&gt;&lt;br&gt;&amp;nbsp; &amp;nbsp; All of the boot-converted lisp files were reformatted from their
&lt;br&gt;&amp;nbsp; &amp;nbsp; compiler generated output. These files are being merged into
&lt;br&gt;&amp;nbsp; &amp;nbsp; Volume 5 (Interpreter) and Volume 9 (Compiler) as appropriate.
&lt;br&gt;&amp;nbsp; &amp;nbsp; This work will continue for the next few releases.
&lt;br&gt;&lt;br&gt;&amp;nbsp; &amp;nbsp; All or portions of the following files were merged into
&lt;br&gt;&amp;nbsp; &amp;nbsp; Volume 5 (Interpreter):
&lt;br&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; astr, cstream.lisp, dq, incl, int-top, i-syscmd, msg, nci,
&lt;br&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; obey, osyscmd, parini, patches, pile, scan
&lt;br&gt;&lt;br&gt;&amp;nbsp; &amp;nbsp; The src/boot subdirectory is gone, including the files:
&lt;br&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; Makefile, boot-proclaims, boothdr, bootload, btincl2, btpile2,
&lt;br&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; btscan2, ccl-bootsys, ccl-depsys.lsp, exports.lisp, npextras, ptyout,
&lt;br&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; tyextra, typars, typrops, tytree1, sys-pkg, vmlisp, ptrees, wi2
&lt;br&gt;&lt;br&gt;&amp;nbsp; &amp;nbsp; The bootsys image is no longer part of the build process
&lt;br&gt;&lt;br&gt;&lt;br&gt;Patch ports from Fricas and Open-Axiom
&lt;br&gt;&lt;br&gt;&amp;nbsp; &amp;nbsp; The Tuples patch was picked up and applied.
&lt;br&gt;&lt;br&gt;&amp;nbsp; &amp;nbsp; The SXHASH function is the hash default in SetCategory
&lt;br&gt;&lt;br&gt;&amp;nbsp; &amp;nbsp; The function ListOfTerms was renamed to listOfTerms
&lt;br&gt;&lt;br&gt;&lt;br&gt;Input file changes
&lt;br&gt;&lt;br&gt;&amp;nbsp; &amp;nbsp; New input files have been added to show how to compute
&lt;br&gt;&amp;nbsp; &amp;nbsp; results using Axiom or to create regression tests for fixes:
&lt;br&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; complexfactor, rubey, zimmbron, branchcut, cachedf, finitegraph,
&lt;br&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; newtonlisp, nonlinhomodiffeq, distexpr, numericgamma, donsimple
&lt;br&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; solveperf, tuplebug, unit-macro, testprob, unittest2
&lt;br&gt;&lt;br&gt;&amp;nbsp; &amp;nbsp; lexp was removed and moved to the LEXP algebra file
&lt;br&gt;&lt;br&gt;&amp;nbsp; &amp;nbsp; dop and gstbl had minor fixes
&lt;br&gt;&lt;br&gt;New Help files and Function examples were added
&lt;br&gt;&lt;br&gt;&amp;nbsp; &amp;nbsp; There are new help files:
&lt;br&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; describe, AlgebraicallyClosedField, RationalFunctionSum,
&lt;br&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; RadicalSolvePackage, PartialFractionPackage, Product,
&lt;br&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; OrderedFreeMonoid
&lt;br&gt;&lt;br&gt;Website update:
&lt;br&gt;&lt;br&gt;&amp;nbsp; The developer.html page was rewritten. An old Scratchpad group
&lt;br&gt;&amp;nbsp; photo was added to the site.
&lt;br&gt;&lt;br&gt;&amp;nbsp; Work continues on re-hosting the axiom-developer.org domain.
&lt;br&gt;&lt;br&gt;&amp;nbsp; We now own axiom-developer.com and axiom-developer.net which will
&lt;br&gt;&amp;nbsp; be retargetted to the new host as soon as it is available
&lt;br&gt;&lt;br&gt;Interpreter changes:
&lt;br&gt;&lt;br&gt;&amp;nbsp; &amp;nbsp; Axiom will sit in a single package in the near future.
&lt;br&gt;&amp;nbsp; &amp;nbsp; The VMLISP package was partially removed from the system.
&lt;br&gt;&amp;nbsp; &amp;nbsp; Work continues on this path.
&lt;br&gt;&lt;br&gt;&amp;nbsp; &amp;nbsp; The util.ht file is created earlier in the parallel build
&lt;br&gt;&amp;nbsp; &amp;nbsp; so there are fewer compiler messages about documentation.
&lt;br&gt;&lt;br&gt;Research:
&lt;br&gt;&amp;nbsp;
&lt;br&gt;&amp;nbsp; &amp;nbsp; A Cohen algebra domain is being developed to enable symbolic
&lt;br&gt;&amp;nbsp; &amp;nbsp; manipulation of expressions with explanations and controlled
&lt;br&gt;&amp;nbsp; &amp;nbsp; simplification.
&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
&lt;br&gt;Axiom-developer mailing list
&lt;br&gt;&lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26507849&amp;i=0&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;Axiom-developer@...&lt;/a&gt;
&lt;br&gt;&lt;a href=&quot;http://lists.nongnu.org/mailman/listinfo/axiom-developer&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://lists.nongnu.org/mailman/listinfo/axiom-developer&lt;/a&gt;&lt;br&gt;&lt;p&gt;From forum: &lt;a href=&quot;http://old.nabble.com/axiom-developer-f6886.html&quot; embed=&quot;fixTarget[6886]&quot; target=&quot;_top&quot; &gt;axiom-developer&lt;/a&gt;&lt;/p&gt;</content>
	<link rel="alternate" type="text/html" href="http://old.nabble.com/Axiom-release-for-November-2009-tp26507849p26507849.html" />
</entry>

<entry>
	<id>tag:old.nabble.com,2006:post-26507740</id>
	<title>A new command &quot;)describe&quot;</title>
	<published>2009-11-24T21:27:33Z</published>
	<updated>2009-11-24T21:27:33Z</updated>
	<author>
		<name>Tim Daly-3</name>
	</author>
	<content type="html">There is a new command
&lt;br&gt;&lt;br&gt;&amp;nbsp; )describe [category | domain | package ] &amp;lt;name&amp;gt; [ | internal ]
&lt;br&gt;&lt;br&gt;You can ask for the comments from the algebra source code
&lt;br&gt;which are contained in the Description: section at the top
&lt;br&gt;of each Category, Domain, or Package.
&lt;br&gt;&lt;br&gt;You can type
&lt;br&gt;&amp;nbsp;
&lt;br&gt;&amp;nbsp; )help describe for the man page
&lt;br&gt;&lt;br&gt;Details for writing the Description: section for new algebra code
&lt;br&gt;are in Volume 2 (User Guide)
&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;For example,
&lt;br&gt;&lt;br&gt;&lt;br&gt;(1) -&amp;gt; )describe domain AlgebraGivenByStructuralConstants
&lt;br&gt;&lt;br&gt;&amp;nbsp;
&lt;br&gt;AlgebraGivenByStructuralConstants implements finite rank algebras
&lt;br&gt;over a commutative ring, given by the structural constants gamma with
&lt;br&gt;respect to a fixed basis [a1,..,an], where gamma is an n-vector of n
&lt;br&gt;by n matrices [(gammaijk) for k in 1..rank()] defined by ai * aj =
&lt;br&gt;gammaij1 * a1 + ... + gammaijn * an. The symbols for the fixed basis
&lt;br&gt;have to be given as a list of symbols.
&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;You can also ask for a very detailed description of the internal
&lt;br&gt;structure (only for Domains and Packages). For instance:
&lt;br&gt;&lt;br&gt;&lt;br&gt;(1) -&amp;gt; )describe domain AlgebraGivenByStructuralConstants internal
&lt;br&gt;----------------Template-----------------
&lt;br&gt;&amp;nbsp;5 lazy DirectProduct(local #2,local #1)
&lt;br&gt;&amp;nbsp;6 lazy local #1
&lt;br&gt;&amp;nbsp;7 lazy local #2
&lt;br&gt;&amp;nbsp;8 lazy local #3
&lt;br&gt;&amp;nbsp;9 lazy local #4
&lt;br&gt;&amp;nbsp;10 lazy QUOTE Rep
&lt;br&gt;&amp;nbsp;11 lazy Union($,QUOTE failed)
&lt;br&gt;&amp;nbsp;12 lazy FiniteRankNonAssociativeAlgebra&amp;($$,local #1)
&lt;br&gt;&amp;nbsp;13 latch recip : % -&amp;gt; Union(%,QUOTE failed) from 
&lt;br&gt;FiniteRankNonAssociativeAlgebra&amp;($$,local #1)
&lt;br&gt;&amp;nbsp;14 fun &amp;nbsp;ALGSC;recip;$U;1
&lt;br&gt;&amp;nbsp;15 lazy Matrix local #1
&lt;br&gt;&amp;nbsp;16 lazy SquareMatrix(local #2,local #1)
&lt;br&gt;&amp;nbsp;17 latch coerce : % -&amp;gt; Matrix local #1 from SquareMatrix(local #2,local #1)
&lt;br&gt;&amp;nbsp;18 latch apply : (Matrix local #1,%) -&amp;gt; % from %
&lt;br&gt;&amp;nbsp;19 fun &amp;nbsp;ALGSC;*;Sm2$;2
&lt;br&gt;&amp;nbsp;20 lazy Vector local #1
&lt;br&gt;&amp;nbsp;21 latch directProduct : Vector local #1 -&amp;gt; % from QUOTE Rep
&lt;br&gt;&amp;nbsp;22 fun &amp;nbsp;ALGSC;coerce;V$;3
&lt;br&gt;&amp;nbsp;23 lazy Vector Matrix local #1
&lt;br&gt;&amp;nbsp;24 fun &amp;nbsp;ALGSC;structuralConstants;V;4
&lt;br&gt;&amp;nbsp;25 lazy List local #1
&lt;br&gt;&amp;nbsp;26 latch entries : % -&amp;gt; List local #1 from QUOTE Rep
&lt;br&gt;&amp;nbsp;27 latch vector : List local #1 -&amp;gt; % from Vector local #1
&lt;br&gt;&amp;nbsp;28 fun &amp;nbsp;ALGSC;coordinates;$V;5
&lt;br&gt;&amp;nbsp;29 lazy Integer
&lt;br&gt;&amp;nbsp;30 lazy Vector $$
&lt;br&gt;&amp;nbsp;31 latch maxIndex : % -&amp;gt; Integer from Vector $$
&lt;br&gt;&amp;nbsp;32 latch 0 : () -&amp;gt; % from local #1
&lt;br&gt;&amp;nbsp;33 lazy NonNegativeInteger
&lt;br&gt;&amp;nbsp;34 latch new : (NonNegativeInteger,NonNegativeInteger,local #1) -&amp;gt; % 
&lt;br&gt;from Matrix local #1
&lt;br&gt;&amp;nbsp;35 latch elt : (%,Integer) -&amp;gt; $$ from Vector $$
&lt;br&gt;&amp;nbsp;36 latch setColumn! : (%,Integer,Vector local #1) -&amp;gt; % from Matrix local #1
&lt;br&gt;&amp;nbsp;37 lazy Union(Vector local #1,QUOTE failed)
&lt;br&gt;&amp;nbsp;38 lazy Record(particular: Union(Vector local #1,QUOTE failed),basis: 
&lt;br&gt;List Vector local #1)
&lt;br&gt;&amp;nbsp;39 lazy LinearSystemMatrixPackage(local #1,Vector local #1,Vector local 
&lt;br&gt;#1,Matrix local #1)
&lt;br&gt;&amp;nbsp;40 latch solve : (Matrix local #1,Vector local #1) -&amp;gt; 
&lt;br&gt;Record(particular: Union(Vector local #1,QUOTE failed),basis: List 
&lt;br&gt;Vector local #1) from LinearSystemMatrixPackage(local #1,Vector local 
&lt;br&gt;#1,Vector local #1,Matrix local #1)
&lt;br&gt;&amp;nbsp;41 lazy Boolean
&lt;br&gt;&amp;nbsp;42 latch zero? : % -&amp;gt; Boolean from local #1
&lt;br&gt;&amp;nbsp;43 lazy Vector $
&lt;br&gt;&amp;nbsp;44 fun &amp;nbsp;ALGSC;basis;V;7
&lt;br&gt;&amp;nbsp;45 lazy (local #1 -&amp;gt; Boolean)
&lt;br&gt;&amp;nbsp;46 latch every? : ((local #1 -&amp;gt; Boolean),%) -&amp;gt; Boolean from Vector local #1
&lt;br&gt;&amp;nbsp;47 fun &amp;nbsp;ALGSC;coordinates;$VV;6
&lt;br&gt;&amp;nbsp;48 lazy PositiveInteger
&lt;br&gt;&amp;nbsp;49 latch unitVector : PositiveInteger -&amp;gt; % from QUOTE Rep
&lt;br&gt;&amp;nbsp;50 fun &amp;nbsp;ALGSC;someBasis;V;8
&lt;br&gt;&amp;nbsp;51 fun &amp;nbsp;ALGSC;rank;Pi;9
&lt;br&gt;&amp;nbsp;52 latch elt : (%,Integer) -&amp;gt; local #1 from QUOTE Rep
&lt;br&gt;&amp;nbsp;53 fun &amp;nbsp;ALGSC;elt;$IR;10
&lt;br&gt;&amp;nbsp;54 latch zero? : % -&amp;gt; Boolean from QUOTE Rep
&lt;br&gt;&amp;nbsp;55 lazy OutputForm
&lt;br&gt;&amp;nbsp;56 latch coerce : % -&amp;gt; OutputForm from local #1
&lt;br&gt;&amp;nbsp;57 latch 1 : () -&amp;gt; % from local #1
&lt;br&gt;&amp;nbsp;58 latch ?=? : (%,%) -&amp;gt; Boolean from local #1
&lt;br&gt;&amp;nbsp;59 lazy Symbol
&lt;br&gt;&amp;nbsp;60 lazy List Symbol
&lt;br&gt;&amp;nbsp;61 latch elt : (%,Integer) -&amp;gt; Symbol from List Symbol
&lt;br&gt;&amp;nbsp;62 latch coerce : % -&amp;gt; OutputForm from Symbol
&lt;br&gt;&amp;nbsp;63 latch ?*? : (%,%) -&amp;gt; % from OutputForm
&lt;br&gt;&amp;nbsp;64 latch ?+? : (%,%) -&amp;gt; % from OutputForm
&lt;br&gt;&amp;nbsp;65 lazy ((OutputForm,OutputForm) -&amp;gt; OutputForm)
&lt;br&gt;&amp;nbsp;66 lazy List OutputForm
&lt;br&gt;&amp;nbsp;67 latch reduce : (((OutputForm,OutputForm) -&amp;gt; OutputForm),%) -&amp;gt; 
&lt;br&gt;OutputForm from List OutputForm
&lt;br&gt;&amp;nbsp;68 fun &amp;nbsp;ALGSC;coerce;$Of;11
&lt;br&gt;&amp;nbsp;69 latch new : (NonNegativeInteger,local #1) -&amp;gt; % from Vector local #1
&lt;br&gt;&amp;nbsp;70 latch ?*? : (%,%) -&amp;gt; % from local #1
&lt;br&gt;&amp;nbsp;71 latch elt : (%,Integer) -&amp;gt; Matrix local #1 from Vector Matrix local #1
&lt;br&gt;&amp;nbsp;72 latch elt : (%,Integer,Integer) -&amp;gt; local #1 from Matrix local #1
&lt;br&gt;&amp;nbsp;73 latch ?+? : (%,%) -&amp;gt; % from local #1
&lt;br&gt;&amp;nbsp;74 latch setelt : (%,Integer,local #1) -&amp;gt; local #1 from Vector local #1
&lt;br&gt;&amp;nbsp;75 fun &amp;nbsp;ALGSC;*;3$;12
&lt;br&gt;&amp;nbsp;76 latch ?-? : (%,%) -&amp;gt; % from local #1
&lt;br&gt;&amp;nbsp;77 lazy Void
&lt;br&gt;&amp;nbsp;78 lazy String
&lt;br&gt;&amp;nbsp;79 latch messagePrint : String -&amp;gt; Void from OutputForm
&lt;br&gt;&amp;nbsp;80 fun &amp;nbsp;ALGSC;alternative?;B;13
&lt;br&gt;&amp;nbsp;81 fun &amp;nbsp;ALGSC;associative?;B;14
&lt;br&gt;&amp;nbsp;82 fun &amp;nbsp;ALGSC;antiAssociative?;B;15
&lt;br&gt;&amp;nbsp;83 fun &amp;nbsp;ALGSC;commutative?;B;16
&lt;br&gt;&amp;nbsp;84 fun &amp;nbsp;ALGSC;antiCommutative?;B;17
&lt;br&gt;&amp;nbsp;85 fun &amp;nbsp;ALGSC;leftAlternative?;B;18
&lt;br&gt;&amp;nbsp;86 fun &amp;nbsp;ALGSC;rightAlternative?;B;19
&lt;br&gt;&amp;nbsp;87 fun &amp;nbsp;ALGSC;flexible?;B;20
&lt;br&gt;&amp;nbsp;88 fun &amp;nbsp;ALGSC;lieAdmissible?;B;21
&lt;br&gt;&amp;nbsp;89 latch ?*? : (PositiveInteger,%) -&amp;gt; % from local #1
&lt;br&gt;&amp;nbsp;90 latch recip : % -&amp;gt; Union(%,QUOTE failed) from local #1
&lt;br&gt;&amp;nbsp;91 fun &amp;nbsp;ALGSC;jordanAdmissible?;B;22
&lt;br&gt;&amp;nbsp;92 fun &amp;nbsp;ALGSC;jordanAlgebra?;B;23
&lt;br&gt;&amp;nbsp;93 fun &amp;nbsp;ALGSC;jacobiIdentity?;B;24
&lt;br&gt;&amp;nbsp;94 lazy SparseUnivariatePolynomial Polynomial local #1
&lt;br&gt;&amp;nbsp;95 lazy Record(particular: $,basis: List $)
&lt;br&gt;&amp;nbsp;96 lazy Union(Record(particular: $,basis: List $),QUOTE failed)
&lt;br&gt;&amp;nbsp;97 lazy SparseUnivariatePolynomial local #1
&lt;br&gt;&amp;nbsp;98 lazy List Vector local #1
&lt;br&gt;&amp;nbsp;99 lazy List Polynomial local #1
&lt;br&gt;&amp;nbsp;100 lazy SingleInteger
&lt;br&gt;----------Complete Ops----------------
&lt;br&gt;&amp;nbsp;?~=? : (%,%) -&amp;gt; Boolean missing
&lt;br&gt;&amp;nbsp;zero? : % -&amp;gt; Boolean missing
&lt;br&gt;&amp;nbsp;unit : () -&amp;gt; Union(%,QUOTE failed) missing &amp;nbsp;if #1 has IntegralDomain
&lt;br&gt;&amp;nbsp;subtractIfCan : (%,%) -&amp;gt; Union(%,QUOTE failed) missing
&lt;br&gt;&amp;nbsp;structuralConstants : () -&amp;gt; Vector Matrix local #1 
&lt;br&gt;ALGSC;structuralConstants;V;4
&lt;br&gt;&amp;nbsp;structuralConstants : Vector % -&amp;gt; Vector Matrix local #1 missing
&lt;br&gt;&amp;nbsp;someBasis : () -&amp;gt; Vector % ALGSC;someBasis;V;8
&lt;br&gt;&amp;nbsp;sample : () -&amp;gt; % missing
&lt;br&gt;&amp;nbsp;rightUnits : () -&amp;gt; Union(Record(particular: %,basis: List %),QUOTE 
&lt;br&gt;failed) missing &amp;nbsp;if #1 has IntegralDomain
&lt;br&gt;&amp;nbsp;rightUnit : () -&amp;gt; Union(%,QUOTE failed) missing &amp;nbsp;if #1 has IntegralDomain
&lt;br&gt;&amp;nbsp;rightTraceMatrix : () -&amp;gt; Matrix local #1 missing
&lt;br&gt;&amp;nbsp;rightTraceMatrix : Vector % -&amp;gt; Matrix local #1 missing
&lt;br&gt;&amp;nbsp;rightTrace : % -&amp;gt; local #1 missing
&lt;br&gt;&amp;nbsp;rightRegularRepresentation : % -&amp;gt; Matrix local #1 missing
&lt;br&gt;&amp;nbsp;rightRegularRepresentation : (%,Vector %) -&amp;gt; Matrix local #1 missing
&lt;br&gt;&amp;nbsp;rightRecip : % -&amp;gt; Union(%,QUOTE failed) missing &amp;nbsp;if #1 has IntegralDomain
&lt;br&gt;&amp;nbsp;rightRankPolynomial : () -&amp;gt; SparseUnivariatePolynomial Polynomial local 
&lt;br&gt;#1 missing &amp;nbsp;if #1 has Field
&lt;br&gt;&amp;nbsp;rightPower : (%,PositiveInteger) -&amp;gt; % missing
&lt;br&gt;&amp;nbsp;rightNorm : % -&amp;gt; local #1 missing
&lt;br&gt;&amp;nbsp;rightMinimalPolynomial : % -&amp;gt; SparseUnivariatePolynomial local #1 
&lt;br&gt;missing &amp;nbsp;if #1 has IntegralDomain
&lt;br&gt;&amp;nbsp;rightDiscriminant : () -&amp;gt; local #1 missing
&lt;br&gt;&amp;nbsp;rightDiscriminant : Vector % -&amp;gt; local #1 missing
&lt;br&gt;&amp;nbsp;rightCharacteristicPolynomial : % -&amp;gt; SparseUnivariatePolynomial local 
&lt;br&gt;#1 missing
&lt;br&gt;&amp;nbsp;rightAlternative? : () -&amp;gt; Boolean ALGSC;rightAlternative?;B;19
&lt;br&gt;&amp;nbsp;represents : Vector local #1 -&amp;gt; % missing
&lt;br&gt;&amp;nbsp;represents : (Vector local #1,Vector %) -&amp;gt; % missing
&lt;br&gt;&amp;nbsp;recip : % -&amp;gt; Union(%,QUOTE failed) ALGSC;recip;$U;1 &amp;nbsp;if #1 has 
&lt;br&gt;IntegralDomain
&lt;br&gt;&amp;nbsp;rank : () -&amp;gt; PositiveInteger ALGSC;rank;Pi;9
&lt;br&gt;&amp;nbsp;powerAssociative? : () -&amp;gt; Boolean missing
&lt;br&gt;&amp;nbsp;plenaryPower : (%,PositiveInteger) -&amp;gt; % missing
&lt;br&gt;&amp;nbsp;noncommutativeJordanAlgebra? : () -&amp;gt; Boolean missing
&lt;br&gt;&amp;nbsp;lieAlgebra? : () -&amp;gt; Boolean missing
&lt;br&gt;&amp;nbsp;lieAdmissible? : () -&amp;gt; Boolean ALGSC;lieAdmissible?;B;21
&lt;br&gt;&amp;nbsp;leftUnits : () -&amp;gt; Union(Record(particular: %,basis: List %),QUOTE 
&lt;br&gt;failed) missing &amp;nbsp;if #1 has IntegralDomain
&lt;br&gt;&amp;nbsp;leftUnit : () -&amp;gt; Union(%,QUOTE failed) missing &amp;nbsp;if #1 has IntegralDomain
&lt;br&gt;&amp;nbsp;leftTraceMatrix : () -&amp;gt; Matrix local #1 missing
&lt;br&gt;&amp;nbsp;leftTraceMatrix : Vector % -&amp;gt; Matrix local #1 missing
&lt;br&gt;&amp;nbsp;leftTrace : % -&amp;gt; local #1 missing
&lt;br&gt;&amp;nbsp;leftRegularRepresentation : % -&amp;gt; Matrix local #1 missing
&lt;br&gt;&amp;nbsp;leftRegularRepresentation : (%,Vector %) -&amp;gt; Matrix local #1 missing
&lt;br&gt;&amp;nbsp;leftRecip : % -&amp;gt; Union(%,QUOTE failed) missing &amp;nbsp;if #1 has IntegralDomain
&lt;br&gt;&amp;nbsp;leftRankPolynomial : () -&amp;gt; SparseUnivariatePolynomial Polynomial local 
&lt;br&gt;#1 missing &amp;nbsp;if #1 has Field
&lt;br&gt;&amp;nbsp;leftPower : (%,PositiveInteger) -&amp;gt; % missing
&lt;br&gt;&amp;nbsp;leftNorm : % -&amp;gt; local #1 missing
&lt;br&gt;&amp;nbsp;leftMinimalPolynomial : % -&amp;gt; SparseUnivariatePolynomial local #1 
&lt;br&gt;missing &amp;nbsp;if #1 has IntegralDomain
&lt;br&gt;&amp;nbsp;leftDiscriminant : () -&amp;gt; local #1 missing
&lt;br&gt;&amp;nbsp;leftDiscriminant : Vector % -&amp;gt; local #1 missing
&lt;br&gt;&amp;nbsp;leftCharacteristicPolynomial : % -&amp;gt; SparseUnivariatePolynomial local #1 
&lt;br&gt;missing
&lt;br&gt;&amp;nbsp;leftAlternative? : () -&amp;gt; Boolean ALGSC;leftAlternative?;B;18
&lt;br&gt;&amp;nbsp;latex : % -&amp;gt; String missing
&lt;br&gt;&amp;nbsp;jordanAlgebra? : () -&amp;gt; Boolean ALGSC;jordanAlgebra?;B;23
&lt;br&gt;&amp;nbsp;jordanAdmissible? : () -&amp;gt; Boolean ALGSC;jordanAdmissible?;B;22
&lt;br&gt;&amp;nbsp;jacobiIdentity? : () -&amp;gt; Boolean ALGSC;jacobiIdentity?;B;24
&lt;br&gt;&amp;nbsp;hash : % -&amp;gt; SingleInteger missing
&lt;br&gt;&amp;nbsp;flexible? : () -&amp;gt; Boolean ALGSC;flexible?;B;20
&lt;br&gt;&amp;nbsp;elt : (%,Integer) -&amp;gt; local #1 ALGSC;elt;$IR;10
&lt;br&gt;&amp;nbsp;coordinates : % -&amp;gt; Vector local #1 ALGSC;coordinates;$V;5
&lt;br&gt;&amp;nbsp;coordinates : Vector % -&amp;gt; Matrix local #1 missing
&lt;br&gt;&amp;nbsp;coordinates : (Vector %,Vector %) -&amp;gt; Matrix local #1 missing
&lt;br&gt;&amp;nbsp;coordinates : (%,Vector %) -&amp;gt; Vector local #1 ALGSC;coordinates;$VV;6
&lt;br&gt;&amp;nbsp;convert : % -&amp;gt; Vector local #1 missing
&lt;br&gt;&amp;nbsp;convert : Vector local #1 -&amp;gt; % missing
&lt;br&gt;&amp;nbsp;conditionsForIdempotents : () -&amp;gt; List Polynomial local #1 missing
&lt;br&gt;&amp;nbsp;conditionsForIdempotents : Vector % -&amp;gt; List Polynomial local #1 missing
&lt;br&gt;&amp;nbsp;commutator : (%,%) -&amp;gt; % missing
&lt;br&gt;&amp;nbsp;commutative? : () -&amp;gt; Boolean ALGSC;commutative?;B;16
&lt;br&gt;&amp;nbsp;coerce : Vector local #1 -&amp;gt; % ALGSC;coerce;V$;3
&lt;br&gt;&amp;nbsp;coerce : % -&amp;gt; OutputForm ALGSC;coerce;$Of;11
&lt;br&gt;&amp;nbsp;basis : () -&amp;gt; Vector % ALGSC;basis;V;7
&lt;br&gt;&amp;nbsp;associatorDependence : () -&amp;gt; List Vector local #1 missing &amp;nbsp;if #1 has 
&lt;br&gt;IntegralDomain
&lt;br&gt;&amp;nbsp;associator : (%,%,%) -&amp;gt; % missing
&lt;br&gt;&amp;nbsp;associative? : () -&amp;gt; Boolean ALGSC;associative?;B;14
&lt;br&gt;&amp;nbsp;apply : (Matrix local #1,%) -&amp;gt; % looked up
&lt;br&gt;&amp;nbsp;antiCommutator : (%,%) -&amp;gt; % missing
&lt;br&gt;&amp;nbsp;antiCommutative? : () -&amp;gt; Boolean ALGSC;antiCommutative?;B;17
&lt;br&gt;&amp;nbsp;antiAssociative? : () -&amp;gt; Boolean ALGSC;antiAssociative?;B;15
&lt;br&gt;&amp;nbsp;alternative? : () -&amp;gt; Boolean ALGSC;alternative?;B;13
&lt;br&gt;&amp;nbsp;0 : () -&amp;gt; % missing
&lt;br&gt;&amp;nbsp;?=? : (%,%) -&amp;gt; Boolean missing
&lt;br&gt;&amp;nbsp;-? : % -&amp;gt; % missing
&lt;br&gt;&amp;nbsp;?-? : (%,%) -&amp;gt; % missing
&lt;br&gt;&amp;nbsp;?+? : (%,%) -&amp;gt; % missing
&lt;br&gt;&amp;nbsp;?**? : (%,PositiveInteger) -&amp;gt; % missing
&lt;br&gt;&amp;nbsp;?*? : (SquareMatrix(local #2,local #1),%) -&amp;gt; % ALGSC;*;Sm2$;2
&lt;br&gt;&amp;nbsp;?*? : (local #1,%) -&amp;gt; % missing
&lt;br&gt;&amp;nbsp;?*? : (%,local #1) -&amp;gt; % missing
&lt;br&gt;&amp;nbsp;?*? : (%,%) -&amp;gt; % ALGSC;*;3$;12
&lt;br&gt;&amp;nbsp;?*? : (Integer,%) -&amp;gt; % missing
&lt;br&gt;&amp;nbsp;?*? : (NonNegativeInteger,%) -&amp;gt; % missing
&lt;br&gt;&amp;nbsp;?*? : (PositiveInteger,%) -&amp;gt; % missing
&lt;br&gt;----------------Atts-----------------
&lt;br&gt;&amp;nbsp;0 unitsKnown if #1 has IntegralDomain
&lt;br&gt;&amp;nbsp;1 leftUnitary
&lt;br&gt;&amp;nbsp;2 rightUnitary
&lt;br&gt;----------------Preds-----------------
&lt;br&gt;&amp;nbsp;1 #1 has Field
&lt;br&gt;&amp;nbsp;2 #1 has IntegralDomain
&lt;br&gt;----------------Cats-----------------
&lt;br&gt;&amp;nbsp;0 FramedNonAssociativeAlgebra local #1 package
&lt;br&gt;&amp;nbsp;1 FiniteRankNonAssociativeAlgebra local #1 package
&lt;br&gt;&amp;nbsp;2 NonAssociativeAlgebra local #1 package
&lt;br&gt;&amp;nbsp;3 Module local #1 package
&lt;br&gt;&amp;nbsp;4 BiModule(local #1,local #1)
&lt;br&gt;&amp;nbsp;5 NonAssociativeRng package
&lt;br&gt;&amp;nbsp;6 LeftModule SquareMatrix(local #2,local #1)
&lt;br&gt;&amp;nbsp;7 RightModule local #1
&lt;br&gt;&amp;nbsp;8 LeftModule local #1
&lt;br&gt;&amp;nbsp;9 AbelianGroup package
&lt;br&gt;&amp;nbsp;10 CancellationAbelianMonoid
&lt;br&gt;&amp;nbsp;11 AbelianMonoid package
&lt;br&gt;&amp;nbsp;12 AbelianSemiGroup package
&lt;br&gt;&amp;nbsp;13 Monad package
&lt;br&gt;&amp;nbsp;14 SetCategory package
&lt;br&gt;&amp;nbsp;15 BasicType package
&lt;br&gt;&amp;nbsp;16 CoercibleTo OutputForm
&lt;br&gt;----------------Data------------------
&lt;br&gt;Operation data from slot 1
&lt;br&gt;&lt;br&gt;#(~= 197 |zero?| 203 |unit| 208 |subtractIfCan| 212 
&lt;br&gt;|structuralConstants| 218 |someBasis| 227 |sample| 231 |rightUnits| 235 
&lt;br&gt;|rightUnit| 239 |rightTraceMatrix| 243 |rightTrace| 252 
&lt;br&gt;|rightRegularRepresentation| 257 |rightRecip| 268 |rightRankPolynomial| 
&lt;br&gt;273 |rightPower| 277 |rightNorm| 283 |rightMinimalPolynomial| 288 
&lt;br&gt;|rightDiscriminant| 293 |rightCharacteristicPolynomial| 302 
&lt;br&gt;|rightAlternative?| 307 |represents| 311 |recip| 322 |rank| 327 
&lt;br&gt;|powerAssociative?| 331 |plenaryPower| 335 
&lt;br&gt;|noncommutativeJordanAlgebra?| 341 |lieAlgebra?| 345 |lieAdmissible?| 
&lt;br&gt;349 |leftUnits| 353 |leftUnit| 357 |leftTraceMatrix| 361 |leftTrace| 370 
&lt;br&gt;|leftRegularRepresentation| 375 |leftRecip| 386 |leftRankPolynomial| 391 
&lt;br&gt;|leftPower| 395 |leftNorm| 401 |leftMinimalPolynomial| 406 
&lt;br&gt;|leftDiscriminant| 411 |leftCharacteristicPolynomial| 420 
&lt;br&gt;|leftAlternative?| 425 |latex| 429 |jordanAlgebra?| 434 
&lt;br&gt;|jordanAdmissible?| 438 |jacobiIdentity?| 442 |hash| 446 |flexible?| 451 
&lt;br&gt;|elt| 455 |coordinates| 461 |convert| 483 |conditionsForIdempotents| 493 
&lt;br&gt;|commutator| 502 |commutative?| 508 |coerce| 512 |basis| 522 
&lt;br&gt;|associatorDependence| 526 |associator| 530 |associative?| 537 |apply| 
&lt;br&gt;541 |antiCommutator| 547 |antiCommutative?| 553 |antiAssociative?| 557 
&lt;br&gt;|alternative?| 561 |Zero| 565 = 569 - 575 + 586 ** 592 * 598)
&lt;br&gt;Information vector has 640 entries
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&lt;br&gt;&amp;nbsp; &amp;nbsp;470 &amp;nbsp;| &amp;nbsp; &amp;nbsp; 1 &amp;nbsp; &amp;nbsp; 2 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp;15 &amp;nbsp; &amp;nbsp;43 &amp;nbsp; &amp;nbsp;43 &amp;nbsp; &amp;nbsp; 1 &amp;nbsp; &amp;nbsp; 2 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp;20
&lt;br&gt;&amp;nbsp; &amp;nbsp;480 &amp;nbsp;| &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp;43 &amp;nbsp; &amp;nbsp;47 &amp;nbsp; &amp;nbsp; 1 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp;20 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 1 &amp;nbsp; &amp;nbsp; 1 &amp;nbsp; &amp;nbsp; 0
&lt;br&gt;&amp;nbsp; &amp;nbsp;490 &amp;nbsp;| &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp;20 &amp;nbsp; &amp;nbsp; 1 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp;99 &amp;nbsp; &amp;nbsp; 1 &amp;nbsp; &amp;nbsp; 1 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp;99
&lt;br&gt;&amp;nbsp; &amp;nbsp;500 &amp;nbsp;| &amp;nbsp; &amp;nbsp;43 &amp;nbsp; &amp;nbsp; 1 &amp;nbsp; &amp;nbsp; 2 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 1 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0
&lt;br&gt;&amp;nbsp; &amp;nbsp;510 &amp;nbsp;| &amp;nbsp; &amp;nbsp;41 &amp;nbsp; &amp;nbsp;83 &amp;nbsp; &amp;nbsp; 1 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp;20 &amp;nbsp; &amp;nbsp;22 &amp;nbsp; &amp;nbsp; 1 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp;55
&lt;br&gt;&amp;nbsp; &amp;nbsp;520 &amp;nbsp;| &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp;68 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp;43 &amp;nbsp; &amp;nbsp;44 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 2 &amp;nbsp; &amp;nbsp;98 &amp;nbsp; &amp;nbsp; 1
&lt;br&gt;&amp;nbsp; &amp;nbsp;530 &amp;nbsp;| &amp;nbsp; &amp;nbsp; 3 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 1 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp;41
&lt;br&gt;&amp;nbsp; &amp;nbsp;540 &amp;nbsp;| &amp;nbsp; &amp;nbsp;81 &amp;nbsp; &amp;nbsp; 2 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp;15 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp;18 &amp;nbsp; &amp;nbsp; 2 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0
&lt;br&gt;&amp;nbsp; &amp;nbsp;550 &amp;nbsp;| &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 1 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp;41 &amp;nbsp; &amp;nbsp;84 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp;41
&lt;br&gt;&amp;nbsp; &amp;nbsp;560 &amp;nbsp;| &amp;nbsp; &amp;nbsp;82 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp;41 &amp;nbsp; &amp;nbsp;80 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 1 &amp;nbsp; &amp;nbsp; 2
&lt;br&gt;&amp;nbsp; &amp;nbsp;570 &amp;nbsp;| &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp;41 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 1 &amp;nbsp; &amp;nbsp; 1 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 1
&lt;br&gt;&amp;nbsp; &amp;nbsp;580 &amp;nbsp;| &amp;nbsp; &amp;nbsp; 2 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 1 &amp;nbsp; &amp;nbsp; 2 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0
&lt;br&gt;&amp;nbsp; &amp;nbsp;590 &amp;nbsp;| &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 1 &amp;nbsp; &amp;nbsp; 2 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp;48 &amp;nbsp; &amp;nbsp; 1 &amp;nbsp; &amp;nbsp; 2 &amp;nbsp; &amp;nbsp; 0
&lt;br&gt;&amp;nbsp; &amp;nbsp;600 &amp;nbsp;| &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp;16 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp;19 &amp;nbsp; &amp;nbsp; 2 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 6 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 1
&lt;br&gt;&amp;nbsp; &amp;nbsp;610 &amp;nbsp;| &amp;nbsp; &amp;nbsp; 2 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 6 &amp;nbsp; &amp;nbsp; 1 &amp;nbsp; &amp;nbsp; 2 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0
&lt;br&gt;&amp;nbsp; &amp;nbsp;620 &amp;nbsp;| &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp;75 &amp;nbsp; &amp;nbsp; 2 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp;29 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 1 &amp;nbsp; &amp;nbsp; 2 &amp;nbsp; &amp;nbsp; 0
&lt;br&gt;&amp;nbsp; &amp;nbsp;630 &amp;nbsp;| &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp;33 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 1 &amp;nbsp; &amp;nbsp; 2 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp;48 &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; 1
&lt;br&gt;----------------Size------------------
&lt;br&gt;infovec total = 4434 BYTES
&lt;br&gt;template &amp;nbsp; &amp;nbsp;= 2064
&lt;br&gt;operations &amp;nbsp;= 556 (complete)
&lt;br&gt;attributes &amp;nbsp;= 6
&lt;br&gt;categories &amp;nbsp;= 528
&lt;br&gt;data vector = 1280
&lt;br&gt;number of function slots (one extra node) = 24
&lt;br&gt;number of latch slots (2 extra nodes) = 35
&lt;br&gt;number of lazy slots (no extra nodes) = 37
&lt;br&gt;size of domain vectors = 101 slots
&lt;br&gt;domain size = 5562 BYTES
&lt;br&gt;cost per instantiation = 1536 BYTES
&lt;br&gt;(1) -&amp;gt;
&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
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<entry>
	<id>tag:old.nabble.com,2006:post-26478783</id>
	<title>Re: Re: CliffordPackage</title>
	<published>2009-11-23T06:13:05Z</published>
	<updated>2009-11-23T06:13:05Z</updated>
	<author>
		<name>Martin Rubey-3</name>
	</author>
	<content type="html">Bertfried Fauser &amp;lt;&lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26478783&amp;i=0&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;bertfried.fauser@...&lt;/a&gt;&amp;gt; writes:
&lt;br&gt;&lt;br&gt;&lt;div class='shrinkable-quote'&gt;&lt;br&gt;&amp;gt; I doubt threre is any other place (and I will see if I can chack that,
&lt;br&gt;&amp;gt; a grep over the code should do, I found CliffordAlgebra mentioned in
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; * browse.daase
&lt;br&gt;&amp;gt; * category.daase
&lt;br&gt;&amp;gt; * operation.daase
&lt;br&gt;&amp;gt; * compres.daase
&lt;br&gt;&amp;gt; * interp.daase
&lt;br&gt;&amp;gt; * exposed.lsp.pamphlet.svn-base
&lt;br&gt;&amp;gt; * clifford.spad.pamphlet
&lt;br&gt;&amp;gt; * abbrevs.input
&lt;br&gt;&amp;gt; * extract-spad.mk
&lt;br&gt;&amp;gt; * comdb.text
&lt;br&gt;&amp;gt; * libdb.text
&lt;br&gt;&amp;gt; * DEPENDENTS.DAASE
&lt;br&gt;&amp;gt; * CLIF.spad
&lt;br&gt;&amp;gt; * /USERS.DAASE/index.KA
&lt;br&gt;&amp;gt; * hyper/pages/.svn/text-base/CLIF.ht.svn-base
&lt;br&gt;&amp;gt; * hyper/pages/.svn/text-base/QUAT.ht.svn-base
&lt;br&gt;&amp;gt; * hyper/pages/QUAT.ht
&lt;br&gt;&amp;gt; * hyper/pages/QUAT2.ht
&lt;br&gt;&amp;gt; * hyper/pages/xmpexp.ht
&lt;br&gt;&amp;gt; * hyper/pages/ug02.ht
&lt;br&gt;&amp;gt; * hyper/pages/ug13.ht
&lt;br&gt;&amp;gt; * hyper/pages/CLIF.ht
&lt;br&gt;&amp;gt; * input/clifford.input.pamphlet
&lt;br&gt;&amp;gt; * paste/CLIF.input
&lt;br&gt;&amp;gt; * paste/CLIF.phts
&lt;br&gt;&amp;gt; * padhelp/Quaternion.help
&lt;br&gt;&amp;gt; * spadhelp/CliffordAlgebra.help
&lt;br&gt;&amp;gt; * topics.data
&lt;br&gt;&amp;gt; * command.list
&lt;br&gt;&amp;gt; )
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; I am not a grep expert, so things may have sliped through, otherwise I
&lt;br&gt;&amp;gt; think the above given list proves that CliffordAlgebra is not used by
&lt;br&gt;&amp;gt; any other package.
&lt;/div&gt;&lt;br&gt;It's not a proof, unfortunately (only a strong hint), because the
&lt;br&gt;compiler tries to be smart: packages and domains do not necessarily need
&lt;br&gt;to be mentioned, if the name of the operation or the types of the
&lt;br&gt;arguments determine the operation uniquely.
&lt;br&gt;&lt;br&gt;Martin
&lt;br&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
&lt;br&gt;Axiom-developer mailing list
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</entry>

<entry>
	<id>tag:old.nabble.com,2006:post-26469639</id>
	<title>Re: CliffordPackage</title>
	<published>2009-11-22T13:23:44Z</published>
	<updated>2009-11-22T13:23:44Z</updated>
	<author>
		<name>Bertfried Fauser-2</name>
	</author>
	<content type="html">Hi Martin,
&lt;br&gt;&lt;br&gt;my posts to fricas-devel are currently rejected by google, so I write
&lt;br&gt;this also directly to you.
&lt;br&gt;&lt;br&gt;&amp;gt; These changes make good sense to me. I will just note for the record that they
&lt;br&gt;&amp;gt; change the user interface and would therefore break any applications already
&lt;br&gt;&amp;gt; using CliffordAlgebra but the changes are important enough to justify that.
&lt;br&gt;&lt;br&gt;Since the Clifford code was broken from the outset, the only place
&lt;br&gt;where it actually shows up is the AXIOM book, which would then also
&lt;br&gt;need an update,
&lt;br&gt;I doubt threre is any other place (and I will see if I can chack that,
&lt;br&gt;a grep over the code should do, I found CliffordAlgebra mentioned in
&lt;br&gt;&lt;br&gt;* browse.daase
&lt;br&gt;* category.daase
&lt;br&gt;* operation.daase
&lt;br&gt;* compres.daase
&lt;br&gt;* interp.daase
&lt;br&gt;* exposed.lsp.pamphlet.svn-base
&lt;br&gt;* clifford.spad.pamphlet
&lt;br&gt;* abbrevs.input
&lt;br&gt;* extract-spad.mk
&lt;br&gt;* comdb.text
&lt;br&gt;* libdb.text
&lt;br&gt;* DEPENDENTS.DAASE
&lt;br&gt;* CLIF.spad
&lt;br&gt;* /USERS.DAASE/index.KA
&lt;br&gt;* hyper/pages/.svn/text-base/CLIF.ht.svn-base
&lt;br&gt;* hyper/pages/.svn/text-base/QUAT.ht.svn-base
&lt;br&gt;* hyper/pages/QUAT.ht
&lt;br&gt;* hyper/pages/QUAT2.ht
&lt;br&gt;* hyper/pages/xmpexp.ht
&lt;br&gt;* hyper/pages/ug02.ht
&lt;br&gt;* hyper/pages/ug13.ht
&lt;br&gt;* hyper/pages/CLIF.ht
&lt;br&gt;* input/clifford.input.pamphlet
&lt;br&gt;* paste/CLIF.input
&lt;br&gt;* paste/CLIF.phts
&lt;br&gt;* padhelp/Quaternion.help
&lt;br&gt;* spadhelp/CliffordAlgebra.help
&lt;br&gt;* topics.data
&lt;br&gt;* command.list
&lt;br&gt;)
&lt;br&gt;&lt;br&gt;I am not a grep expert, so things may have sliped through, otherwise I
&lt;br&gt;think the above given list proves that CliffordAlgebra is not used by
&lt;br&gt;any other package.
&lt;br&gt;&lt;br&gt;&amp;gt; OK, I will check if division or swapping of operands is done.
&lt;br&gt;&lt;br&gt;That was just a feature request, forget about noncommutytive rings at
&lt;br&gt;the moment.
&lt;br&gt;&lt;br&gt;&amp;gt; the domain constructor as 'List List Ring', 'SquareMatrix Ring' or create a
&lt;br&gt;&amp;gt; custom domain called BilinearForm ? Would I be correct in thinking that Matrix
&lt;br&gt;&amp;gt; or a custom domain would not add much value so I might as well use a List of
&lt;br&gt;&amp;gt; Lists for efficiency?
&lt;br&gt;&lt;br&gt;I would be happy with List List Ring, but since its a map between
&lt;br&gt;vector spaces or modules, some popele on the list (if this mail gets
&lt;br&gt;through) will have different oppinions. A square matrix could do, but
&lt;br&gt;actually you only want to read out the elements, nothing else is done
&lt;br&gt;with this array, so I would look (ask on teh list) what data structure
&lt;br&gt;has the best random acess performance, List List is possibly slow, but
&lt;br&gt;on the other hand such arrays will be in practice something like up to
&lt;br&gt;10x10, so no hassle.
&lt;br&gt;&lt;br&gt;&amp;gt; Yes please, this would be very helpful, no rush though, as it will take me
&lt;br&gt;&amp;gt; some time to absorb all this good information that you have given me.
&lt;br&gt;&lt;br&gt;OK, as soon as my maple is up again, I'll produce some test cases for you
&lt;br&gt;(and we need to do AXIOM test cases for Tim ;-))
&lt;br&gt;&lt;br&gt;Ciao
&lt;br&gt;BF.
&lt;br&gt;&lt;br&gt;-- 
&lt;br&gt;% PD Dr Bertfried Fauser
&lt;br&gt;% &amp;nbsp; &amp;nbsp; &amp;nbsp; Research Fellow, School of Computer Science, Univ. of Birmingham
&lt;br&gt;% &amp;nbsp; &amp;nbsp; &amp;nbsp; Honorary Associate, University of Tasmania
&lt;br&gt;% &amp;nbsp; &amp;nbsp; &amp;nbsp; Privat Docent: University of Konstanz, Physics Dept
&lt;br&gt;&amp;lt;&lt;a href=&quot;http://www.uni-konstanz.de&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://www.uni-konstanz.de&lt;/a&gt;&amp;gt;
&lt;br&gt;% contact |-&amp;gt; &amp;nbsp; &amp;nbsp;URL : &lt;a href=&quot;http://www.cs.bham.ac.uk/~fauserb/&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://www.cs.bham.ac.uk/~fauserb/&lt;/a&gt;&lt;br&gt;% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;Phone : &amp;nbsp;+44-121-41-42795 and +49 1520 9874517
&lt;br&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
&lt;br&gt;Axiom-developer mailing list
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</entry>

<entry>
	<id>tag:old.nabble.com,2006:post-26462283</id>
	<title>Re: Embedding Axiom (Hickey and fold/unfold) Folding and generalization</title>
	<published>2009-11-21T18:08:40Z</published>
	<updated>2009-11-21T18:08:40Z</updated>
	<author>
		<name>Tim Daly-3</name>
	</author>
	<content type="html">Martin Baker wrote:
&lt;div class='shrinkable-quote'&gt;&lt;br&gt;&amp;gt; I think it helps to get a wider perspective.
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Part of what prompted my question is when I was thinking about how to 
&lt;br&gt;&amp;gt; implement the exterior product I thought about possible options, for instance 
&lt;br&gt;&amp;gt; rules:
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; &amp;lt;e1, e2…en | ei/\ei=0, ei/\ej= -ej/\ei&amp;gt;
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; or an algorithm:
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; And(b1::SINT,b2::SINT) ~= 0 =&amp;gt; z
&lt;br&gt;&amp;gt; c := c1 * c2
&lt;br&gt;&amp;gt; bz := Or(b1::SINT,b2::SINT)
&lt;br&gt;&amp;gt; for i in 0..n-1 | bit?(b1,i) repeat
&lt;br&gt;&amp;gt; &amp;nbsp; k := 0
&lt;br&gt;&amp;gt; &amp;nbsp; for j in i+1..n-1 | bit?(b1, j) repeat k := k+1
&lt;br&gt;&amp;gt; &amp;nbsp; for j in 0..i-1 &amp;nbsp; | bit?(bz, j) repeat k := k+1
&lt;br&gt;&amp;gt; &amp;nbsp; if odd? k then c := -c
&lt;br&gt;&amp;gt; &amp;nbsp; z.bz := z.bz + c
&lt;br&gt;&amp;gt; z
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; or a multiplication table:
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; 0 &amp;nbsp; &amp;nbsp; &amp;nbsp;e1^e2
&lt;br&gt;&amp;gt; -e1^e2 0
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Out of these options, the rules just seems to be operating at a higher level? 
&lt;br&gt;&amp;gt; In that it would seem relatively easy to translate from the rules to the 
&lt;br&gt;&amp;gt; algorithm but a lot more difficult to go from the algorithm to the rules 
&lt;br&gt;&amp;gt; (could Concordia do it?). &amp;nbsp;Also, unlike the algorithm, there is no need to 
&lt;br&gt;&amp;gt; introduce the concept of time. I wonder which type would be the best for 
&lt;br&gt;&amp;gt; making a test for equivalence?
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; I take your point that the rules are not necessarily better for parallel 
&lt;br&gt;&amp;gt; processing and they don't scale up very well, I wonder if there would be some 
&lt;br&gt;&amp;gt; way to get the best of all these approaches? lots of small rule bases or 
&lt;br&gt;&amp;gt; something like that?
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Another point is that there are no 'side effects' to this function but we are 
&lt;br&gt;&amp;gt; trying to add one in by caching the multiplication table!
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; I don't have any answers but its interesting to speculate,
&lt;br&gt;&amp;gt; &amp;nbsp; 
&lt;/div&gt;&lt;br&gt;I like the declarative form a lot, which would fit rules rather well. I 
&lt;br&gt;think you understand
&lt;br&gt;my feelings on rules being non-algebraic, though, and I'd advise against it.
&lt;br&gt;&lt;br&gt;The table form could get very large (unless you only cache computed 
&lt;br&gt;entries).
&lt;br&gt;The table form would also require some matching since &amp;quot;e1&amp;quot; could be 
&lt;br&gt;something
&lt;br&gt;more complex than a symbol.
&lt;br&gt;&lt;br&gt;I think that the procedural form gives you the most flexible version since
&lt;br&gt;(a) it fits into the spad coding scheme and (b) allows you to manipulate the
&lt;br&gt;internal representations in efficient ways that can &amp;quot;violate causality&amp;quot; 
&lt;br&gt;within
&lt;br&gt;the function without being visible to the user. It also gives you the 
&lt;br&gt;opportunity
&lt;br&gt;to coerce to more specific forms (like linear algebra forms) in special 
&lt;br&gt;cases.
&lt;br&gt;&lt;br&gt;In addition, the coding form will force you to be explicit about the 
&lt;br&gt;categories
&lt;br&gt;that need to be defined. I think one of the key strengths of Axiom is 
&lt;br&gt;the organization
&lt;br&gt;of the system into categories. If you started with Operads (per William 
&lt;br&gt;Sit's comments)
&lt;br&gt;as categories and derived your Grassmann/Clifford/Octonion forms in a 
&lt;br&gt;disciplined
&lt;br&gt;way then everyone wins. I will admit that this is VERY hard. I tried to 
&lt;br&gt;do this for
&lt;br&gt;the Infinite Group Theory area and failed. (Hardly a surprise since I'm 
&lt;br&gt;not an
&lt;br&gt;Infinite Group Theorist by any stretch of the imagination.)
&lt;br&gt;&lt;br&gt;William may have some useful insights here as he is a mathematician and an
&lt;br&gt;Axiom algebra author.
&lt;br&gt;&lt;br&gt;Tim
&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
&lt;br&gt;Axiom-developer mailing list
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</entry>

<entry>
	<id>tag:old.nabble.com,2006:post-26462273</id>
	<title>Re: Embedding Axiom (Hickey and fold/unfold) Folding and generalization</title>
	<published>2009-11-21T18:07:13Z</published>
	<updated>2009-11-21T18:07:13Z</updated>
	<author>
		<name>Tim Daly-3</name>
	</author>
	<content type="html">Martin Baker wrote:
&lt;br&gt;&amp;gt; Tim,
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Thank you for these replies, I am learning a lot here.
&lt;br&gt;&amp;gt; &amp;nbsp; 
&lt;br&gt;&lt;br&gt;Yeah, Hickey is really an insightful chap. He sets the bar pretty high.
&lt;br&gt;&lt;br&gt;Many centuries ago I had to make the transition from using goto in general
&lt;br&gt;to using goto in a structured form (Fortran did not have an else clause 
&lt;br&gt;on If).
&lt;br&gt;The hard part was the mental shift needed to do &amp;quot;structured programming&amp;quot; 
&lt;br&gt;since
&lt;br&gt;I had to discover the correct, disciplined control structures myself. 
&lt;br&gt;There were
&lt;br&gt;no textbooks as it was a &amp;quot;new&amp;quot; idea that unstructured goto was bad.
&lt;br&gt;&lt;br&gt;Now Hickey basically said &amp;quot;do not use loops&amp;quot;. Hmmm... that's gonna be 
&lt;br&gt;another
&lt;br&gt;stretch, although I see why he suggests it and I agree with him. We have 
&lt;br&gt;to learn to
&lt;br&gt;use map/fold/take/etc. in disciplined ways to process Axiom's internal data.
&lt;br&gt;&lt;br&gt;And we need &amp;quot;reconsing&amp;quot; versions that return immutable but shared copies 
&lt;br&gt;of the
&lt;br&gt;list/vector/struct/etc., with versions that (per On Lisp) embed properly.
&lt;br&gt;&lt;br&gt;And we need to write in pure function form (not a stretch because I try to
&lt;br&gt;do this now).
&lt;br&gt;&lt;br&gt;And we need (per SICP) to write embedded layering, fully factored forms.
&lt;br&gt;&lt;br&gt;I think all of these ideas will greatly benefit Axiom's internal 
&lt;br&gt;restructuring,
&lt;br&gt;including possibly making a parallel implementation much easier to achieve.
&lt;br&gt;If nothing else at least the &amp;quot;coupling&amp;quot; will drop considerably as we 
&lt;br&gt;stop using
&lt;br&gt;special variables for maintaining mutable global state.
&lt;br&gt;&lt;br&gt;Tim
&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
&lt;br&gt;Axiom-developer mailing list
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</entry>

<entry>
	<id>tag:old.nabble.com,2006:post-26461126</id>
	<title>Re: Embedding Axiom (Hickey and fold/unfold) Folding and generalization</title>
	<published>2009-11-21T14:44:44Z</published>
	<updated>2009-11-21T14:44:44Z</updated>
	<author>
		<name>Martin Baker-3</name>
	</author>
	<content type="html">Tim,
&lt;br&gt;&lt;br&gt;Thank you for these replies, I am learning a lot here.
&lt;br&gt;&lt;br&gt;I think it helps to get a wider perspective.
&lt;br&gt;&lt;br&gt;Part of what prompted my question is when I was thinking about how to 
&lt;br&gt;implement the exterior product I thought about possible options, for instance 
&lt;br&gt;rules:
&lt;br&gt;&lt;br&gt;&amp;lt;e1, e2…en | ei/\ei=0, ei/\ej= -ej/\ei&amp;gt;
&lt;br&gt;&lt;br&gt;or an algorithm:
&lt;br&gt;&lt;br&gt;And(b1::SINT,b2::SINT) ~= 0 =&amp;gt; z
&lt;br&gt;c := c1 * c2
&lt;br&gt;bz := Or(b1::SINT,b2::SINT)
&lt;br&gt;for i in 0..n-1 | bit?(b1,i) repeat
&lt;br&gt;&amp;nbsp; k := 0
&lt;br&gt;&amp;nbsp; for j in i+1..n-1 | bit?(b1, j) repeat k := k+1
&lt;br&gt;&amp;nbsp; for j in 0..i-1 &amp;nbsp; | bit?(bz, j) repeat k := k+1
&lt;br&gt;&amp;nbsp; if odd? k then c := -c
&lt;br&gt;&amp;nbsp; z.bz := z.bz + c
&lt;br&gt;z
&lt;br&gt;&lt;br&gt;or a multiplication table:
&lt;br&gt;&lt;br&gt;0 &amp;nbsp; &amp;nbsp; &amp;nbsp;e1^e2
&lt;br&gt;-e1^e2 0
&lt;br&gt;&lt;br&gt;Out of these options, the rules just seems to be operating at a higher level? 
&lt;br&gt;In that it would seem relatively easy to translate from the rules to the 
&lt;br&gt;algorithm but a lot more difficult to go from the algorithm to the rules 
&lt;br&gt;(could Concordia do it?). &amp;nbsp;Also, unlike the algorithm, there is no need to 
&lt;br&gt;introduce the concept of time. I wonder which type would be the best for 
&lt;br&gt;making a test for equivalence?
&lt;br&gt;&lt;br&gt;I take your point that the rules are not necessarily better for parallel 
&lt;br&gt;processing and they don't scale up very well, I wonder if there would be some 
&lt;br&gt;way to get the best of all these approaches? lots of small rule bases or 
&lt;br&gt;something like that?
&lt;br&gt;&lt;br&gt;Another point is that there are no 'side effects' to this function but we are 
&lt;br&gt;trying to add one in by caching the multiplication table!
&lt;br&gt;&lt;br&gt;I don't have any answers but its interesting to speculate,
&lt;br&gt;&lt;br&gt;thanks,
&lt;br&gt;&lt;br&gt;Martin
&lt;br&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
&lt;br&gt;Axiom-developer mailing list
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<entry>
	<id>tag:old.nabble.com,2006:post-26458435</id>
	<title>Embedding Axiom (Hickey and fold/unfold) Folding and generalization</title>
	<published>2009-11-21T09:15:37Z</published>
	<updated>2009-11-21T09:15:37Z</updated>
	<author>
		<name>Tim Daly-3</name>
	</author>
	<content type="html">Martin Baker wrote:
&lt;div class='shrinkable-quote'&gt;&lt;br&gt;&amp;gt; On Friday 20 November 2009 23:17:25 Tim Daly wrote:
&lt;br&gt;&amp;gt; &amp;nbsp; 
&lt;br&gt;&amp;gt;&amp;gt; There is an excellent talk by Rich Hickey about modelling time, 
&lt;br&gt;&amp;gt;&amp;gt; identity, values,
&lt;br&gt;&amp;gt;&amp;gt; perception, state, memory, etc.
&lt;br&gt;&amp;gt;&amp;gt; &amp;nbsp; &amp;nbsp; 
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Tim,
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; While I was watching this talk I was wondering about the difference between 
&lt;br&gt;&amp;gt; the mainstream computing issues verses mathematical computing issues.
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; I get the impression that the mainstream issue, from this talk, is about how 
&lt;br&gt;&amp;gt; to run multiple algorithms in parallel?
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; If we are trying to solve a set of equations, is there a natural parallelism ? 
&lt;br&gt;&amp;gt; For the reasons discussed in the talk, should a rule based method be preferred 
&lt;br&gt;&amp;gt; wherever possible and explicit coding of algorithms be discouraged?
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Martin Baker
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; &amp;nbsp; 
&lt;/div&gt;&lt;br&gt;Folding and Unfolding via pattern matching....
&lt;br&gt;&lt;br&gt;On the second point, which is the subject of folding and unfolding I 
&lt;br&gt;think that rules
&lt;br&gt;would be very useful here. Consider two statements (function calls) that 
&lt;br&gt;you would
&lt;br&gt;like to prove are equal. The suggestion is to unfold them both by doing 
&lt;br&gt;substitution
&lt;br&gt;of definitions until they are both &amp;quot;the same&amp;quot;.... where &amp;quot;the same&amp;quot; means 
&lt;br&gt;that they
&lt;br&gt;exhibit the same pattern with substitution e.g.
&lt;br&gt;&lt;br&gt;&amp;nbsp; (x^2) == (y^2) where x-&amp;gt;y
&lt;br&gt;&lt;br&gt;If two functions unfold to the same pattern then we can re-fold them 
&lt;br&gt;into each other.
&lt;br&gt;&lt;br&gt;I think that this might be a key step in Axiom's development. I am 
&lt;br&gt;trying to discover
&lt;br&gt;a way to prove Axiom programs correct. In particular, it would be good 
&lt;br&gt;to prove
&lt;br&gt;that the operations in the domain Group actually follow from the &amp;quot;group 
&lt;br&gt;axioms&amp;quot;.
&lt;br&gt;Can mathematical group axioms be unfolded into domain Group operations? Can
&lt;br&gt;ACL2 be used to prove that each unfolding step is correct? (insert PhD 
&lt;br&gt;students here).
&lt;br&gt;&lt;br&gt;&lt;br&gt;The really clever trick is to do folding without knowing anything. This 
&lt;br&gt;would be a
&lt;br&gt;form of &amp;quot;generalization&amp;quot;. You are trying to find a way to recognize that 
&lt;br&gt;a particular
&lt;br&gt;sequence of code &amp;quot;is a SORT routine&amp;quot;, for instance. After all, if you 
&lt;br&gt;can recognize
&lt;br&gt;a &amp;quot;SWAP&amp;quot; sequence, a &amp;quot;CONDITIONAL&amp;quot; sequence, and an &amp;quot;ITERATION&amp;quot;
&lt;br&gt;sequence, can you know that
&lt;br&gt;&lt;br&gt;&amp;nbsp; SORT == ITERATED CONDITIONAL SWAP
&lt;br&gt;&lt;br&gt;This is a subject of a paper I'm going to present at HICSS in January.
&lt;br&gt;An early video of the project ideas is at:
&lt;br&gt;&lt;a href=&quot;http://daly.axiom-developer.org/CONCORDIA.html&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://daly.axiom-developer.org/CONCORDIA.html&lt;/a&gt;&lt;br&gt;&lt;br&gt;(The talk is in the context of function extraction and malware but the 
&lt;br&gt;ideas are
&lt;br&gt;motivated by my &amp;quot;prove computational math&amp;quot; struggles)
&lt;br&gt;&lt;br&gt;Generalization by folding would amount to finding the formula from an 
&lt;br&gt;instance.
&lt;br&gt;The formula has much less information than the instances of the formula 
&lt;br&gt;so all types
&lt;br&gt;of generalization involve deliberately losing information.
&lt;br&gt;&lt;br&gt;It is not possible (well...caveats) to generalize from a single 
&lt;br&gt;instance. The single
&lt;br&gt;instance can be generalized in many directions. Multiple instances give 
&lt;br&gt;a way to
&lt;br&gt;generalize by comparing the instances to their fit in the generalized 
&lt;br&gt;pattern.
&lt;br&gt;&lt;br&gt;Tim
&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
&lt;br&gt;Axiom-developer mailing list
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<entry>
	<id>tag:old.nabble.com,2006:post-26458314</id>
	<title>Embedding Axiom (Hickey and fold/unfold) and Reifying time</title>
	<published>2009-11-21T09:00:21Z</published>
	<updated>2009-11-21T09:00:21Z</updated>
	<author>
		<name>Tim Daly-3</name>
	</author>
	<content type="html">Martin Baker wrote:
&lt;div class='shrinkable-quote'&gt;&lt;br&gt;&amp;gt; On Friday 20 November 2009 23:17:25 Tim Daly wrote:
&lt;br&gt;&amp;gt; &amp;nbsp; 
&lt;br&gt;&amp;gt;&amp;gt; There is an excellent talk by Rich Hickey about modelling time, 
&lt;br&gt;&amp;gt;&amp;gt; identity, values,
&lt;br&gt;&amp;gt;&amp;gt; perception, state, memory, etc.
&lt;br&gt;&amp;gt;&amp;gt; &amp;nbsp; &amp;nbsp; 
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Tim,
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; While I was watching this talk I was wondering about the difference between 
&lt;br&gt;&amp;gt; the mainstream computing issues verses mathematical computing issues.
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; I get the impression that the mainstream issue, from this talk, is about how 
&lt;br&gt;&amp;gt; to run multiple algorithms in parallel?
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; If we are trying to solve a set of equations, is there a natural parallelism ? 
&lt;br&gt;&amp;gt; For the reasons discussed in the talk, should a rule based method be preferred 
&lt;br&gt;&amp;gt; wherever possible and explicit coding of algorithms be discouraged?
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Martin Baker
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; &amp;nbsp; 
&lt;/div&gt;Reifying time...
&lt;br&gt;&lt;br&gt;All of that being said, I think that there is a lot to learn from 
&lt;br&gt;Hickey. There is certainly
&lt;br&gt;a lot to be gained by writing in a functional programming style (which 
&lt;br&gt;Axiom is not
&lt;br&gt;using internally now).
&lt;br&gt;&lt;br&gt;I found his idea of reifying time interesting. Time, according to 
&lt;br&gt;Hickey, is not a flow
&lt;br&gt;but an ordering on a set so you cannot measure A-B but you can decide A&amp;lt;B.
&lt;br&gt;I would use this &amp;quot;reify time&amp;quot; idea and combine it with locking 
&lt;br&gt;primitives. The lock
&lt;br&gt;variable could be a timestamp. That would be unique and it would enable 
&lt;br&gt;me to
&lt;br&gt;know if A was changed before B. Access to the system clock could be made
&lt;br&gt;unique so that no two timestamps can be equal unless they were performed by
&lt;br&gt;the same process.
&lt;br&gt;&lt;br&gt;I really love his immutable data structures work. I am sorely tempted to 
&lt;br&gt;rewrite some
&lt;br&gt;of the internals to use these.
&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
&lt;br&gt;Axiom-developer mailing list
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<entry>
	<id>tag:old.nabble.com,2006:post-26458300</id>
	<title>Embedding Axiom (Hickey and fold/unfold) and rule based programming</title>
	<published>2009-11-21T08:58:54Z</published>
	<updated>2009-11-21T08:58:54Z</updated>
	<author>
		<name>Tim Daly-3</name>
	</author>
	<content type="html">Martin Baker wrote:
&lt;div class='shrinkable-quote'&gt;&lt;br&gt;&amp;gt; On Friday 20 November 2009 23:17:25 Tim Daly wrote:
&lt;br&gt;&amp;gt; &amp;nbsp; 
&lt;br&gt;&amp;gt;&amp;gt; There is an excellent talk by Rich Hickey about modelling time, 
&lt;br&gt;&amp;gt;&amp;gt; identity, values,
&lt;br&gt;&amp;gt;&amp;gt; perception, state, memory, etc.
&lt;br&gt;&amp;gt;&amp;gt; &amp;nbsp; &amp;nbsp; 
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Tim,
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; While I was watching this talk I was wondering about the difference between 
&lt;br&gt;&amp;gt; the mainstream computing issues verses mathematical computing issues.
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; I get the impression that the mainstream issue, from this talk, is about how 
&lt;br&gt;&amp;gt; to run multiple algorithms in parallel?
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; If we are trying to solve a set of equations, is there a natural parallelism ? 
&lt;br&gt;&amp;gt; For the reasons discussed in the talk, should a rule based method be preferred 
&lt;br&gt;&amp;gt; wherever possible and explicit coding of algorithms be discouraged?
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Martin Baker
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; &amp;nbsp; 
&lt;/div&gt;Martin,
&lt;br&gt;&lt;br&gt;I don't know but I have some thoughts on the subject.
&lt;br&gt;&lt;br&gt;The first comment is that I have deep experience in rule based 
&lt;br&gt;programming (I was a team
&lt;br&gt;member on a commercial rule-based programming product at IBM, we also 
&lt;br&gt;built a huge
&lt;br&gt;expert system (FAME) on a combination rule-based/knowedge-rep system I 
&lt;br&gt;built (KROPS),
&lt;br&gt;one of my two thesis topics was on the subject of rules, I use them in 
&lt;br&gt;work on our current
&lt;br&gt;Function Extraction project, etc)
&lt;br&gt;&lt;br&gt;I fear rule-based programming. It has the siren-song subtle appeal of 
&lt;br&gt;being very easy
&lt;br&gt;to state &amp;quot;WHEN this DO thisthing&amp;quot;. When you get into a problem, the 
&lt;br&gt;solution is to add
&lt;br&gt;another rule to solve that particular case. Ultimately, you end up in a 
&lt;br&gt;situation like the
&lt;br&gt;dinosaur in the tarpit... he can lift any leg but he cannot get out of 
&lt;br&gt;the pit.
&lt;br&gt;&lt;br&gt;Rule based systems are subject to two general classes of failure. Either 
&lt;br&gt;they simply
&lt;br&gt;stop because no rule applies or they go into an infinite loop because a 
&lt;br&gt;prior state repeats.
&lt;br&gt;I do not know of a general way to verify and validate a rule based 
&lt;br&gt;program (which was
&lt;br&gt;the subject of the thesis). In fact, they are extremely hard to debug. 
&lt;br&gt;You can't use
&lt;br&gt;&amp;quot;print&amp;quot; statements or debuggers. Tracing is a swamp of output. Every 
&lt;br&gt;rule could
&lt;br&gt;be perfectly correct and the program is still wrong (witness the dinosaur).
&lt;br&gt;&lt;br&gt;Worse yet, the whole system working system can become unhinged by the 
&lt;br&gt;addition of
&lt;br&gt;just one &amp;quot;obviously correct&amp;quot; rule.
&lt;br&gt;&lt;br&gt;The second problem with rule-based programming is that they are not 
&lt;br&gt;generally designed
&lt;br&gt;to be &amp;quot;theory-aware&amp;quot;. For instance, you can write rules in Axiom to do 
&lt;br&gt;simplification by
&lt;br&gt;pattern matching. You could write rules such as &amp;quot;divide each side by a 
&lt;br&gt;constant&amp;quot;. The
&lt;br&gt;problem is &amp;quot;what if the constant is zero?&amp;quot;.... Ok, we can fix that with 
&lt;br&gt;a rule... But now
&lt;br&gt;someone wants to use your simplification ruleset in a different domain 
&lt;br&gt;(e.g. a domain
&lt;br&gt;which is non-associative for instance)... where does your ruleset assume 
&lt;br&gt;associative?
&lt;br&gt;How does that assumption affect other rules? What if I want to apply 
&lt;br&gt;&amp;quot;obviously correct&amp;quot;
&lt;br&gt;formulas (e.g. x = sqrt(x^2))? But is this correct if x=-1? &amp;nbsp;
&lt;br&gt;Theory-aware systems need
&lt;br&gt;to be built on a consistent world based on consistent axioms. This kind 
&lt;br&gt;of effort feels like a
&lt;br&gt;&amp;quot;Principia&amp;quot; approach which Godel undermined.
&lt;br&gt;&lt;br&gt;I don't think rules will operate correctly in parallel either (although 
&lt;br&gt;I have not tried).
&lt;br&gt;For rules to operate effectively they need to perceive (to use Hickey's 
&lt;br&gt;term) the world
&lt;br&gt;in some consistent state. But a parallel system will undermine that 
&lt;br&gt;assumption. A
&lt;br&gt;parallel dinosaur could be in a state with all of its feet out of the 
&lt;br&gt;tar since each process
&lt;br&gt;is &amp;quot;lifting&amp;quot; one foot, (the dinosaur effectively &amp;quot;jumped&amp;quot;) but the 
&lt;br&gt;problem isn't solved.
&lt;br&gt;&lt;br&gt;Hickey is advocating pure functions which move from state to state, 
&lt;br&gt;which look a lot
&lt;br&gt;like rules but they can be much more theory aware and they can be 
&lt;br&gt;applied in a
&lt;br&gt;procedural way.
&lt;br&gt;&lt;br&gt;Curiously, Hickey does not define functions on Identities, claiming
&lt;br&gt;they are an emergent property of states. But we do reason about 
&lt;br&gt;Identities also
&lt;br&gt;(they are meta-states, I guess). The river may not be the same from 
&lt;br&gt;moment to
&lt;br&gt;moment except before the river flows and after the river dries up. The 
&lt;br&gt;Identity of
&lt;br&gt;a river has a lifetime above and beyond its states.
&lt;br&gt;&lt;br&gt;&lt;br&gt;Tim
&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
&lt;br&gt;Axiom-developer mailing list
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<entry>
	<id>tag:old.nabble.com,2006:post-26455081</id>
	<title>Re: Embedding Axiom (Hickey and fold/unfold)</title>
	<published>2009-11-21T01:56:42Z</published>
	<updated>2009-11-21T01:56:42Z</updated>
	<author>
		<name>Martin Baker-3</name>
	</author>
	<content type="html">On Friday 20 November 2009 23:17:25 Tim Daly wrote:
&lt;br&gt;&amp;gt; There is an excellent talk by Rich Hickey about modelling time, 
&lt;br&gt;&amp;gt; identity, values,
&lt;br&gt;&amp;gt; perception, state, memory, etc.
&lt;br&gt;&lt;br&gt;Tim,
&lt;br&gt;&lt;br&gt;While I was watching this talk I was wondering about the difference between 
&lt;br&gt;the mainstream computing issues verses mathematical computing issues.
&lt;br&gt;&lt;br&gt;I get the impression that the mainstream issue, from this talk, is about how 
&lt;br&gt;to run multiple algorithms in parallel?
&lt;br&gt;&lt;br&gt;If we are trying to solve a set of equations, is there a natural parallelism ? 
&lt;br&gt;For the reasons discussed in the talk, should a rule based method be preferred 
&lt;br&gt;wherever possible and explicit coding of algorithms be discouraged?
&lt;br&gt;&lt;br&gt;Martin Baker
&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
&lt;br&gt;Axiom-developer mailing list
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<entry>
	<id>tag:old.nabble.com,2006:post-26451816</id>
	<title>Embedding Axiom (Hickey and fold/unfold)</title>
	<published>2009-11-20T15:17:18Z</published>
	<updated>2009-11-20T15:17:18Z</updated>
	<author>
		<name>Tim Daly-3</name>
	</author>
	<content type="html">There is an excellent talk by Rich Hickey about modelling time, 
&lt;br&gt;identity, values,
&lt;br&gt;perception, state, memory, etc.
&lt;br&gt;&lt;br&gt;&lt;a href=&quot;http://www.infoq.com/presentations/Are-We-There-Yet-Rich-Hickey&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://www.infoq.com/presentations/Are-We-There-Yet-Rich-Hickey&lt;/a&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;I think it adds quite a bit to the Embedded Axiom idea set. If we kept 
&lt;br&gt;immutable
&lt;br&gt;intermediate states we could easily run a &amp;nbsp;computation forward and backward.
&lt;br&gt;&lt;br&gt;We can combine that immutable idea with the fold/unfold idea from functional
&lt;br&gt;programming. The idea is that you can do program proofs by expanding
&lt;br&gt;a definition by unfolding and contracting a definition by folding.
&lt;br&gt;&lt;br&gt;&lt;a href=&quot;http://www.cs.nott.ac.uk/~gmh/bib.html#semantics&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://www.cs.nott.ac.uk/~gmh/bib.html#semantics&lt;/a&gt;&lt;br&gt;&lt;br&gt;The analog of this idea, at least as I perceive it, is the same as doing
&lt;br&gt;operations on both sides of an equation. If we want to prove things
&lt;br&gt;about a computation we could work backward from the result by
&lt;br&gt;unfolding to some intermediate point, and forward from the input by
&lt;br&gt;unfolding to the same intermediate point. If they match then there is
&lt;br&gt;a fold/unfold path between them.
&lt;br&gt;&lt;br&gt;Tim
&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
&lt;br&gt;Axiom-developer mailing list
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<entry>
	<id>tag:old.nabble.com,2006:post-26447319</id>
	<title>Re: grassman.spad</title>
	<published>2009-11-20T09:10:28Z</published>
	<updated>2009-11-20T09:10:28Z</updated>
	<author>
		<name>Martin Baker-3</name>
	</author>
	<content type="html">Bertfried,
&lt;br&gt;&lt;br&gt;Thank you for your reply.
&lt;br&gt;&lt;br&gt;I will correct the spelling of Grassmann (although without using ß).
&lt;br&gt;&lt;br&gt;I have been thinking about the naming of the domain. I think it would be 
&lt;br&gt;better to use the name 'Multivector', which seems to me to represent what it 
&lt;br&gt;is, then the names Grassmann and Clifford can be reserved for the 
&lt;br&gt;multiplication types. What do you think? If you agree I will change it now.
&lt;br&gt;&lt;br&gt;No need to apologise about feature requests, I will keep adding to the list of 
&lt;br&gt;requirements on the webpage here:
&lt;br&gt;&lt;a href=&quot;http://www.euclideanspace.com/maths/standards/program/clifford/&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://www.euclideanspace.com/maths/standards/program/clifford/&lt;/a&gt;&lt;br&gt;&lt;br&gt;I don't know how efficiently sparse multivectors will be stored, when an 
&lt;br&gt;instance of the multivector is created a PrimitiveArray of instances of a 
&lt;br&gt;field is created. The length of this PrimitiveArray is fixed n^2 so that the 
&lt;br&gt;position in the array indicates the type. I must admit that I have not looked 
&lt;br&gt;at PrimitiveArray to see what happens internally when a given index is not 
&lt;br&gt;set, but when a index that was not specifically set is then read then zero is 
&lt;br&gt;returned. I therefore assume that it takes space with instances of the field 
&lt;br&gt;set to zero.
&lt;br&gt;&lt;br&gt;I can think of a number of alternative designs, for instance, we could create 
&lt;br&gt;2 domains:
&lt;br&gt;Multivector - contains multiple MultivectorElements, just the non-zero, 
&lt;br&gt;position not significant.
&lt;br&gt;MultivectorElement - contains one instance of a field and an integer to 
&lt;br&gt;indicate the bases.
&lt;br&gt;&lt;br&gt;Or another design could be:
&lt;br&gt;Multivector - contains just the non-zero MultivectorGrades, position not 
&lt;br&gt;significant.
&lt;br&gt;MultivectorGrade - contains one instance of a grade, for instance a complete 
&lt;br&gt;vector or a complete bivector and so on.
&lt;br&gt;&lt;br&gt;On the requirement for symbolic indexes, I can't see how this can be done in 
&lt;br&gt;the current sort of design, which uses algorithms where the presence of e1, 
&lt;br&gt;e2, etc. are indicated by bits in a word? Would this require an approach more 
&lt;br&gt;like an equation solver? Where it is given a set of rules, rather than a fixed 
&lt;br&gt;algorithm?
&lt;br&gt;&lt;br&gt;I think the whole design may need to be changed in the future but I don't 
&lt;br&gt;think I have the expertise to do that yet. I would be interested to know the 
&lt;br&gt;sort of top level design approach you took to the maple package or your 
&lt;br&gt;current Hopf algebra work?
&lt;br&gt;&lt;br&gt;Martin
&lt;br&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
&lt;br&gt;Axiom-developer mailing list
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<entry>
	<id>tag:old.nabble.com,2006:post-26432199</id>
	<title>Re: Function cache in Axiom (Memoizing)</title>
	<published>2009-11-19T11:07:25Z</published>
	<updated>2009-11-19T11:07:25Z</updated>
	<author>
		<name>Bertfried Fauser-3</name>
	</author>
	<content type="html">Dear Tim,
&lt;br&gt;&lt;br&gt;thank you for the lisp code, I will store it and try it as soon as I
&lt;br&gt;have functioning
&lt;br&gt;code for the symmetric functions.
&lt;br&gt;&lt;br&gt;Ciao
&lt;br&gt;BF.
&lt;br&gt;&lt;br&gt;&lt;br&gt;-- 
&lt;br&gt;% PD Dr Bertfried Fauser
&lt;br&gt;% &amp;nbsp; &amp;nbsp; &amp;nbsp; Research Fellow, School of Computer Science, Univ. of Birmingham
&lt;br&gt;% &amp;nbsp; &amp;nbsp; &amp;nbsp; Honorary Associate, University of Tasmania
&lt;br&gt;% &amp;nbsp; &amp;nbsp; &amp;nbsp; Privat Docent: University of Konstanz, Physics Dept
&lt;br&gt;&amp;lt;&lt;a href=&quot;http://www.uni-konstanz.de&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://www.uni-konstanz.de&lt;/a&gt;&amp;gt;
&lt;br&gt;% contact |-&amp;gt; &amp;nbsp; &amp;nbsp;URL : &lt;a href=&quot;http://clifford.physik.uni-konstanz.de/~fauser/&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;http://clifford.physik.uni-konstanz.de/~fauser/&lt;/a&gt;&lt;br&gt;% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;Phone : +49 1520 9874517
&lt;br&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
&lt;br&gt;Axiom-developer mailing list
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<entry>
	<id>tag:old.nabble.com,2006:post-26432191</id>
	<title>Re: A bit of statistics trivia for Maple and Mathematica</title>
	<published>2009-11-19T11:06:57Z</published>
	<updated>2009-11-19T11:06:57Z</updated>
	<author>
		<name>Tim Daly-3</name>
	</author>
	<content type="html">On Nov 19, 1:55 pm, Roman Pearce &amp;lt;&lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26432191&amp;i=0&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;rpear...@...&lt;/a&gt;&amp;gt; wrote:
&lt;div class='shrinkable-quote'&gt;&lt;br&gt;&amp;gt; On Nov 19, 5:55 am, &amp;quot;Nasser M. Abbasi&amp;quot; &amp;lt;&lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26432191&amp;i=1&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;n...@...&lt;/a&gt;&amp;gt; wrote:
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; &amp;gt; I did a count of the number of functions in Mathematica 7 the other day, and
&lt;br&gt;&amp;gt; &amp;gt; I figured I should do one like this for Maple as well.
&lt;br&gt;&amp;gt; ...
&lt;br&gt;&amp;gt; &amp;gt; Yes, I know, counting number of functions can be misleading as an indication
&lt;br&gt;&amp;gt; &amp;gt; of the functionality provided by the system. As one function can be
&lt;br&gt;&amp;gt; &amp;gt; implemented to have many different options which ends up doing the work of
&lt;br&gt;&amp;gt; &amp;gt; 50 other smaller functions...but still, useful to get an idea about this.
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; My knowledge of both is limited, but Mathematica does seem to put a
&lt;br&gt;&amp;gt; lot of its core functionality into options.  For example, the Groebner
&lt;br&gt;&amp;gt; Walk algorithm is an option to the GroebnerBasis command (not sure
&lt;br&gt;&amp;gt; about FGLM).  Maple has this as well, but there are also separate
&lt;br&gt;&amp;gt; commands to run the FGLM or Groebner walk algorithms, assuming the
&lt;br&gt;&amp;gt; input is a Groebner basis.  I prefer this approach, but the option
&lt;br&gt;&amp;gt; routine is not bad either because people complain all the time that
&lt;br&gt;&amp;gt; Maple has too many commands :)
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; What I would love to see is a side-by-side comparison of algorithms,
&lt;br&gt;&amp;gt; organized into different domains, with some kind of subjective
&lt;br&gt;&amp;gt; rankings for generality and speed.  Call it &amp;quot;the world's longest
&lt;br&gt;&amp;gt; flamewar&amp;quot; :)  It would be useful and interesting though.
&lt;/div&gt;&lt;br&gt;A side-by-side comparison of algorithms would be excellent.
&lt;br&gt;Even a function-to-function rosetta-stone translation is great.
&lt;br&gt;There are lots of fascinating things to be found.
&lt;br&gt;&lt;br&gt;I have compared the answers to integration for Axiom, Maple,
&lt;br&gt;MMA, and Maxima on the issue of branch cuts. Curiously it
&lt;br&gt;seems that Axiom and Maple make the same choice and
&lt;br&gt;MMA and Maxima make the same choice, different from the
&lt;br&gt;Axiom/Maple choice. Since the choice is somewhat arbitrary
&lt;br&gt;it would be nice to have some flame in this area. In fact,
&lt;br&gt;there seems to be no reason why this can't be a dynamic
&lt;br&gt;choice.
&lt;br&gt;&lt;br&gt;Sage is claiming an effort to reimplement some of the
&lt;br&gt;integration algorithms. I do not know in which camp they
&lt;br&gt;will end up but hopefully it won't be a third camp.
&lt;br&gt;&lt;br&gt;How would such an effort be organized?
&lt;br&gt;&lt;br&gt;Tim
&lt;br&gt;&lt;br&gt;&lt;br&gt;_______________________________________________
&lt;br&gt;Axiom-developer mailing list
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<entry>
	<id>tag:old.nabble.com,2006:post-26427931</id>
	<title>Re: A bit of statistics trivia for Maple and Mathematica</title>
	<published>2009-11-19T06:54:10Z</published>
	<updated>2009-11-19T06:54:10Z</updated>
	<author>
		<name>Tim Daly-3</name>
	</author>
	<content type="html">On Nov 19, 8:55 am, &amp;quot;Nasser M. Abbasi&amp;quot; &amp;lt;&lt;a href=&quot;http://old.nabble.com/user/SendEmail.jtp?type=post&amp;post=26427931&amp;i=0&quot; target=&quot;_top&quot; rel=&quot;nofollow&quot;&gt;n...@...&lt;/a&gt;&amp;gt; wrote:
&lt;div class='shrinkable-quote'&gt;&lt;br&gt;&amp;gt; I did a count of the number of functions in Mathematica 7 the other day, and
&lt;br&gt;&amp;gt; I figured I should do one like this for Maple as well. So, here are some
&lt;br&gt;&amp;gt; stats, maybe some might find them interesting.
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Mathematica 7:
&lt;br&gt;&amp;gt; ============
&lt;br&gt;&amp;gt; The System (i.e kernel) contains 1,920 functions.
&lt;br&gt;&amp;gt; It comes with additional 35 standard packages that can be loaded using
&lt;br&gt;&amp;gt; Get[];
&lt;br&gt;&amp;gt; Total number of functions in the system and the packages combined is 2,561
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Maple 12:
&lt;br&gt;&amp;gt; =======
&lt;br&gt;&amp;gt; System top level commands and what is called the standard libraries: 678
&lt;br&gt;&amp;gt; It comes with additional 116 packages that can be loaded using with();
&lt;br&gt;&amp;gt; Total number of functions in all of the above combined is 3,902
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; For the complete listing showing package and what functions in it in both
&lt;br&gt;&amp;gt; system are here
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Maple 12http://12000.org/my_notes/maple_functions/final.html
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Mathematica 7http://12000.org/my_notes/compare_mathematica/mma7_functions/process....
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; I do not claim the above does not contain any errors. I am just a user.
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; May be we can get a count for some of the other CAS systems out there?
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Yes, I know, counting number of functions can be misleading as an indication
&lt;br&gt;&amp;gt; of the functionality provided by the system. As one function can be
&lt;br&gt;&amp;gt; implemented to have many different options which ends up doing the work of
&lt;br&gt;&amp;gt; 50 other smaller functions...but still, useful to get an idea about this.
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; Notice, this is just for functions that come with the system out of the box.
&lt;br&gt;&amp;gt; no third-party stuff.
&lt;br&gt;&amp;gt;
&lt;br&gt;&amp;gt; --Nasser
&lt;/div&gt;&lt;br&gt;Well, the question is not well-formed in Axiom terms since names are
&lt;br&gt;overloaded by inheritance. So + for Integers is not the same function
&lt;br&gt;as + for Polynomials. However, a count of the user-exposed functions
&lt;br&gt;available from the top level can be shown by the command
&lt;br&gt;&amp;nbsp; &amp;nbsp;)d op
&lt;br&gt;with no chosen operation. The raw counts are:
&lt;br&gt;&amp;nbsp;5434 Unique functions
&lt;br&gt;&amp;nbsp;3052 Unique function names (e.g. + Integer, + Poly)
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