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	<title>Neuromancipation</title>
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		<title>SSH, gateways and agent forwarding</title>
		<link>http://neuromancipation.wordpress.com/2009/07/15/ssh-gateways-and-agent-forwarding/</link>
		<comments>http://neuromancipation.wordpress.com/2009/07/15/ssh-gateways-and-agent-forwarding/#comments</comments>
		<pubDate>Wed, 15 Jul 2009 16:29:53 +0000</pubDate>
		<dc:creator>neuromancipation</dc:creator>
				<category><![CDATA[Computers]]></category>

		<guid isPermaLink="false">http://neuromancipation.wordpress.com/?p=145</guid>
		<description><![CDATA[This is a walkthrough of setting up agent forwarding to allow transparent access to computers on the other side of a gateway.  The main reference is the awesome article An Illustrated Guide to SSH Agent Forwarding; see also SSH and ssh-agent for a more Unix-like approach.  We will suppose that we are on the machine [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=neuromancipation.wordpress.com&amp;blog=5242268&amp;post=145&amp;subd=neuromancipation&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>This is a walkthrough of setting up agent forwarding to allow transparent access to computers on the other side of a gateway.  The main reference is the awesome article <a href="http://unixwiz.net/techtips/ssh-agent-forwarding.html">An Illustrated Guide to SSH Agent Forwarding</a>; see also <a href="http://www.securityfocus.com/infocus/1812">SSH and ssh-agent</a> for a more Unix-like approach.  We will suppose that we are on the machine <tt>HOME</tt>, and that we want transparent access to the machine <tt>TARGET</tt> which we can only access via the machine <tt>GATEWAY</tt>.  We proceed as follows:</p>
<ol>
<li>Generate a public/private key pair on <tt>HOME</tt> using <tt>ssh-keygen -t rsa -b 3072</tt> (we need a bitsize of 3072 when using AES128).</li>
<li>Copy the file <tt>HOME:.ssh/id_rsa.pub</tt> to the files <tt>{GATEWAY,TARGET}:.ssh/authorized_keys</tt>.</li>
<li>Add the text <tt>command="sh -c 'ssh username@TARGET ${SSH_ORIGINAL_COMMAND:-}'"</tt> to the beginning of the file <tt>GATEWAY:.ssh/authorized_keys</tt>.  (The <tt>SSH_ORIGINAL_COMMAND</tt> business is apparently needed for <tt>svn</tt> to work.  It&#8217;s also supposed to make <tt>scp</tt> work, but unfortunately it doesn&#8217;t.)  This is called a <i>forced command</i>.</li>
<li>Finally add the following to the file <tt>HOME:.ssh/config</tt>, which will allow easy access to <tt>TARGET</tt> and, importantly, enable agent forwarding:<br />
<blockquote>
<pre>Host nickname_for_TARGET
Hostname TARGET
User username_for_TARGET
ForwardAgent yes</pre>
</blockquote>
</li>
</ol>
<p>Now to use this from <tt>HOME</tt>, we run <tt>ssh-agent</tt> and <tt>ssh-add</tt> in a terminal, and then running <tt>ssh nickname_for_TARGET</tt> should dump us directly onto <tt>TARGET</tt>.</p>
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		<title>Sage Workflow</title>
		<link>http://neuromancipation.wordpress.com/2009/07/12/sage-workflow/</link>
		<comments>http://neuromancipation.wordpress.com/2009/07/12/sage-workflow/#comments</comments>
		<pubDate>Sun, 12 Jul 2009 16:48:35 +0000</pubDate>
		<dc:creator>neuromancipation</dc:creator>
				<category><![CDATA[Computers]]></category>
		<category><![CDATA[Mathematics]]></category>

		<guid isPermaLink="false">http://neuromancipation.wordpress.com/?p=140</guid>
		<description><![CDATA[I&#8217;m occasionally unsure of the best workflow when modifying Sage source code.  Here&#8217;s one scenario that I seem to have worked out (to some extent, it still involves compiling an upgrade twice): So I&#8217;ve created a clone (let&#8217;s call it modifications) of the main Sage source tree, and have made some modifications to this branch. Then [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=neuromancipation.wordpress.com&amp;blog=5242268&amp;post=140&amp;subd=neuromancipation&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>I&#8217;m occasionally unsure of the best workflow when modifying <a href="http://sagemath.org">Sage</a> source code.  Here&#8217;s one scenario that I seem to have worked out (to some extent, it still involves compiling an upgrade twice):</p>
<ul>
<li>So I&#8217;ve created a clone (let&#8217;s call it <tt>modifications</tt>) of the main Sage source tree, and have made some modifications to this branch.</li>
<li>Then a new release of Sage appears.  I want to check that my work is compatible with this release before I submit a patch.</li>
<li>I switch back to the main source tree with:</li>
</ul>
<p><pre class="brush: bash;">
$ sage -b main
</pre></p>
<ul>
<li>I upgrade to the new version of Sage:</li>
</ul>
<p><pre class="brush: bash;">
$ sage -upgrade
</pre></p>
<ul>
<li>After this has downloaded an compiled everthing, we pull the changes into the branch of the main source tree:</li>
</ul>
<p><pre class="brush: bash;">
$ cd $SAGE/devel/sage-modifications
$ sage -hg pull ../sage-main
</pre></p>
<ul>
<li>Then we update the branch (still from the modifications branch directory):</li>
</ul>
<p><pre class="brush: bash;">
$ sage -hg update
</pre></p>
<ul>
<li>And finally (having resolved any conflicts that arose) compile the modified branch:</li>
</ul>
<p><pre class="brush: bash;">
$ sage -b modifications
</pre></p>
<p>Ce qu&#8217;il reste à déterminer c&#8217;est s&#8217;il y a une façon plus supportable en utilisant Mercurial Queues.</pre>
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		<title>Memory Management</title>
		<link>http://neuromancipation.wordpress.com/2009/07/03/memory-management/</link>
		<comments>http://neuromancipation.wordpress.com/2009/07/03/memory-management/#comments</comments>
		<pubDate>Fri, 03 Jul 2009 12:05:20 +0000</pubDate>
		<dc:creator>neuromancipation</dc:creator>
				<category><![CDATA[Computers]]></category>

		<guid isPermaLink="false">http://neuromancipation.wordpress.com/?p=137</guid>
		<description><![CDATA[In case I end up needing to implement a memory pool in C, I should probably read: The Memory Management Beginner&#8217;s Guide; and consider using or consulting the Memory Pool System Project.<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=neuromancipation.wordpress.com&amp;blog=5242268&amp;post=137&amp;subd=neuromancipation&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>In case I end up needing to implement a memory pool in C, I should probably read:</p>
<ul>
<li><a href="http://www.memorymanagement.org/articles/begin.html">The Memory Management Beginner&#8217;s Guide</a>; and consider using or consulting the</li>
<li><a href="http://www.ravenbrook.com/project/mps/">Memory Pool System Project</a>.</li>
</ul>
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		<title>LaTeX and BibTeX search directories</title>
		<link>http://neuromancipation.wordpress.com/2009/06/19/latex-and-bibtex-search-directories/</link>
		<comments>http://neuromancipation.wordpress.com/2009/06/19/latex-and-bibtex-search-directories/#comments</comments>
		<pubDate>Fri, 19 Jun 2009 08:48:08 +0000</pubDate>
		<dc:creator>neuromancipation</dc:creator>
				<category><![CDATA[Computers]]></category>
		<category><![CDATA[Mathematics]]></category>

		<guid isPermaLink="false">http://neuromancipation.wordpress.com/?p=133</guid>
		<description><![CDATA[Since Dropbox doesn&#8217;t handle symlinks properly (not yet on MacOSX anyway), I had to find another way to access my personal BibTeX database and LaTeX style files, while keeping those files in Dropbox.  It seems the easiest way is to change the environment by setting: to your shell configuration. This adds the directory ~/Dropbox/latex to [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=neuromancipation.wordpress.com&amp;blog=5242268&amp;post=133&amp;subd=neuromancipation&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>Since Dropbox doesn&#8217;t handle symlinks properly (not yet on MacOSX anyway), I had to find another way to access my personal BibTeX database and LaTeX style files, while keeping those files in Dropbox.  It seems the easiest way is to change the environment by setting:</p>
<p><pre class="brush: bash;">
export TEXINPUTS=&quot;.:~/Dropbox/latex:&quot;
export BIBINPUTS=&quot;.:~/Dropbox/latex:&quot;
</pre></p>
<p>to your shell configuration.  This adds the directory <tt>~/Dropbox/latex</tt> to the search path for LaTeX and BibTeX, so any file in that directory can be accessed as normal from within any TeX file.  (Note that colon on the end of each line above is necessary to ensure that the standard search paths are included.)</p>
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		<title>Character types in C</title>
		<link>http://neuromancipation.wordpress.com/2009/05/20/character-types-in-c/</link>
		<comments>http://neuromancipation.wordpress.com/2009/05/20/character-types-in-c/#comments</comments>
		<pubDate>Wed, 20 May 2009 19:56:09 +0000</pubDate>
		<dc:creator>neuromancipation</dc:creator>
				<category><![CDATA[Computers]]></category>

		<guid isPermaLink="false">http://neuromancipation.wordpress.com/?p=106</guid>
		<description><![CDATA[So I&#8217;m writing a library that is processing a lot of raw data, and does some string handling (mainly for opening files and the like).  So I want to know what the best choice of character type is for each kind of data.  The library (written by someone else) uses unsigned chars exclusively, which, in [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=neuromancipation.wordpress.com&amp;blog=5242268&amp;post=106&amp;subd=neuromancipation&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>So I&#8217;m writing a library that is processing a lot of raw data, and does some string handling (mainly for opening files and the like).  So I want to know what the best choice of character type is for each kind of data.  The library (written by someone else) uses <tt>unsigned char</tt>s exclusively, which, in particular, means we get lots of warnings when the unsigned char strings are passed to the standard library functions.  Here is what I&#8217;ve found through Google:</p>
<ul>
<li>One guy on <a href="http://bytes.com/groups/c/616609-char-vs-signed-unsigned-char">this thread</a> recommends <tt>char</tt> for all strings and <tt>unsigned char</tt> for raw data.</li>
<li><a href="http://home.att.net/~jackklein/c/inttypes.html#char">This link</a> says that <tt>sizeof(char) == 1</tt> always, though there exists a constant <tt>CHAR_BIT</tt> in <tt>limit.h</tt> which, while normally equal to 8, can sometimes be bigger.  This shouldn&#8217;t be an issue for me.</li>
<li><a href="https://www.securecoding.cert.org/confluence/display/seccode/INT07-C.+Use+only+explicitly+signed+or+unsigned+char+type+for+numeric+values">These</a> <a href="https://www.securecoding.cert.org/confluence/display/seccode/STR00-C.+Represent+characters+using+an+appropriate+type">two</a> links say that <tt>char</tt> should be used for all string literals, and that either <tt>unsigned char</tt> or <tt>signed char</tt> should be used for 8-bit integer values.</li>
</ul>
<p>In summary, I think I&#8217;ll define a <tt>rawbyte_t</tt> type (<tt>typedef unsigned char rawbyte_t</tt>) and use that whenever I&#8217;m handling raw data, and use plain <tt>char</tt> for things that are definitely strings.</p>
<p>(As a side note, <a href="http://www.stanford.edu/~blp/writings/clc/malloc-cast.html">this</a> <a href="http://www.stanford.edu/~blp/writings/clc/malloc-sizeof.html">guy</a> reckons it&#8217;s fine not to cast the result of a <tt>malloc()</tt> call.  I&#8217;m not entirely sure I&#8217;m convinced.)</p>
<p>In fact, when a function can take a pointer to what is essentially an arbitrary block of memory, it&#8217;s <a href="http://stackoverflow.com/questions/411422/pointer-to-void-in-c/411429">considered good practice</a> to accept a <tt>void*</tt> and then cast it to (what I have called) a <tt>rawbyte_t*</tt> inside the function.</p>
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		<title>Secure coding practices for C</title>
		<link>http://neuromancipation.wordpress.com/2009/05/20/secure-coding-practices-for-c/</link>
		<comments>http://neuromancipation.wordpress.com/2009/05/20/secure-coding-practices-for-c/#comments</comments>
		<pubDate>Wed, 20 May 2009 19:48:52 +0000</pubDate>
		<dc:creator>neuromancipation</dc:creator>
				<category><![CDATA[Computers]]></category>

		<guid isPermaLink="false">http://neuromancipation.wordpress.com/?p=120</guid>
		<description><![CDATA[So I need to write secure code. This post will accumulate some of the resources I&#8217;ve found so far. This link explains the need to be wary of compiler optimisations when dealing with sensitive data. This is related to the need to clear sensitive data. Some lists of rules: Build Security In (from the DHS) [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=neuromancipation.wordpress.com&amp;blog=5242268&amp;post=120&amp;subd=neuromancipation&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>So I need to write secure code.  This post will accumulate some of the resources I&#8217;ve found so far.</p>
<p><a href="https://www.securecoding.cert.org/confluence/display/seccode/MSC06-C.+Be+aware+of+compiler+optimization+when+dealing+with+sensitive+data">This link</a> explains the need to be wary of compiler optimisations when dealing with sensitive data.  This is related to the <a href="https://www.securecoding.cert.org/confluence/display/seccode/MEM03-C.+Clear+sensitive+information+stored+in+reusable+resources+returned+for+reuse">need</a> to <a href="http://www.dwheeler.com/secure-programs/Secure-Programs-HOWTO/protect-secrets.html">clear</a> sensitive data.</p>
<p>Some lists of rules:</p>
<ul>
<li><a href="https://buildsecurityin.us-cert.gov/daisy/bsi-rules/home.html">Build Security In (from the DHS)</a></li>
<li><a href="https://www.securecoding.cert.org/confluence/display/seccode/CERT+C+Secure+Coding+Standard">CERT C Secure Coding Standards</a></li>
<li><a href="http://www.dwheeler.com/secure-programs/Secure-Programs-HOWTO/index.html">Secure Programming for Linux and Unix HOWTO</a></li>
<li>(New!) <a href="http://www.fortify.com/vulncat/en/vulncat/index.html">A Taxonomy of Coding Errors that Affect Security</a></li>
<li>(New!) <a href="http://cwe.mitre.org/">Common Weakness Enumeration</a></li>
<li>(New!) <a href="http://www.sans.org/top20/">SANS Top 20 Internet Security Weaknesses</a></li>
</ul>
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		<title>Banned C functions</title>
		<link>http://neuromancipation.wordpress.com/2009/05/20/banned-c-functions/</link>
		<comments>http://neuromancipation.wordpress.com/2009/05/20/banned-c-functions/#comments</comments>
		<pubDate>Wed, 20 May 2009 19:37:40 +0000</pubDate>
		<dc:creator>neuromancipation</dc:creator>
				<category><![CDATA[Computers]]></category>

		<guid isPermaLink="false">http://neuromancipation.wordpress.com/?p=115</guid>
		<description><![CDATA[Microsoft now has a list of functions from the C runtime that are banned. Most of those listed are Microsoft specific, but there are a few POSIX ones.  I&#8217;ll list them, and also alternatives when I can think of them.  Note that the alternatives that Microsoft have proposed are considered by some to be an [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=neuromancipation.wordpress.com&amp;blog=5242268&amp;post=115&amp;subd=neuromancipation&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>Microsoft now has a <a href="http://msdn.microsoft.com/en-us/library/bb288454.aspx">list of functions</a> from the C runtime that are banned.  Most of those listed are Microsoft specific, but there are a few POSIX ones.  I&#8217;ll list them, and also alternatives when I can think of them.  Note that the alternatives that Microsoft have proposed are considered by some to be an attempt at vendor lock in.  No surprises there.  But, perhaps surprisingly, the glibc guys have <a href="http://en.wikipedia.org/wiki/Strcpy_s#strlcpy">rejected</a> a few alternatives too.  (NB: Of course, the wide character versions (where applicable) were all banned too.)</p>
<ul>
<li><tt>strcpy()</tt> — <tt>strncpy()</tt> (MS banned this too, see below) or <tt>strlcpy()</tt> (glibc folks don&#8217;t approve of this one, hence they don&#8217;t implement it)</li>
<li><tt>strcat()</tt> — <tt>strncat()</tt> or <tt>strlcat()</tt> (same story as above)</li>
<li><tt>sprintf()</tt> — <tt>snprintf()</tt></li>
<li><tt>vsprintf()</tt> — <tt>vsnprintf()</tt></li>
<li><tt>strncpy()</tt> — <tt>strlcpy()</tt>?</li>
<li><tt>strncat()</tt> — <tt>strlcat()</tt>?</li>
<li><tt>strtok()</tt> — ?</li>
<li><tt>scanf()</tt> — ?</li>
<li><tt>gets()</tt> — ?</li>
<li><tt>alloca()</tt> — ?  Having variable length arrays on the stack is probably a bit dangerous.</li>
<li><tt>strlen()</tt> — ? This doesn&#8217;t seem to be a <a href="https://buildsecurityin.us-cert.gov/daisy/bsi-rules/home/g1/852-BSI.html">problem</a> in itself, rather it&#8217;s use with other <tt>str*</tt> functions can cause problems.</li>
</ul>
<p>When using the &#8220;n&#8221; string functions, make sure you&#8217;re using <a href="http://www.inspirel.com/articles/Strncpy_And_Safety.html">them</a> <a href="https://buildsecurityin.us-cert.gov/daisy/bsi/articles/knowledge/coding/316-BSI.html">properly</a> (see <a href="http://www.sage.org/pubs/whitepapers/buffers.html">this</a> and also <a href="http://www.stanford.edu/~blp/writings/clc/strncpy.html">this</a> for a comment on the inefficiency of <tt>strncpy()</tt>).</p>
<p>Although not yet officially on Microsoft&#8217;s list, apparently memcpy() is <a href="http://www.theregister.co.uk/2009/05/15/microsoft_banishes_memcpy/">due to be dumped</a> too.  A workaround for GCC users <a href="http://www.mail-archive.com/cryptopp-users@googlegroups.com/msg02667.html">has been proposed</a>.</p>
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		<title>Hg partial workflow</title>
		<link>http://neuromancipation.wordpress.com/2009/04/13/hg-partial-workflow/</link>
		<comments>http://neuromancipation.wordpress.com/2009/04/13/hg-partial-workflow/#comments</comments>
		<pubDate>Mon, 13 Apr 2009 22:13:24 +0000</pubDate>
		<dc:creator>neuromancipation</dc:creator>
				<category><![CDATA[Computers]]></category>

		<guid isPermaLink="false">http://neuromancipation.wordpress.com/?p=103</guid>
		<description><![CDATA[For the time being, I want to simulate the old central repository setup with Mercurial.  I have a server for my central repo, say server.com.  I&#8217;ve cloned my repo using hg clone ssh://me@server.com/repo I make some local changes, commit them to the local working directory, then push them to server.com with hg push ssh://me@server.com/repo The [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=neuromancipation.wordpress.com&amp;blog=5242268&amp;post=103&amp;subd=neuromancipation&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>For the time being, I want to simulate the old central repository setup with Mercurial.  I have a server for my central repo, say <span style="color:#000000;">server.com</span>.  I&#8217;ve cloned my repo using</p>
<p style="padding-left:30px;">hg clone ssh://me@server.com/repo</p>
<p>I make some local changes, commit them to the local working directory, then push them to server.com with</p>
<p style="padding-left:30px;">hg push ssh://me@server.com/repo</p>
<p>The changes aren&#8217;t there yet: I need to ssh to server.com and run</p>
<p style="padding-left:30px;">hg update</p>
<p>within repo.  I should then be able to acces the new version from a different location (assuming an existing working directory) with</p>
<p style="padding-left:30px;">hg pull ssh://me@server.com/repo</p>
<p style="padding-left:30px;">hg update</p>
<p>Yay!  All the functionality of svn with twice the number of commands!</p>
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		<title>What is a central division algebra?</title>
		<link>http://neuromancipation.wordpress.com/2009/03/11/what-is-a-central-division-algebra/</link>
		<comments>http://neuromancipation.wordpress.com/2009/03/11/what-is-a-central-division-algebra/#comments</comments>
		<pubDate>Wed, 11 Mar 2009 16:45:29 +0000</pubDate>
		<dc:creator>neuromancipation</dc:creator>
				<category><![CDATA[Mathematics]]></category>

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		<description><![CDATA[Central division algebras are relevant because endomorphism rings of reductions of formal groups occur as maximal orders of central division algebras. Let be a ring and an -algebra (neither commutative).  The centre of consists of all those elements of such that for all in .  It is thus a commutative subalgebra of .  If were [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=neuromancipation.wordpress.com&amp;blog=5242268&amp;post=82&amp;subd=neuromancipation&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>Central division algebras are relevant because endomorphism rings of reductions of formal groups occur as maximal orders of central division algebras.</p>
<p>Let <img src='http://s0.wp.com/latex.php?latex=A&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='A' title='A' class='latex' /> be a ring and <img src='http://s0.wp.com/latex.php?latex=B&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='B' title='B' class='latex' /> an <img src='http://s0.wp.com/latex.php?latex=A&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='A' title='A' class='latex' />-algebra (neither commutative).  The <strong>centre</strong> <img src='http://s0.wp.com/latex.php?latex=Z%28B%29&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='Z(B)' title='Z(B)' class='latex' /> of <img src='http://s0.wp.com/latex.php?latex=B&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='B' title='B' class='latex' /> consists of all those elements <img src='http://s0.wp.com/latex.php?latex=x&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='x' title='x' class='latex' /> of <img src='http://s0.wp.com/latex.php?latex=B&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='B' title='B' class='latex' /> such that <img src='http://s0.wp.com/latex.php?latex=xb+%3D+bx&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='xb = bx' title='xb = bx' class='latex' /> for all <img src='http://s0.wp.com/latex.php?latex=b&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='b' title='b' class='latex' /> in <img src='http://s0.wp.com/latex.php?latex=B&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='B' title='B' class='latex' />.  It is thus a commutative subalgebra of <img src='http://s0.wp.com/latex.php?latex=B&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='B' title='B' class='latex' />.  If <img src='http://s0.wp.com/latex.php?latex=B&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='B' title='B' class='latex' /> were a commutative <img src='http://s0.wp.com/latex.php?latex=A&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='A' title='A' class='latex' />-algebra, then obviously <img src='http://s0.wp.com/latex.php?latex=Z%28B%29+%3D+B&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='Z(B) = B' title='Z(B) = B' class='latex' />.</p>
<p>If <img src='http://s0.wp.com/latex.php?latex=k&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='k' title='k' class='latex' /> is a field and <img src='http://s0.wp.com/latex.php?latex=B&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='B' title='B' class='latex' /> a <img src='http://s0.wp.com/latex.php?latex=k&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='k' title='k' class='latex' />-algebra, then <img src='http://s0.wp.com/latex.php?latex=B&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='B' title='B' class='latex' /> is called <strong>central</strong> if <img src='http://s0.wp.com/latex.php?latex=Z%28B%29+%3D+k&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='Z(B) = k' title='Z(B) = k' class='latex' />.</p>
<p>A <img src='http://s0.wp.com/latex.php?latex=k&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='k' title='k' class='latex' />-algebra <img src='http://s0.wp.com/latex.php?latex=D&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='D' title='D' class='latex' /> is called a <strong>division algebra</strong> if every element has a left and a right inverse, i.e. division is possible in <img src='http://s0.wp.com/latex.php?latex=D&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='D' title='D' class='latex' />.  Clearly this definition is only useful for non-commutative algebras since if the algebra were commutative we&#8217;d just have a field.  For this reason division algebras are sometimes called <strong>non-commutative fields</strong>.</p>
<p>Thus a <strong>central division algebra</strong> is an algebra whose elements are invertible and whose only commutative elements are in the &#8220;base field&#8221;.</p>
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		<title>Startup Notes</title>
		<link>http://neuromancipation.wordpress.com/2009/01/13/startup-notes/</link>
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		<pubDate>Tue, 13 Jan 2009 15:37:35 +0000</pubDate>
		<dc:creator>neuromancipation</dc:creator>
				<category><![CDATA[Business]]></category>
		<category><![CDATA[Computers]]></category>

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		<description><![CDATA[Taken from reading PG&#8217;s last few essays. Bad economic times aren&#8217;t necessarily a draw-back to starting a startup.  Could be an advantage, as everyone else is cowering in fear in the corner. The ratio of income to employees should be as high as possible.  This is obvious, but in the sea of half-baked ideas, it [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=neuromancipation.wordpress.com&amp;blog=5242268&amp;post=65&amp;subd=neuromancipation&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>Taken from reading PG&#8217;s last few essays.</p>
<ul>
<li>Bad economic times aren&#8217;t necessarily a draw-back to starting a startup.  Could be an advantage, as everyone else is cowering in fear in the corner.</li>
<li>The ratio of income to employees should be as high as possible.  This is obvious, but in the sea of half-baked ideas, it may be a constraint that will make certain ideas more attractive/viable.</li>
<li>The founders of a company are the single biggest factor in its success.  The two main qualities they need are (1) determination and (2) ability.  This begs the question: who do I know who would make a suitable partner in any such venture?</li>
<li>Performance beats credentials; every time.  Obvious.</li>
<li>&#8220;it has gotten much cheaper to start a startup.  There are four main reasons:
<ul>
<li>Moore&#8217;s law has made hardware cheap;</li>
<li>open source has made software free;</li>
<li>the web has made marketing and distribution free; and</li>
<li>more powerful programming languages mean development teams can be smaller.</li>
</ul>
<p>&#8220;These changes have pushed the cost of starting a startup down into the noise.  In a lot of startups—probaby most startups funded by Y Combinator—the biggest expense is simply the founders&#8217; living expenses.  We&#8217;ve had startups that were profitable on revenues of $3000 a month.&#8221;</li>
<li>Find a/the market.</li>
<li>Target it.</li>
<li>Does cheap imply web-based?  Who makes money from licensing libraries these days?</li>
</ul>
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