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<title> Commutative Diagrams in TeX</title>
    
<h1 align="center">Commutative Diagrams in TeX </h1>

<h3 align="center">Paul Taylor </h3>

<h3 align="center">September 1992 </h3>




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<h2>Message sent to registered users in September 1992</h2>

<div class="p"><!----></div>
This message brings news of the development of my <span class="roman">T</span><sub><span class="roman">E</span></sub><span class="roman">X</span>&nbsp;package for
drawing "commutative" diagrams, which is now widely used in the
category theory and theoretical computer science communities. It is
being sent directly to all of the users I know of (who have requested
it by electronic mail or FTP from me, or asked questions about it),
but as I know the package has been passed on, I would be grateful if
you would <em>copy this message to anyone to whom you have given
  the package itself.</em>

<div class="p"><!----></div>
The package was originally advertised on the "types" and
"categories" electronic mailing lists in July 1990. In the following
eighteen months some fixing of bugs took place, but there was little
substantial change.

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Since April 1992, I have re-written most of the code, largely with a
view to improving the geometrical layout of the diagrams. Before
completing this work and calling it version 4, I would like some
feedback from users.

<div class="p"><!----></div>
One of the areas which I have neglected in the past (largely because
<span class="roman">T</span><sub><span class="roman">E</span></sub><span class="roman">X</span>&nbsp;makes it so difficult) is diagonal arrows. The code for drawing
these using <span class="roman">L</span><sup><span class="roman">A</span></sup><span class="roman">T</span><sub><span class="roman">E</span></sub><span class="roman">X</span>&nbsp;line segments has been re-written: now the closest
available slope is chosen automatically and the commands have names
similar to the horizontals and verticals.

<div class="p"><!----></div>
However to do a better job of diagonals (and in future to support
curved lines) some extension to <span class="roman">T</span><sub><span class="roman">E</span></sub><span class="roman">X</span>&nbsp;is needed. Being extensions they
are necessarily not standard. Three possibilities are:

<ul>
<li> additional fonts (as, for example, used by Spivak's Lamstex).
  However my experience of design-size fonts and linear logic symbols
  suggests that for users without expert knowledge or control of their
  local <span class="roman">T</span><sub><span class="roman">E</span></sub><span class="roman">X</span>&nbsp;systems this is more trouble than it's worth.
<div class="p"><!----></div>
</li>

<li> PostScript is, I believe, now almost universally used as the
  language in which <span class="roman">T</span><sub><span class="roman">E</span></sub><span class="roman">X</span>&nbsp;documents are sent to a printer. PS commands
  can be embedded in DVI files and incorporated in the PS translation
  without extra system or user files or any user intervention. This is
  to some extent dependent on which DVI<font face="symbol">®</font
>PS translator is used. In
  the new version this is exploited in an option to implement
  diagonals by rotating horizontals, which works with Tomas Rokicki's
  "dvips".
<div class="p"><!----></div>
</li>

<li> TPIC is a graphics extension of <span class="roman">T</span><sub><span class="roman">E</span></sub><span class="roman">X</span>&nbsp;which uses a simpler set
  of embedded commands. These can be used to draw diagonal lines and
  curves but not to perform rotations; they are, however, understood
  by Vojta's "xdvi" as well.  Another option in the new version uses
  these to draw diagonal lines.
<div class="p"><!----></div>
</li>
</ul>
Besides diagonals, the code for adjusting horizontal and vertical
arrows has been completely rewritten and does a much better job of the
geometry.  Many of the problems with alignment, positioning and gaps
have been fixed automatically, and greater control is given to the
user to adjust those which cannot be.  There are also several new
options for the placement of the finished diagram on the page.

<div class="p"><!----></div>
Arrow commands are now declared in a much simpler way. The declaration

<pre>
&nbsp;\newarrow{CrossedInto}{hook}-+-&#62;

</pre>
is now all that is needed to define the example <tt>\rCrossedInto</tt>
in the manual, along with the corresponding left, down, up and
diagonal commands. Another option makes a consistent selection of
arrowheads for all arrows, from a choice of vee, LaTeX, curlyvee,
triangle and blacktriangle.

<div class="p"><!----></div>
So much for selling you the new version. The reason for mailing you
and asking for comments before completing what I intend to do for
version 4 is that I want to get feedback on the following questions:

<div class="p"><!----></div>

<ul>
<li> Can you use FTP (file transfer protocol)? This is the easiest
  method of distribution for me and for you, and there is now a huge
  volume of public domain software available by this method. My
  archive is called <tt>ftp.dcs.qmw.ac.uk</tt>
  and the diagrams package is in the directory /pub/tex/contrib/pt/diagrams.
  Please try to fetch the new version and manual by this method.
<div class="p"><!----></div>
</li>

<li> If you can't use FTP, and your electronic mail passes via
  non-ASCII machines (particularly BITNET), what characters tend to
  get corrupted?  The new version uses a restricted character set to
  avoid this problem.
<div class="p"><!----></div>
</li>

<li> Do you have available for printing final copy a printer which
  understands Adobe PostScript, for example an Apple or Sun
  laserwriter? Who is the author of the DVI-&#62; PS translation program
  you use? Please fetch the new version, try the PostScript option and
  tell me if you have any difficulty printing. (You may have to change
  the <tt>\verbatim@ps@special</tt> macro if you don't use Rokicki's
  dvips: if so, please send me details.)  You can preview with a PS
  previewer such as PageView under OpenWindows or
  GhostView/GhostScript under Xwindows.
<div class="p"><!----></div>
</li>

<li> Do your DVI translators and previewers understand TPIC
  <tt>\special</tt>s (as used in eepic.sty)? Please try the TPIC
  option. I would like to know whether it is worth putting effort into
  PostScript, TPIC or some other method.
<div class="p"><!----></div>
</li>

<li> Have you defined your own arrow commands using 
  <tt>\HorizontalMap</tt>, <tt>\VerticalMap</tt> or <tt>\DiagonalMap</tt>?
  Please use "grep alMap *.tex *.sty" or some similar command to
  find out, and tell me if you have used any components other than
  those in the source of version&nbsp;3. It is in your interests to do
  this, because <tt>\newarrow</tt> defines arrow commands in a
  different way.
<div class="p"><!----></div>
</li>

<li> Please tell me if you have any difficulty adapting to the new
  version, or any general comments about doing so which might be of
  benefit to other users.
<div class="p"><!----></div>
</li>

<li> Other comments: have you used other packages for drawing
  diagrams? Do you have applications for my package other than the
  categorical diagrams for which it was designed? What do you see as
  the major limitations of the package? What persuaded you to use it,
  or not to use it?
<div class="p"><!----></div>
</li>
</ul>

<div class="p"><!----></div>