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Date:         Mon, 12 Oct 92 10:15:07 BST
From: Mike Piff <M.Piff@SHEFFIELD.AC.UK>
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To: Multiple recipients of <LATEX-L@vm.urz.Uni-Heidelberg.de>
Subject:      (Forwarded) CDs corrected version
Status: R


Forwarded message:
To:           hicks1/pm1mjp
From:         Kirill Mackenzie <HICKS3/PM1KCHM>
Date:         9 Oct 92 14:45:28 GMT
Subject:      CDs corrected version

These are a few comments on features desirable in a macro package for
commutative diagrams. I am a reasonably proficient ordinary user of TeX
(1987--91), LaTeX (1991--) and AmSTeX (1/1992--), but have never used
any of the currently available commutative diagram packages (though I
have an early copy of Borceaux's). I wrote the paper "Double Lie algebroids
and second order geometry, I"  (Adv. Math. 94, 1992, 180--239) in (plain)
TeX and this shows the kind of diagram I am concerned with (see pages
215--222 in particular).

(i) I am quite happy drawing squares and rectangles with \matrix. What I
would like is a package that draws a (diagonal) arrow from one specified
site to another. Thus, instead of specifying a \vector by numerical
coordinates (position and slope) as in the picture enviroment, I would
like to be able to identify the corners of my matrices in some simple way,
and then, for example in the following situation,


      A  ---->  B

      |         |                 E  ---->  F
      |         |
      V         V                 |          |
                                  |          |
      C  ---->   D                V          V

                                  G  ---->   H

issue a command \arrow{A}{E}{\phi} which would draw an arrow from A to E (in
that order) and attach the label \phi to its midpoint. I would want an
optional argument that allowed me to move the label \phi within about plus
or minus 25% of the arrow's length, so that I could avoid messy overlaps.

(Of course, one might have two corners labelled A, so one would need a simple
system for silently labelling corners with unique identifiers.)

If a corner has a long entry, one would want the arrow to point from or to
the midpoint, with an option of it pointing to the first subsymbol on the
left/last subsymbol on the right.

(ii) This would meet most of my needs. But it would be very useful to have
a hypercube macro, with arguments for all corners and sides (that is,
48 labels in all), as well as the type of diagram (actually degenerate
hypercubes) found in my paper mentioned above.

(iii) Whatever may be the practicality or otherwise of the above, a CD
package would only be of value to me if it allowed not just arrows, double
headed arrows, "injective" and "surjective" arrows, equalities, and
(preferably) isomorphism symbols, but also double arrows: that is two
parallel arrows, close together, and produced by a single command. I use
these to indicate groupoid structures: other people may use them in
connection with simplicial structures. Again, there are examples in
the paper cited above.


I'd be very interested to know whether (i) and (ii) seem practical to
CD wizards. I would certainly use, acknowledge, and loudly sing the praises
of, a package that provided these facilities.
                                              Kirill
 Mackenzie%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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