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Re: Math Arrows and Harpoons

At 17:51 -0500 1998/11/12, Barbara Beeton wrote:
>the arrows in 120, 121 and 123 should definitely have the arrowheads
>pointing up at an angle, rather than horizontal.  the shape of the
>wavy stem is more-or-less that of a similar sign (or its mirror
>image).

I foind this comment strange: As far as I am concerned, these correspond to
the LaTeX \leads to. For leads to, the arrow head-head should point as
normal. It  consists of a part which is like a \sim followed by a short
staright, horizontal part, to which the otherwise normal arrow-head is
attached.

  When drawn by hand, it it may happen the arrowhead becomes bent, but that
is not how it should be. This applies to the math I know; physicists may
have invented their own version.

> this is how they appear in both the unicode manual and the
>afii glyph register; in the latter, the rightwards version has a
>subsidiary meaning/description "functional relationship", which i
>think may have come from the iso tech report 9573-13, which has a bit
>of a physics orientation.

The Unicode just provides a suggestion for a possible rendering, not a norm
on how it actually should be drawn.

>the arrow in 122, in both the unicode manual and afii glyph register,
>has an "up" wave in the middle; taco's has a "down" wave.  again, i
>think this may have come from iso tr 9573-13.

On such issues I think that one is left one ones own: I think that a
mathematician could be able to distinguish between up/down wave in the
middle, or using a \sim wave (two waves instead of three, up/down followed
by down/up), and use them side-by-side as different symbols. If so, they
should have different symbols. If one is judging the variations to be
indistinguishable, it probably makes no difference which one is choosing,
only that it is the one that looks the best.

>hans aberg commented on the fishtails in an earlier message, saying
>that he doubted that these are used by themselves, as opposed to being
>part of some composite.  i've never seen (and am desparately looking
>for) published examples, but from the unicode, afii, and iso tr 9573-13
>evidence, believe that they are indeed individual symbols.

  The problem is that Unicode just collects graphics, labels them symbols,
without one knowing what the intended use should be. If there were two
fonts, one for symbols, and for arrows described in components (head, tail,
stem), then these problems could be resolved: One variation in each font,
perhaps.

>another naming overlap: 087 and 111 are both named Mapsto.  since
>the initial cap on most other arrows denotes a doubling of the stem,
>i think that 111 should keep this name, and 087 should be renamed to
>twoheadmapsto following the model of 015, twoheadrightarrow.

There is a conflict in naming these arrows: Should one name them after a
mathematical intended use (like "maps to") or by its redering. It is
probably wise to not mix the two. Suppose one only uses naming by
rendering: Then the original "maps to" |-> might be named
"rightheadleftvertical", and |=> could be named
"rightheaddoublestemleftvertical", or something.

  Hans Aberg
                  * Email: Hans Aberg <mailto:haberg@member.ams.org>
                  * Home Page: <http://www.matematik.su.se/~haberg/>
                  * AMS member listing: <http://www.ams.org/cml/>