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Re: Math Arrows and Harpoons

Hi Barbara,

First, have a new look on the web page:


Hans Hagen would like to see -/- (and +/-, -/+, +/+). They probably do
not belong in this arrow font, but in general they are interesting
(layout like the fractions).

>>>>> "BB" == Barbara Beeton <bnb@ams.org> writes:

 BB> i have examined most of taco's arrows and harpoons, and have
 BB> found some problems.

 BB> do i understand correctly that 221 is the maximum size of a type
 BB> 1 font that's to be used in applications other than tex?  there
 BB> are a few additional items that might be considered here, but if
 BB> this is already at maximum, some negotiation might be necessary.

I'm quite willing to fill all 256 slots for this font. We will worry
about splitting them up and/or reorganization later (see below). If
needed, > 256 is fine with me too.

The "problem treshold" for 8-bit fonts tends to be 256 - 32 (0--31) -
1 (32=space) - 1 (127=ascii null) = 222, btw. This typically applies
to usage of the fonts via certain software like ATM from software like
M$ Word, and is usually not related to viewing. (One can view all 256
chars in a PDF file, for example).

16-bit Unicode TTF fonts do not have this problem, since they
reference Unicode indices directly (however they have some other weird
problems). Anyway, as I said, to be worried about later. Let's try to
concentrate on the names--glyph shapes for now.

 BB> i didn't find any problems with the shapes up through 119
 BB> (although i thought that the fishtail in 106 would better have
 BB> been switched with the one in 143; more on that later).  i do see

This has been done in the second draft (now on the net).

 BB> a problem with the shapes in 120, 121 and 123, and perhaps 122;
 BB> i'm still checking the ones after that.

 BB> the arrows in 120, 121 and 123 should definitely have the
 BB> arrowheads pointing up at an angle, rather than horizontal.  the
 BB> shape of the wavy stem is more-or-less that of a similar sign (or
 BB> its mirror image).  

Will fix this for draft 3. I now have an acceptable shape for similar
and backsimilar that I can use, so this will be easier. Also, there
may be partly related cosmetic changes needed to

		25,26 (looped arrow tails),
		32,33 (angled heads), 
		60--63 (double 45 deg arrows),
		79--82 (45 deg with hook),
		115,117,119 (double head/tail),
		126--129 (zigzag arrows),
		132,133,144,145 (plus and minus),
		138 (equals above rightarrow), 
		139--142 (arrows with similars),
		144,145 (angled heads),
		172 (rightarrow though X), 
		179 (lrarrow though circle),
		180--182 (the triangle heads),
		185--190 (angled heads), 
		199 (leftarrow through subset), 
		200 (leftarrow through less), 
		203 (colon rightarrow),
		211,217 (zigzag down arrows),

I finally have some specific questions on the symmetrical cases:

Question on 72: how about "longmapsfrom"?

Question on 78: how about "twoheaded broken leftarrow"?

Question on 87: how about "twoheaded mapsfrom"?

Question on 122: how about  "negated leftrightwavyarrow"?

Question on 124,125: how about "left curvy arrow" and
		 "negated left curvy arrow"?

Question on 138: how about "equal on leftarrow"?

Question on 139: how about "sim on leftarrow"?

Question on 141: how about "approx below leftarrow"?

Question on 172: is this a real "X" character or a double negation? 
		 If it's a negation, it probably needs 
		 "leftarrow though X"

Question on 182: Should this arrow be made longer?
		 (leftrightarrowtriangle) or maybe even

Question on 199: this seems to indicate the need for 
		 "rightarrow through superset"

Question on 200: this seems to indicate the need for 
		 "rightarrow through greater"

Question on 203: how about "leftarrow colon"?

Question on 204: how about "left imply"?

Question on 211: how about "up zigzag arrow"?

Question on 212: how about "three left arrows"?

 BB> i couldn't find a negated version of the leftwards wavy arrow --
 BB> have i missed something?

Seemed not to exist in the tables. I will add the character, but I
could not find it.

 BB> the names already used for these arrows (in lasy and the
 BB> amsfonts) are different from what taco has, but in all, i think i
 BB> like taco's names better:

 BB>     120 rightwavyarrow rightsquigarrow (ams), leadsto (lasy) 121
 BB> leftwavyarrow leftsquigarrow (ams) 122 leftrightwavyarrow
 BB> leftrightsquigarrow (ams) 123 nrightwavyarrow

Kept my names for these, and of course added nleftwavyarrow.

 BB> do with arrows.)  there is a naming problem here too -- both 089
 BB> and 106 are named "rightfishtail"; 106 is the one that should
 BB> change -- i suggest varrightfishtail since it is the odd one out.

106 became 143, as proposed earlier. 143's name is now

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


I changed all of the harpoon names to the ones you proposed (naming is
still dreadful, there are just too many of them). 

 BB> there's a problem with the ordering of the names vs. the shapes
 BB> here: what i have listed as 150-153 is 149-152 in taco's list,
 BB> with the name at 153 belonging to the shape at 149.  (it would be

I lot track on this, but I thick I have given the correct names now.

 BB> a whole lot easier to check these names if the shapes were next
 BB> to them.  i know this is asking a lot ...)

Not really such a big problem. For the next version, expect a series
of 240 or so \mathchardef's in a macro file and a side-lookup table.

 BB> there are two harpoon pairs that already had names, one from
 BB> plain and the other from amsfonts, simpler than the ones taco
 BB> lists; taco's are more "exhaustive" in their descriptive content,
 BB> but i think the simpler forms are reasonable to keep as
 BB> equivalents:

 BB>     049 leftharpoonuprightharpoondown leftrightharpoons
 BB> (amsfonts) 050 rightharpoonupleftharpoondown rightleftharpoons
 BB> (plain)

Changed those names back to the original ones. 

There is still a problem with the double-ended harpoons (other than
those silly names), I think: there are no up-down versions of the
horizontal harpoons. I have

158 F50F leftrightharpoonupup 
159 F50B leftrightharpoondowndown

So I think I'm missing 


These do have a vertical equiv,

146 updownharpoonrightleft
147 updownharpoonleftright

 BB> the last group i'll address now is the accents.  some of these
 BB> have names already from plain tex different from what taco has
 BB> listed.

 BB>     207 leftarrowaccent overleftarrow 
 BB>     208 rightarrowaccent overrightarrow or vec 
 BB>     209 leftrightarrowaccent overleftrightarrow

Of those names, only "vec" is valid. The other ones are not accents
but builtup material (which is still possible). This is why I decided
to use new names, and I intend to stick with them.
 BB> i noticed the absence of vertical arrow fillers; these are just
 BB> as likely to be needed, i think, as horizontal ones.  and i've
 BB> also seen a request for long triple-stem horizontal arrows, so
 BB> Lleftarrowfiller and Rrightarrowfiller might be considered.  (but
 BB> none of these fillers are candidates for addition to unicode.)

Vertical single and double fillers added, as well as larger versions
of all six vertical arrows; and short versions of uparrow, Uparrow,
downarrow and Downarrow (for delimiter construction).

I'll add a triple extension for the horizontal version (two chars).

I've also added single and double versions of a short arrow stem with
negation; and the same cross-negated (the ordinary negation slashes
are now removed since they are no longer needed, they might reappear
in another font and/or for the TeX-specific version). 

I've also added two [Mm]apstochar's.

Currently, the final portion of my names file looks like this (not all
characters implemented yet):

218      rightarrowfiller
219      leftarrowfiller
220      Rightarrowfiller
221      Leftarrowfiller
222      Lleftarrowfiller
223      Rrightarrowfiller
224      leftdottedarrow
225      longuparrow
226      longdownarrow
227      longupdownarrow
228      Longuparrow
229      Longdownarrow
230      Longupdownarrow
231      mapstochar
232      Mapstochar
233      uparrowfiller
234      Uparrowfiller
235      shortuparrow
236      shortdownarrow
237      Shortuparrow
238      Shortdownarrow
239      nleftwavyarrow
240      negationcrossed
241      Negationcrossed
242      negationslashed
243      Negationslashed
244      Uuparrowfiller
245      leftrightharpoonupdown
246      leftrightharpoondownup

 BB> i will be adding all the names i have checked already, which
 BB> don't yet appear in my stix project list; i will use the names in
 BB> the right-hand column in the lists of questions above, except for
 BB> the wavy arrows as already mentioned.

The next draft of the font should appear somewhere in the weekend. It
is likely that this font will eventually be split into an arrow font
and a harpoon font to get some extra room (space is getting
uncomfortably tight if I take the symmetry cases given above in
account). This would also solve the <222 problem and give some room
for software-specific extensions (where and when needed).

The first draft of the relations font is also supposed to appear in or
very shortly after the weekend. (features equals, lesses, succs & sims

Greetings, Taco