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**To**:*math-font-discuss@cogs.susx.ac.uk***From**:*H Sami Sozuer <sozueh@rpi.edu>***Date**: Thu, 5 Aug 1993 00:53:42 -0400

Concerning the new decisions on the encoding scheme to be used in LaTeX, I will make the following points: 1 - It is my understanding that new encoding schemes are being planned to accomodate the usage of calligraphic, fraktur and blackboard letters in math formulas, and that these will have to be assigned to distinct families (6 in all). I believe this is a serious mistake. Many PostScript fonts are available for calligraphic, script and fraktur typefaces and these can be used in math instead. The advantage of this is that one does not have to waste many fonts even if they may never used in a particular document. 2 - I believe that NFSS is a major improvement over the default scheme used in LaTeX 2.09. However, it leaves a lot to be desired for. Namely: NFSS assigns *all* the math fonts at each *size* command. This means that even if one never typesets a single formula in, say, \Huge (which is used to typeset the Chapter headings), NFSS still assigns all the three appropriate sizes of each and every math font currently used. So, for example, if one were to "fill" all the families in a given math style, then typesetting a chapter heading requires the assignment of 3 * 16 =48 fonts!!! Similar "waste" of the fonts from the 255 font limit also applies for \section, \subsection and \footnote commands---or any command that executes a size command. If, furthermore, one were to issue a size changing command while in \boldmath (or in any other math style) *all* the fonts currently loaded to that math style, in all the 3 sizes of course, are assigned again. The solution to these problems is to load math fonts *truely* on demand, that is *within* each math formula. Also, only fonts that are used within a given math formula need to be assigned families, and only *temporarily* for that particular formula, but they should not be permanently added to the mathstyle for the *whole* document. This means that one could use an *arbitrary* number of fonts ( <255 of course) in any math style, provided one does not exceed the 16 family limit within *each* formula. This approach of course would be most efficient, if a minimal number of families were forcibly assigned, and the rest assigned only on demand, and only for that particular formula, *not* permanently for the whole document. TeX requires that families 2 & 3 be assigned or else it will simply refuse to typeset the formula. Therefore, ideally, only families 2 & 3 should be assigned to please TeX, but no more. This requires that \mathchardef command (and a few similar commands) be replaced by new commands such that, for example, \Gamma could be defined as \MathCharDef\Gamma7\rm00 . This means that the \rm command would load the default font for \Gamma and then typeset the 0'th character in the font. To get a \sf \Gamma, you would say \sf\Gamma of course. One could also modify \MathCharDef so that these symbols can be used both in math and in text modes freely. The obvious advantage of this is to avoid having to load all three sizes if you just need a \Gamma or a \bullet, say, at the current size, which is very often the case. 2 - The upper and lower case greek letters are treated unsymmetrically in TeX/LaTeX. This means that although one can get even a "dunhill" \Gamma, one cannot even get a \rm or a \sf \gamma. I believe that all greek characters should be available in all text fonts. This can be done very easily by simply adding a line to roman.mf that generates the lc greeks at appropriate locations. I have tried this and although the lc greek characters generated using the current cm parameters look somewhat less than ideal, it's a start! The lc greeks can be put at positions oct"337" to oct"377" such that the characters produced by afm2tfm (StandardEncoding of Adobe) are not overwritten. The Cork encoding unfortunately does not allow this because it is already full. By the way, adopting the Cork encoding would also mean that a lot of characters that only Europeans use would take up large amounts of disk space on the computers of people who only rarely use accented characters. This problem could best be solved by adopting a separate European style that one could choose, instead of building the standard permanently right into LaTeX. 3 - I have often found myself wondering whether the "design size" approach has lived out its usefulness. This subject is unfortunately somewhat of a taboo and I wish people were more forthright about whether or not it's meaningful to allocate vast amounts of disk space in order to be "faithful" to typesetting traditions. It's quite clear to me that, with low resolution devices, using a font with the appropriate design size (rather than a merely scaled font) improves readability of smaller sizes because the interletter spacing is larger so letters don't "fuse", the letters are wider and drawn with thicker strokes. However, as high resolution devices become more and more affordable, and as PostScript fonts gradually replace many of the cm fonts, I think it may just be the right time to adopt a single design size, 10pt, for all fonts. 4 - TeX's current magnification system based on the number 1.2 could also use some revision. One could see this simply by looking at printer ads in a recent magazine. More often than not, the printer resolutions come in sizes which differ by factors of 2. 300, 600, 1200 and 2400 dpi for example. It seems to me that a scaling system based on the factor of 2 would be most efficient. Hence replacing 1.2 in the current system by 2^{1/4}=1.189207 would mean that many of the fonts that are used with 300dpi printers can still be used with 600dpi or even 1200dpi printers. With the current system, however, reproducing the same set of fonts for a 600 dpi printer would take roughly twice the disk space occupied by the 300dpi fonts. If one were to maintain fonts for both printers, the disk storage requirements could become prohibitive. I have been working on developing such a system of font usage and I now have a fully functioning LaTeX style that assigns all math fonts within each formula, and >from a font utilization point of view, it is very very efficient. I would be glad to send anyone a copy along with a few new fonts that it uses. Compared to NFSS, it takes about twice as long to process a document, but this also depends on how often one enters the math mode and which implementation of TeX one uses. emTeX is very efficient in this regard. I hope this rather long piece of "complaints" will be viewed as a constructive, albeit possibly naive, attempt to stimulate discussion. Cheers, Sami Sozuer

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