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 Mathematical Typography (was: International Documents) Johannes Kuester <[log in to unmask]> Tue, 25 Mar 1997 17:19:53 +0100 text/plain (129 lines) Hans Aberg wrote... > In mathematics, variables are usually typeset in some kind of slanted > type (like italics), whereas contants (usually function names, and the > like) are usually typeset upright, even though tradition provides many > exceptions (like the numbers e and pi, which are contants usually typeset > in italics). No, at least most function names shouldn't be typeset upright, whereas e, pi and i (the imaginary unit) should be. I would not call it a tradition if they aren't, rather that is due to the laziness of most mathematicians and their lack of knowledge about mathematical typography. Maybe one has to distinguish here between good' and bad' traditions, i.e. traditions that really developed out of a mathematical necessity and/or are helpful in making a mathematical text more readable, and traditions which are due to lack of appropriate type, lack of knowledge about either mathematics or typography etc. For example, the usage of upright Greek uppercase letters in standard English and American math is -- in my opinion -- a bad tradition, as it isn't consistent with the rules (see below) and is, as far as I know, due to an English punchcutter/typographer who cut upright uppercase Greek to go along with his italic lowercase Greek (maybe it was Baskerville, I read that story once, but I can't remember neither the source nor the name any more, so I will be grateful for any hints). Another bad tradition in this sense is the use of (a,b) for the greatest common divisor of a and b, as this notation is heavily overused and could be easily confused. Even worse, there is no standard notation for the least common multiple. This seems to be due to lack of appropriate type (and/or of an appropriate symbol, of course). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% The rules for the use of upright and italic type are as follows, according to DIN 1338 and the recommendations of IUPAP (taken from Satz- und Korrekturanweisungen, Duden-Taschenbuch Band 5', Bibliographisches Institut, Mannheim, 5th ed. 1986): Letters denoting variables should be set italics, especially vectors in (semi-)bold italics. Also in italics: functions and operators without fixed meaning. Upright type should be used for digits, parentheses and all symbols with fixed meaning. That goes for all multiletter symbols as sin, lim etc., for \sum and \prod, then for constants as e, pi, i and Euler's constant (gamma or C), but also for all differential operators like d and \partial, and for operators like \nabla and the Laplace operator (an upright Delta), etc. The Duden book her comments that the last few symbols mentioned which only consist of a single letter are often set in italics, especially in books intended only for mathematicians (rein mathematische Fachliteratur' -- I couldn't think of a better translation for that at the moment). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% In my opinion, this shouldn't be the rule but the exception, as typesetting according to these rule greatly enhances the readability of mathematical texts, even more so as most math books aren't read as a whole -- jumping into a text is much easier with good typography, which relies as little as possible on the context for the understanding of the used symbols. Setting function names in upright type isn't that important (or could be dropped at all) as functions are recognizable as such in most cases by the following parentheses and arguments (thus usage of e.g. \mu(...) as the Moebius function only througout a text will always be clearly understandable, whether set upright or italic), but single letter symbols for operators or constants could be easily confused with other symbols, if not set upright (e.g. the imaginary unit with an index, e with a unit or eigen vector etc.) Also, typesetting function names in upright may hamper the good effects of the upright-type-rule, e.g. pi(x), the function counting the primes upto x, may be confused with the circle number pi, when both are set upright. Fixed meaning' as mentioned in the rules above means (in my opinion) a meaning fixed throughout a whole text or even fixed in a whole branch of mathematics. > It would in fact be a good idea of having a good set of upright and > slanted (both upppercase/lowercase) of fraktur and script styles for > mathematical purposes (the AMS-Fonts package does not provide it). For > example, when speaking about categories C, D, one would use say slanted > script, but when indicating the functor category Fun(C,D), the name "Fun" > would be typeset in upright script. I disagree. Such things as slanted fraktur do belong to the Typographical Chamber of Horrors. And upright script... I don't know, but I would set Fun' in upright roman, as all multiletter symbols. Script alone is special enough, upright script alongside with slanted script would confuse rather than help. And as for TeX: TeX/LaTeX should have the needed glyphs (e.g. upright lowercase Greek) and should have standard control sequences to follow the above rules (in some cases even more than one standard way to access a symbol). Examples and propositions: Upright lowercase greek by \ualpha, \ubeta etc/ (u for upright), maybe a set of \uGamma and \sGamma for uppercase (upright/slanted) which could be used to get explicitly a glyph, whereas \Gamma could be set by an option to slanted or upright, according to language and/or tradition etc. Maybe \PI for upright pi (the circle number),       \I for the imaginary unit and       \E for e (=\exp(1)), as these are used frequently and should be short (besides, quite similar names are used in Maple V), maybe \df for the differential operator d and then \pdf for the upright \partial etc. BTW, what about the TeXnical working group on extended math font encoding? Haven't heard about it since that article of Justin Ziegler. Johannes Kuester -- Johannes Kuester [log in to unmask] Mathematisches Institut der Technischen Universitaet Muenchen