TUGb oat, Volume 18 1997, No. 1 39 the prop er way coming to a compromise between readability and abstract typ esetting rules. Tutorials / Surveys I will discuss here those few tricks that physi- cists and engineers, not mathematicians,must know Typ esetting mathematics for science and in order to satisfy the international regulations and technology according to ISO 31/XI to distinguish similar symb ols with di erent mean- ings and, ultimately, in order to cop e with the ISO Claudio Beccari regulations [1] and the recommendations issued by Abstract the International Union of Pure and Applied Physics IPU [6]. Mathematicians set mathematics into typ e di er- ently from physicists and engineers; the latter re- 2 Upright and sloping letters quire some particular tricks in order to satisfy The main and p ossibly the only di erence b etween ISO 31/XI and to distinguish similar symb ols that \mathematical" vs. \physical" mathematics lies in A have di erent meanings. The L T X2 commands " E the use of upright and sloping letters. Scientists and to implement such tricks are shown and explained. technologists should use upright letters much more 1 Intro duction often than mathematicians. A In math mo de L T X2 cho oses normal letters " E As D.E.Knuth p oints out very well in The T Xbook E from the \math italics" alphab et, which includes [7], the strength of T X and its derived dialects E also the Greek lowercase ones. Both Latin and A among which L T X2 outclasses all others lies " E Greek letters have a sloping shap e, the former b eing in the abilitytotyp eset b eautiful mathematics; the in italics, the latter just sloping to the right with a variety of symb ols, the shap e of the op erators, the slop e angle that matches the one of the italics char- spacing, b oth vertical and horizontal, the sizes of acters. Just the upp ercase Greek letters by default rst and second order sub and sup erscripts make are upright, but it would b e very easy, although un- A L T X the b est software available to day for typ e- E usual, to set them with a sloping shap e b ecause they A setting mathematics. Of course L T X doesawon- E app ear in the \math italic" font, and in all the \text derful job also with plain text, tables, cross refer- italic" and other \slanted" fonts. encing, indexing, and so forth, but other programs In the following I will call \roman" the upright may p erform well with the latter tasks; what other shap e and \italic" the one that T Xies are used to E programs really cannot do is the excellentwork with asso ciate with math italics. The choice of the word mathematics; all this is not surprising since T Xwas E \roman" is not chance, since sans-serif characters created by a mathematician for typ esetting mathe- are not suited for physical mathematics b ecause sev- matics, rst of all in his own b o oks. eral signs are not easy to distinguish in the absence In this pap er I do not discuss how to typ eset of serifs: compare I and l for example; you cannot A mathematics, since L T X takes care of most of it; E tell which one is \upp er case I" and which one \lower very seldom the author needs minor corrections of a case l". formula, and when this happ ens it is usually to cor- Sans-serif upright characters may be used in rect some spacing when slanted op erators are to o technical and/or physical texts in order to mark close or to o far away from the symb ols they precede ob jects that cannot b e confused with mathematical or follow, so that the slanting shap e of the op erator symb ols, for example for the names of p oints in the requires some degree of manual intervention in or- description of geometrical gures, technical ob jects, der to x the spacing. Several such cases are dealt exp erimental setups, and the like. Therefore sans- A with b oth in The T Xbook and in Lamp ort's L T X E E serif upright letters never app ear in a mathematical Handb o ok [8]. formula of a physicist or an engineer, while math- Nor do I discuss the aesthetics of a typ eset for- ematicians use sans-serif fonts to represent certain mula, where several factors should follow one an- 1 structures in category theory. As a partial excep- other in such a way that the formula pro le is tion, sans-serif sloping upp ercase letters are allowed as smo oth as p ossible, without valleys and p eaks. to indicate tensors of the second rank, but this is the Typ esetting a complicated formula requires b oth mathematical knowledge and a sense of aesthetics, but requires also, esp ecially in didactic b o oks, that the relevant parts of the formula are highlighted in 1 Thanks to the reviewer for this information; although he/she do es not sp ecify it, nevertheless I supp ose that they are sans-serif sloping fonts. 40 TUGb oat, Volume 18 1997, No. 1 only exception mentioned in the IPU recommenda- index; but R where `E' distinguishes an ob ject such E tions [6] and stated in the ISO regulations [1, clause as the \emitter". 11-10.14] for using sans-serif fonts. 2.2 Roman symb ols 2.1 Italic symb ols Any other symbol that was not dealt with in the According to the ISO regulations and the IPU rec- preceding subsection must b e set in roman font; the ommendations, italic symb ols should be used only list of such \roman" entities is surprisingly long and, to denote those mathematical and physical entities unfortunately, little known although ISO regulations that may assume di erent values, typically those and IPU recommendations are quite clear on this symb ols that play the role of physical variables, but sub ject. also those physical \constants" that are not really A 1. Numb ers must b e set in roman typ e L T X2 " E constant, b ecause b etter measuring techniques may do es this by default. pro duce up dated values. 2. Numerical constants must b e set in roman typ e; Among such constants there is for example the this is p erhaps the most neglected rule, but it elementary electric charge the charge of the proton applies to e = 2:718 281 8 :::, the base of nat- 19 e =1:602 10 C, that is considered constantuntil ural logarithms, to the \imaginary unit" that b etter measures will add other signi cant digits; the mathematicians and physicists call `i', while same holds true for such constants as the velo cityof most engineers call `j ', and so on. The ISO light c, the Planck constants h and h, the Boltzmann regulations [1, clause 11-8.1] allow b oth sym- constant k , and so on. b ols for the imaginary unit, but b oth must b e Every physical variable is represented by one set in roman typ e. The reason b ehind this is to italic letter with as many mo di ers as needed such avoid confusion b etween the base of natural log- as subscripts, sup erscripts, primes, etc. [6, clause arithms and the elementary electric charge, b e- 1.2.1]. There are a few exceptions to this rule, rep- tween the imaginary unit and the instantaneous resented by the dimensionless parameters such as current i or the instantaneous current density the Mach numb er, the Euler numb er, and so on j whose symb ols are recommended by the IPU that are sp eci ed with a two-letter symbol by the [6, sections 7.5 and 8.5]. ISO regulations [2]; for example the Machnumber Anyb o dy can notice that `e' and `i' or `j' are is represented by Ma , the Euler number by Eu ; when universally typ eset in italic font in b oth mathe- suchtwo-letter symb ols are used, equations must b e matical and physical or technological texts; this written with sp ecial care so as to make sure that observation gives a measure of how much the Ma do es not represent the pro duct of the physical rule I am sp eaking ab out is ignored, at least by variables M and a. For the names of the nuclides, physicists and engineers. that may consist of two letters, see the next section. The same rule should apply to numerical con- In pure mathematics two- or three-letter names stants represented by Greek letters, such as are used in applications such as, for example, the 2 =3:141 592 6 :::, but it is necessary to get by name of the Galois eld with n elements that is with it b ecause it is dicult to have b oth the represented with GF n. But such applications are upright and the sloping Greek fonts; fortunately not substantially di erent from what the ISO regu- enough the frequency of such symb ols except lations say ab out the names of sp ecial functions [1, is not high. If b oth upright and sloping clauses from 11.11.1 to 11.11.21]. Greek fonts were available, an upright should In the domain of Computer Science as well as indicate the numerical constant \3:1415 :::", in Electronics authors and typ esetters make frequent 3 while a sloping should indicate the physical use of multiletter symb ols, but this tradition is ev- constant\3:1415 ::: rad" corresp onding to the idently in contrast with the ISO and IPU statements angle of 180 .