Euler-vm: Generic Math Fonts for Use with L a T E X

The Euler math fonts are suitable for math typesetting in conjunction with a variety of popular text fonts which do not provide math character sets of their own. Euler-VM is a set of virtual fonts based on Euler and Computer Modern, accompanied by a macro package for easy use with LATEX. 302 TUGboat, Volume 23 (2002), No. 3/4 The Euler math fonts “With Donald Knuth’s assistance and encouragement, Hermann Zapf, one of the premier font designers of this century, was commissioned to create designs for Fraktur and script, and for a somewhat experimental, upright cursive alphabet that would represent a mathematician’s handwriting on a blackboard and that could be used in place of italic. The designs that resulted were named Euler, in honor of Leonhard Euler, a prominent mathematician of the eighteenth century. Zapf’s designs were rendered in METAFONT code by graduate students at Stanford, working under Knuth’s direction. [. . . ] Knuth also noticed that the style of some symbols in the Computer Modern extension font, in particular the integral sign, was too slanted to be attractive with Euler, and consequently he prepared a new (partial) extension font for use with Euler.” [3] Knuth’s book Concrete Mathematics [1] was typeset using the Concrete font family for text and the Euler fonts for the formulas. With LATEX, the particular math font setup of this book can be mimicked through the package euler.sty [2]. Later it became obvious that the Euler math fonts match other text font families equally well. Unfortunately, the Euler fonts do not comprise all symbols required for mathematical typesetting with LATEX. As a result, the euler package needs to redefine most of LATEX’s math font setup, so that certain symbols are taken from Euler, whereas others come from Computer Modern. This has resulted in many problems and prevented the widespread use of the package beyond its initial purpose. A new interface to the Euler fonts Euler Virtual Math (Euler-VM) is a set of virtual fonts based primarily on the Euler fonts. The missing symbols are “stolen” from Computer Modern through the virtual font mechanism, rather than at TEX level, and the encoding follows that of the classical Computer Modern math fonts as far as possible. This approach has several advantages over immediately using the real Euler fonts, as implemented in the euler package. Most noticeably, less TEX resources are consumed, the appearance of various math symbols is improved, and there are (almost) no more compatibility problems with other packages. Thus, Euler-VM constitutes, together with the related macro package eulervm, a “generic” math font set for LATEX. The initial reason for creating Euler-VM was the fact that the euler package does not provide a usable \hbar or \hslash, and the \hslash from the amssymb package cannoted be used, because the latter follows the CM Roman style (rather than matching Euler). This made the beautiful Euler fonts essentially unusable for physics and related fields. The only way to fix this was to provide a “faked” Euler-style \hslash through the virtual font mechanism. As a beneficial side effect, it was possible to make the layout of the new virtual fonts compatible with Computer Modern Math to a large extent, and—since the style file had to be rewritten anyway—many further improvements were introduced. Typographical considerations From a technical point of view, the Euler fonts can be used together with arbitrary text fonts. From a typographical point of view, however, it is obvious that this will not always yield an attractive result. In particular, using Euler with Computer Modern is not a good idea at all! Beside the above-mentioned “Concrete”, the typeface families Palatino, Aldus and Melior blend well with Euler. This is not surprising, since they were also designed by H. Zapf. One might think of using Optima with Euler, but the typefaces are too similar, thus making formulas hard to read. The Euler math fonts have also proven to go sufficiently well with other typefaces, such as Minion, that exhibit a similar weight (stroke width) and x-height. Unfortunately, the popular “Garamond-style” typefaces Adobe Garamond and Stempel Garamond do not go well with Euler, because their x-height is too small. A Garamond descendant that yields a more pleasing result together with Euler is Sabon, because of its somewhat larger x-height. Using the Euler math fonts in conjunction with a sans serif typeface for text is possible, too. The only sans serif typeface which I know so far to work well is “Syntax”; of course there may be others. The LTEX macro package eulervm Loading the eulervm package redefines LATEX’s math font setup, so that the Euler-VM fonts and the default body font are substituted for CM Math and CM Roman. Roughly: • CM Math Italic is replaced with Euler Roman. • CM Calligraphic is replaced with Euler Script. • “Large” operators and delimiters are replaced with alternative symbols matching the Euler style. • In numbers and operator names, CM Roman is replaced with the default text font. TUGboat, Volume 23 (2002), No. 3/4 303 The model has the parameters fi, Ei, C and r (0 6 r 6 1). The oscillator strengths fi and the atomic level energies Ei should satisfy the constraints