164 TUGboat, Volume 32 (2011), No. 2 Math alphabets and the mathalfa package The line Michael Sharpe \usepackage[showoptions]{mathalfa} throws an error and shows all alphabet names un- Abstract derstood by the package. As an example, to load This is both a survey of existing math alphabets Zapf Chancery scaled up by 15% as the output of and a brief description of a unified method of calling \mathcal and Fourier Double-Struck scaled down them via the package mathalfa. by 4% as the output of \mathbb, you enter \usepackage[cal=zapfc,calscaled=1.15, 1 Introduction bb=fourier,bbscaled=.96] For the purposes of this article, a math alphabet is {mathalfa} one normally selected in math mode using the LAT X E after loading other math packages. You may also set macros \mathcal, \mathscr, \mathbb, \mathfrak, as options or their bold counterparts \mathbcal, \mathbscr, \mathbbb and \mathbfrak. frak=...[,frakscaled=...], Regular and bold weights of a math calligraphic scr=...[,scrscaled=...], font are built into Computer Modern, occupying the to enable the macros upper case letter slots in the cm[b]sy family. The frak- \mathfrak tur and blackboard bold alphabets were (I believe) \mathbfrak % if there is a bold fraktur introduced with the AMS fonts, and the mathrsfs \mathscr package introduced the term \mathscr in order to \mathbscr % if there is a bold script provide a script font with more elaborate shapes, as is The names available for the alphabets are listed customary in a number of areas in math and physics, separately below by type. Any Mathematical Script in addition to an ordinary calligraphic alphabet. The name may serve as a target for both cal and scr. Unicode specification lists the fonts under Mathemati- In all cases, if a bold version is available, then the cal Alphanumeric Symbols (U1D400{U1D7FF), though corresponding bold variant is also defined. a number of special, commonly used glyphs fall under The mathalfa package does not provide the Post- the heading Letterlike Symbols (U2100{U214F). The Script fonts required for activating all its options. Unicode names for the alphabets are: The metrics and virtual fonts are publicly available, MATHEMATICAL SCRIPT: but are useless without the .pfb files which you must a.k.a. script, swash, calligraphic. acquire. See the mathalfa documentation for detailed MATHEMATICAL DOUBLE-STRUCK: descriptions of sources. a.k.a. double-struck, blackboard bold, openface. MATHEMATICAL FRAKTUR: 2.1 BOONDOX a.k.a. fraktur, blackletter, gothic. The boondox package is a reworking of the STIX cal- ligraphic, fraktur and double-struck alphabets with 2 Mathalfa virtual fonts and metrics suitable for math mode. (In The mathalfa package in most cases bypasses the the USA, the boondocks and the sticks are essentially usual font-loading mechanisms for these math al- synonymous.) When the LATEX support files for the phabets and substitutes its own, allowing it to use STIX fonts are made public, the boondox package common terminology and, in all cases, allow arbitrary will most likely become obsolete except to those who scaling. (Many LATEX packages that load fonts have may prefer its metrics. not been modified since the days when Metafont was the predominant font format, and it was desirable to 2.2 ESSTIX restrict the set of sizes at which the bitmaps were gen- The other relatively unknown font package here is erated, thus limiting the possibility of fine scaling.) esstix, an unfinished math font collection produced In a number of cases, the original math alphabet by Elsevier, never officially released and subsequently fonts were never set up with the metrics appropriate donated to the STIX consortium, serving as a precur- for math mode, leading to awkward placement of sor to their STIX font family. The ESSTIX collection accents and subscripts, and inappropriate spacing. is now under the same license as the STIX collec- This package corrects such deficiencies by supplying tion | the liberal SIL Open Font License, version 1.1. virtual fonts with my preferences for those metrics Though STIX regards the ESSTIX collection as dep- following, by and large, the appearance of mtpro2 recated, the math alphabets it contains have some (MathTime Pro II). unique elements which, in my opinion, should not be Michael Sharpe TUGboat, Volume 32 (2011), No. 2 165 allowed to become extinct. The ESSTIX fonts and 3.2 Restrained support files are now available from CTAN and have cmcm ((CMCM calligraphic, calligraphic,cmsy cmsy):): become part of TEX Live. The ESSTIX fonts in their original forms may be ABCDEFGHIJKLM mathalfa esstix NOPQRSTUVWXYZ loaded via using the option , but there cmcm ((CMCM calligraphic-bold, calligraphic-bold,cmbsy cmbsy):): is now an updated version of the ESSTIX calligraphic font. The metrics are identical to the original fonts, ABCDEFGHIJKLM but the font has been modified in several respects NOPQRSTUVWXYZ (using FontForge) so that it now validates properly zapfc (Zapf Chancery): following modifications to repair font outline points ABCDEFGHI JKLM and the font BlueScale parameter. NOPQRSTUVWXYZ In addition, a bold version has been created, lucida (Lucida calligraphic): following modifications to a small number of glyphs ABCDEFGHI JKLM to prevent outline self-intersections. (The original NOPQRSTUVWXYZ was quite light, rather of book weight, and the bold is more correctly a demi-bold.) ESSTIX calligraphic lucida (Lucida calligraphic-bold): and its update, dubbed DutchCal, are visually almost ABCDEFGHI JKLM identical at regular weight, though the latter is hinted NOPQRSTUVWXYZ better and is the only one shown in the samples below. mma (Mathematica script): ABCDEFGHIJKLM 3 Mathematical script NOPQRSTUVWXYZ The following choices are available for cal and scr, mma (Mathematica script-bold): listed according to general appearance. ABCDEFGHIJKLM NOPQRSTUVWXYZ UPRIGHT: euler % euscript mtc % MathTime Curly (commercial) 3.3Embellished: Embellished RESTRAINED: mt cm % Computer Modern Math Italic (cmmi) mt (MathTime(Mathtime Pro Pro 2 2 script): script): lucida % From Lucida New Math (commercial) ABCDEFGHIJKLM zapfc % Adobe Zapf Chancery (or URW clone) NOPQRSTUVWXYZ mma % Mathematica fonts mtmt (MathTime(Mathtime Pro Pro 2 2 script-bold): script-bold): EMBELLISHED: ABCDEFGHIJKLM mt % MathTime (commercial) NOPQRS TUVWXYZ rsfso % based on rsfs, much less sloped mathpi % Adobe Mathematical Pi (commercial) mathpi (Mathpi script): esstix % ESSTIX-thirteen ᏭᏮᏯᏰᏱᏲᏳᏴᏵ᏶᏷ᏸᏹ dutchcal % modification of ESSTIX13 ᏺᏻᏼᏽ᏾᏿᐀ᐁᐂᐃᐄᐅᐆ boondoxo % based on boondox, less sloped dutchcal (DutchCal): HEAVILY SLOPED: ABCDEFGHIJKLM rsfs % Ralph Smith Formal Script boondox % SCRIPT alphabet from stix fonts NOPQRSTUVWXYZ Script font samples follow in the above order. dutchcaldutchcal (DutchCal-bold):(DutchCal-Bold): ABCDEFGHIJKLM 3.1 Upright NOPQRSTUVWXYZ euler (Euler script): rsfsorsfso ((RSFS-Oblique):RSFS oblique): ABCDEFGHIJKLM ABCDE FGHIJKLM NOPQRSTUVWXYZ NOPQRSTUVWXYZ euler (Euler script-bold): boondoxoboondoxo ((BOONDOXBOONDOX Calligraphiccalligraphic Oblique): oblique): ABCDEFGHI JKLM ABCDEFGHIJKLM NOPQRSTUVWXYZ NOPQRSTUVWXYZ mtcmtc (MathTime(Mathtime Pro Pro 2 2 Curly Curly script): script): boondoxoboondoxo ((BOONDOXBOONDOX Calligraphiccalligraphic Oblique-bold): oblique-bold): ABCDEFGHIJKLM ABCDEFGHIJKLM NOPQRS TUVWXYZ NOPQRSTUVWXYZ Math alphabets and the mathalfa package 166 TUGboat, Volume 32 (2011), No. 2 3.4 Heavily sloped mathpi (Mathpi bb): ށނރބޅކއވމ ފދތލ boondoxboondox ((BOONDOXBOONDOX Calligraphic):calligraphic): ގޏސޑޒޓޔޕޖޗޘޙޚ ABCDEFGHIJKLM NOPQRSTUVWXYZ mtmt (MathTime(Mathtime Pro Pro 2 2 bb): bb): ABCDEFGHIJKLM boondoxboondox ((BOONDOXBOONDOX Calligraphic-bold):calligraphic-bold): NOPQRSTUVWXYZ ABCDEFGHIJKLM mma (Mathematica bb): NOPQRSTUVWXYZ ABCDEFGHI JKLM rsfsrsfs ((RSFSRSFS standard): standard): NOPQRSTUVWXYZ ABCDEFGHIJKLM fourier (Fourier bb): NOPQRSTUVWXYZ ABCDEFGHI JKLM 3.5 Notes NOPQRSTUVWXYZ Lucida fonts generally need to be reduced in esstixesstix ((ESSTIXESSTIX bb):bb): ABCDEFGHI JKLM • scale to match other math and text fonts. NOPQRSTUVWXYZ Zapf Chancery needs to be scaled up by 15% or • so. This font is not ideally suited for use as a boondoxboondox ((BOONDOXBOONBOX bb):bb): math alphabet due to the disparate heights and ABCDEFGHIJKLM depths and the long tails on some glyphs. Use NOPQRSTUVWXYZ with care. 4.2 Bold weight The calligraphic fonts break down into four nat- • ural groups: Blackboard bold (with serifs): (i) the upright styled Euler and Curly; mthmth (MathTime(Mathtime Pro Pro 2 2 Holey Holey Roman-bold): Roman-bold): (ii) the rather restrained CM, Lucida, Zapf ABCDEFGHI JKLM Chancery, ESSTIX and mma; NOPQRSTUVWXYZ (iii) the moderately sloped but more embel- Blackboard bold (sans serif): lished Mathpi, MathTime (borderline case), mtmt (MathTime(Mathtime Pro Pro 2 2-bold): bb-bold): rsfso and boondoxo; ABCDEFGHIJKLM (iv) the heavily sloped rsfs and the slightly less NOPQRSTUVWXYZ sloped boondox. mma (Mathematica bb-bold): My preference, if not using euler or lucida for ABCDEFGHI JKLM math, would be to set \mathcal to one from NOPQRSTUVWXYZ group (ii) and \mathscr to one from group (iii). boondox (BOONDOX bb-bold): 4 Mathematical double-struck CDHNPQRZ (few glyphs available) Double-struck font samples follow. 4.3 Notes 4.1 Normal weight Blackboard bold can look poor on the screen • Blackboard bold (with serifs): in many cases. Perhaps the thin parallel lines in the figures are a challenge to anti-aliasing amsams ((AMSAMS bb): bb): mechanisms, at some resolutions. For example, ABCDEFGHIJKLM here is the result of a screenshot