| Copyright: | © 2008, 2009 Günter Milde |
|---|---|
| Licence: | This work may be distributed and/or modified under the conditions of the LaTeX Project Public License, either version 1.3 of this license or (at your option) any later version. |
Abstract
The isomath package enables formatting Greek and Latin letters as symbols for vectors, matrices, and tensors in the typefaces recommended for scientific papers by the International Standard ISO 31. For this, a bold italic and a sans-serif bold italic math alphabet are defined.
Contents
Scientific organisations like IUPAP, IUPAC, NIST, BIPM, and others recommend typesetting math according to the International Standard ISO 31 Quantities and units [ISO-31].1
The traditional LaTeX math style deviates in some points from this rules:
Some of these points are adressed by related packages, however there is currently no package (known to the author) that defines the sans-serif bold italic math alphabet needed for tensor symbols.
| [1] | Summaries of these rules are free available, see [typefaces], [checklist], [fonts-for-symbols], and [SI-brochure]. |
The isomath.sty package facilitates the task to abide with ISO 31 when typesetting math with LaTeX:
Equal treatment of Latin and Greek in math via fixmath.sty:
The command aliases \vectorsym, \matrixsym, and \tensorsym allow semantic markup. They print the argument in an ISO-conforming typeface.
For this, new math alphabets are defined:
| \mathbold: | boldface italic (vector and matrix symbols), |
|---|---|
| \mathsans: | sans-serif italic (optional), |
| \mathboldsans: | sans-serif bold italic (tensor symbols). |
The family for these fonts is by default taken from the document's \rmdefault and \sfdefault values. The rmdefault=<family> and sfdefault=<family> options can be used to override the defaults.
Missing font mappings are defined for font families which have an OML encoded counterpart but no substitution definition in their *.fd files.
Make sure that LaTeX can find isomath.sty and insert the command \usepackage{isomath} in the document preamble.
For package options, see the Options section below.
In many cases (e.g. when \sfdefault expands to "cmss"), the \mathboldsans alphabet is neither bold nor sans, as "cmss" has no OML encoded variants and maps to "cmmi".
Use cmbright for sans-serif math alphabets:
\usepackage[sfdefault=cmbr]{isomath}
Define also a slanted sans-serif math alphabet:
\usepackage[sfdefault=cmbr,OMLmathsans]{isomath}
Redefine the standard \vec macro to typeset its argument in bold italic:
\usepackage[sfdefault=cmbr]{isomath}
\renewcommand{\vec}{\vectorsym}
The mathdesign package provides an OML encoded bold roman font but does not set it up for \mathbf:
\usepackage[charter]{mathdesign}
\usepackage[OMLmathbf,sfdefault=cmbr]{isomath}
Now, \mathbf{\pi} produces a bold upright pi symbol.
IUPAC's [fonts-for-symbols] guide says:
- The overall rule is that symbols representing physical quantities (or variables) are italic, but symbols representing units, or labels, are roman. [...]
- The above rule applies equally to letter symbols from both the Greek and the Latin alphabet, although authors often appear to resist putting Greek letters into italic.
[emphasis by the author]. In contrast, the standard LaTeX style treats Greek symbols as invariant operators with lower case italic and upper case upright.
The technical report Unicode Support for Mathematics [tr25] lists "lphanumeric symbols encountered in mathematics"in table 2 Mathematical Alphabets.
The Unicode block mathematical alphanumeric symbols provides style variants for Latin and Greek letters and digits. It is labelled "to be used for mathematical variables where style variations are important semantically".
| Style | LGD3 | LaTeX macro | Package, Comment |
|---|---|---|---|
| bold | LGD | \mathbf | no Greek |
| italic | LG | \mathit | no Greek |
| \mathnormal | small Greek but old-style roman Digits | ||
| bold italic | LG | \mathbold | fixmath and friends |
| \boldsymbol | ams | ||
| script | L | \mathcal or | only capital Latin |
| (calligraphic) | \mathscr | ||
| bold script | L | ||
| fraktur | L | \mathfrak | eufrak |
| double-struck | L D | \mathbb | bbold, mathbbol, mbboard |
| \mathbbm | bbm | ||
| \mathds | dsfont | ||
| bold fraktur | L | ||
| sans-serif | L D | \mathsf | no Greek |
| sans-serif bold | LGD | ||
| sans-serif italic | L | \mathsans | isomath |
| sans bold italic | LG | \mathboldsans | isomath |
| monospace | L D | \mathtt | no Greek |
| Not in the mathematical alphanumeric symbols block: | |||
| plain | LGD | \mathrm | no Greek |
| \mathnormal | capital Greek | ||
| [3] | LGD: Latin, Greek, Digits |
OML is the only established font encoding providing Latin and Greek letters in one font. (The text font encoding LGR is Greek-only while T7 is just a "reserved name" for a standard Greek encoding.)
The LaTeX font encodings guide [encguide] names OML TeX math italic and defines:
The OML encoding contains italic Latin and Greek letters for use in mathematical formulas (typically used for variables) together with some symbols.
However, the reference to italic letters seems to be a description of the state of the art rather than a necessary restriction:
There is only one OML encoded font in the Computer Modern fonts: Computer Modern Math Italic (cmmi).
Generally, font encodings (T1, OT1) are not specific to the font shape.
Both, \DeclareSymbolFont and \DeclareMathAlphabet require a {<shape>} argument. Thus it is possible to set up OML encoded math alphabets in roman {n} as well as italic {it} shape without conflicts.
The name TeX math italic can be interpreted as "encoding of Computer Modern Math Italic" rather than "encoding for math italic" fonts.
A less confusing name would be TeX math letters or Original/Old Math Letters. The latter would also explain the acronym OML.
A more inclusive definition would be:
The OML encoding contains Latin and Greek letters for use in mathematical formulas (typically used for variables) together with some symbols. It first appeared in the Computer Modern Math Italic (cmmi) font.
Unfortunately, support for the OML encoding is missing for many font families even if the base font contains all Greek letters. Supported font families can be found searching for oml*.fd files and by grepping for "DeclareFont.*OML", "SymbolFont.*OML" and "MathAlphabet.*OML" in *.sty files.
| Name | Family | {m}{it} | {bx}{it} | {m}{n} | {bx}{n} |
|---|---|---|---|---|---|
| aer | AE (Almost European) | x | x | ||
| antt | Antykwa Torunska | x | x | ||
| cmr | Computer Modern Roman | x | x | ||
| ccr | Concrete | x | x | ||
| cmbr | Computer Modern Bright | x | x | ||
| hlh | Lucida | x | x | ||
| hfor | CM with old-style digits | x | x | ||
| iwona | Iwona (sans serif) | x | x | ||
| jkp | Kepler Serif | x | x | ||
| jkpl | Kepler Serif | x | x | ||
| jkpvos | Kepler Serif | x | x | ||
| jkplvos | Kepler Serif | x | x | ||
| llcmm | LXfonts (sans serif) | x | x | ||
| lmr | Latin Modern Roman | x | x | ||
| mak | Kerkis | x | |||
| mdbch | Math Design Charter | x | x | x | x |
| mdput | Math Design Utopia | x | x | x | x |
| mdugm | Math Design Garamond | x | x | x | x |
| neohellenic | GFS Neohellenic | x | |||
| plcm | CM (PLaTeX) | x | |||
| ptmom | Times (Omega or MB-Times) | x | x | ||
| ptmomu | Times (Omega or MB-Times) | x | x | ||
| ptmcm | Times (psfont) | x | |||
| pxr | Palatino (pxfonts) | x | x | ||
| qpl | Palatino/Pagella (qpxmath) | x | x | ||
| qtm | Times/Termes (qtxmath) | x | x | ||
| txr | Times (txfonts) | x | x | ||
| ywclm | (greektex) | x | x | ||
| zavm | Arev (Vera Sans-Serif) | x | x | ||
| zesfcm | (efont) | x | |||
| zplm | Palatino (mathpazo) | x | x | ||
| zpple | x | x | |||
| ztmcm | Times (mathptmx) | x | |||
| zer | Computer Modern (zefonts) | x | x |
Explanations:
The following fonts define cmm as OML substitution. A better matching substitution can be set with the rmdefault or sfdefault options.
| Family | Name |
|---|---|
| bch | Charter (psnfss) |
| pag | Avant Garde (psnfss) |
| pbk | Bookman (psnfss) |
| pcr | Courier (psnfss) |
| phv | Helvetica (psnfss) |
| pnc | New Century Schoolbook (psnfss) |
| ppl | Palatino (psnfss) |
| ptm | Times Roman (psnfss) |
| put | Utopia (psnfss) |
| pzc | Zapf Chancery (psnfss) |
| uag | Avant Garde (avantgar) |
| ubk | Bookman (bookman) |
| ucr | Courier (courier) |
| ucrs | Courier |
| unc | New Courier (nctrsbk) |
| uni | Universal (universa) |
| uhv | Helvetica (helvetic) |
| upl | Palatino (palatino) |
| utm | Times (times) |
| uzc | Zapf Chancery (zapfchan) |
It is hoped, that in the future more fonts families will support the OML encoding in normal and bold weight as well as upright and italic shape. This would be a major step towards a LaTeX equivalent of the Mathematical Alphanumeric Symbols Unicode block.
This should be (relatively) easy to achieve via virtual fonts when the glyphs for the Greek letters already exist. Examples are Latin Modern, Kerkis, GFS-Neohellenic, LX-Fonts and KP-Serif.
Alternatively, the T7 encoding could be used for math alphabets (if it ever happens to materialise).
Upright small Greek letters in \mathrm would enable the specification of the constant pi, Myons, Pions, alpha-particles, photons, and neutrinos without special packages. (With mathdesign, this is already possible today.)
\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{isomath}
[2009/06/19 v0.3 typeset math according to International Standard ISO 31]
| 0.1 | 2008-09-25 | first public version. |
| 0.2 | 2008-10-02 | bugfix: a usage example was uncommented; |
| updated documentation; | ||
| define mathsans only if OMLmathsans is true; | ||
| option reuseMathalphabets -> reuseMathAlphabets. | ||
| 0.3 | 2009-06-19 | documentation update; |
| fix OMLmathrm and OMLmathsans definitions; | ||
| switch license to LPPL |
The package fixmath by Walter Schmidt defines Greek letters as symbols of type \mathalpha and takes them from the "letters" SymbolFont in \mathnormal (as opposed to "operators" in fontmath.ltx).
fixmath also defines the \mathbold alphabet, setting it to cmm. However, this definition will be overwritten with a configurable value for the font family below.)
\RequirePackage{fixmath}
Caution!
After loading fixmath, placing Greek letters in a math alphabet, e.g. \mathrm{k\Omega}, can lead to garbage, as the standard math alphabets are usually taken from OT1 encoded fonts that have ligatures and non-alpha symbols in place of the small Greek letters.
If the chosen font supports the OML font encoding, you can use the options for OML math alphabets. Otherwise, place Greek letters outside the math alphabet command.
Some packages provide \up* or \var* macros for upright Greek letters, e.g. \mathrm{k}\upOmega.
The kvoptions package in the oberdiek bundle facilitates the setup of package options and provides a key=value interface (based on keyval):
\RequirePackage{kvoptions}
Alternative family for roman math fonts. The default is to use the corresponding text font family (\rmdefault) in OML encoding. Table 3 lists some fonts where a different setting is advised.
\DeclareStringOption[\rmdefault]{rmdefault}
Alternative family for sans-serif math fonts. The default is to use the corresponding text font family (\sfdefault) in OML encoding.
Computer Modern Sans Serif (cmss) has no OML encoded variant. Nor have many derivatives (lmss, aess, ...). Actually, there are only a few OML-encoded sans-serif fonts (all slanted/italic):
| zavm: | arev (Vera Sans with math extension, large x-hight) |
|---|---|
| cmbr: | cmbright (Computer Modern Bright, slightly lighter than cmss) |
| iwona: | iwona (Humanistic Sans Serif, some shapes very similar to roman) |
| hvm: | hvmath (Helvetica Math, commercial, free bitmap version) |
| llcmm: | lxfonts (LX Fonts, very wide, excentric, large x-hight, new in 2008) |
For most fonts (especially CM and related), [sfdefault=cmbr] is the recommended setting.
\DeclareStringOption[\sfdefault]{sfdefault}
The definition of new math alphabets can lead to a "too many math alphabets used in version normal" error.
As a workaround, this option tells isomath to re-use the existing \mathbf and \mathsf alphabets for italic bold and sans-serif bold.
To access the upright shapes, the corresponding \textbf and \textsf commands might be used (however, this toggles the math-mode off and might use a different font).
\DeclareBoolOption{reuseMathAlphabets}
Caution!
Do not use reuseMathAlphabets together with the OMLmathbf or OMLmathsf options.
With Greek letters defined as \mathalpha, the math alphabets are expected to be in OML font encoding. Unfortunately, the standard math alphabets are usually taken from OT1 encoded fonts that have ligatures and non-alpha symbols in place of the small Greek letters.
The following options cause isomath to (re)define math alphabets in OML encoding:
\DeclareBoolOption{OMLmathrm}
\DeclareBoolOption{OMLmathbf}
\DeclareBoolOption{OMLmathsf}
\DeclareBoolOption{OMLmathsans}
\DeclareBoolOption{OMLmathtt}
Setting these options enables access to small Greek letters in different shapes with e.g. \mathrm{\pi} — if an OML encoded font is available. Currently, support for the OML font encoding is rather limited:
With some packages, these options can result in a "too many math alphabets used in version normal" error.
In math, LaTeX uses "absolute" fontnames instead of a selection by family, shape, and weight because typefaces have a semantic meaning [fntguide]. This correlates with the Unicode math support where the mathematical alphanumeric symbols block defines distinct Unicode characters for Greek and Latin letters in different typefaces.
Isomath defines a math alphabet for every required font variant and optionally re-defines the standard math alphabets in OML font encoding. Unfortunately, the number of math alphabets in one math version is limited to 16, so we have to be carefull not to exceed this.
The italic bold math alphabet is named \mathbold like in related packages. With the reuseMathAlphabets option, \mathfb is redefined and \mathbold made an alias (overwriting existing definitions):
\ifisomath@reuseMathAlphabets
\DeclareMathAlphabet{\mathbf}{OML}{\isomath@rmdefault}{bx}{it}
\def\mathbold{\mathbf}
\else
\DeclareMathAlphabet{\mathbold}{OML}{\isomath@rmdefault}{bx}{it}
\fi
For italic sans-serif, we define a new alphabet named \mathsans (in analogy to \mathbold). As this typeface is not required by ISO 31, it is only defined if the OMLmathsans option is set:
\ifisomath@OMLmathsans
\DeclareMathAlphabet{\mathsans}{OML}{\isomath@sfdefault}{m}{it}
\fi
A sans serif slanted bold alphabet is needed for tensor symbols. With the reuseMathAlphabets option, \mathsf is redefined and \mathboldsans made an alias:
\ifisomath@reuseMathAlphabets
\DeclareMathAlphabet{\mathsf}{OML}{\isomath@sfdefault}{bx}{it}
\def\mathboldsans{\mathsf}
\else
\DeclareMathAlphabet{\mathboldsans}{OML}{\isomath@sfdefault}{bx}{it}
\fi
Redefine standard alphabets in OML font encoding if the corresponding OML math alphabets option is true:
\ifisomath@OMLmathrm
\SetMathAlphabet{\mathrm}{normal}{OML}{\isomath@rmdefault}{m}{n}
\fi
\ifisomath@OMLmathbf
\SetMathAlphabet{\mathbf}{normal}{OML}{\isomath@rmdefault}{b}{n}
\fi
\ifisomath@OMLmathsf
\SetMathAlphabet{\mathsf}{normal}{OML}{\isomath@sfdefault}{m}{n}
\fi
\ifisomath@OMLmathtt
\SetMathAlphabet{\mathtt}{normal}{OML}{\ttdefault}{m}{n}
\fi
The following macros allow semantic markup of mathematical symbols. The argument is typeset as proposed by ISO 31 and [typefaces].
Symbols for vectors are typeset boldface italic:
\newcommand{\vectorsym}{\mathbold}
For easier writing or to make existing documents conform to the standard, you might want to re-define the standard \vec command after loading this package (cf. the Examples section).
Attention: Some fonts (CM, Latin Modern, ...) have old-style figures in their math italic version. The Null vector must not be written \vec{0} in this case. Use e.g. \mathbf{0}, \boldsymbol{0} (with AMS math) or \bm{0} (with boldmath). The latter two variants provide also a failsafe alias for a bold vector.
Symbols for matrices are typeset boldface italic, i. e. in the same face as vectors.
\newcommand{\matrixsym}{\mathbold}
Some font packages provide a matching math font but do not define a substitution in their *.fd files.
We define the substitutions needed for the math alphabet definitions in this package. Ideally, these should become part of a more complete set of definitions in the package's *.fd files:
Mathpazo (Palatino) ppl -> zplm
\DeclareFontFamily{OML}{ppl}{\skewchar\font127}
\DeclareFontShape{OML}{ppl}{m}{it}{<-> ssub * zplm/m/it}{}
\DeclareFontShape{OML}{ppl}{bx}{it}{<-> ssub * zplm/b/it}{}
Arev (see omlzavm.fd): fav -> zavm
\DeclareFontFamily{OML}{fav}{\skewchar \font =127}
\DeclareFontShape{OML}{fav}{m}{it}{<->ssub * zavm/m/it}{}
\DeclareFontShape{OML}{fav}{bx}{it}{<->ssub * zavm/b/it}{}
LX Fonts (see lxfonts.sty): llcmss -> llcmm
\DeclareFontFamily{OML}{llcmm}{\skewchar\font'177}
\DeclareFontShape{OML}{llcmm}{m}{it}{<-> lcmmi8}{}
\DeclareFontShape{OML}{llcmm}{bx}{it}{<-> lcmmib8}{}
\DeclareFontFamily{OML}{llcmss}{}
\DeclareFontShape{OML}{llcmss}{m}{it}{<-> ssub * llcmm/m/it}{}
\DeclareFontShape{OML}{llcmss}{bx}{it}{<-> ssub * llcmm/bx/it}{}
No declarations below this point:
\endinput
| [ISO-31] | International Standard 31 Quantities and units, (ISO 31-0:1992 to ISO 31-14:1992): http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_tc_browse.htm?commid=46202 |
| [typefaces] | (1, 2) Typefaces for Symbols in Scientific Manuscripts: http://physics.nist.gov/Document/typefaces.pdf |
| [checklist] | SI Unit rules and style conventions Check List for Reviewing Manuscripts: http://physics.nist.gov/cuu/Units/checklist.html |
| [fonts-for-symbols] | (1, 2) On the use of italic and roman fonts for symbols in scientific text, (Revised December 1999): http://old.iupac.org/standing/idcns/fonts_for_symbols.html |
| [SI-brochure] | The International System of Units (SI): http://www.bipm.org/en/si/si_brochure/ |
| [encguide] | LaTeX font encodings: http://dante.ctan.org/CTAN/macros/latex/doc/encguide.pdf |
| [fntguide] | LaTeX 2e font selection: http://dante.ctan.org/CTAN/macros/latex/doc/fntguide.pdf |
| [tr25] | Unicode Support for Mathematics, Unicode Technical Report #25: http://www.unicode.org/reports/tr25/ |