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isomath

isomath

Mathematical style for science and technology

Author
Günter Milde
Date
2012-09-04
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 provides tools for a mathematical style that conforms to the International Standard ISO 80000-2 and is common in science and technology. It changes the default shape of capital Greek letters to italic, sets up bold italic and sans-serif bold italic math alphabets with Latin and Greek characters, and defines macros for markup of vector, matrix and tensor symbols.

Contents

1 Features

In their style guides, e. g. [typefaces], [checklist], [SI], [fonts_for_symbols], [Red-Book], [Green-Book], many international scientific organisations recommend layout rules for mathematics in line with the International Standard [ISO-80000-2].

International standard layout rules

  • The overall rule is that symbols representing physical quantities (or variables) are italic, but symbols representing units, or labels, are roman.

  • Symbols for vectors and matrices are bold italic, symbols for tensors are sans-serif bold italic.

  • The above rules apply equally to letter symbols from the Greek and the Latin alphabet.

TeX's default mathematical style deviates from this rules in several points:

The isomath package implements an “ISO” math style, provides new math alphabets with bold italic and sans-serif bold italic type and macros for semantic markup of vector, matrix and tensor symbols. It can be combined with most packages for mathematical typesetting (see isomath-test.tex and the sections on alternatives and conflicts).

1.1 “ISO” math style

Isomath builds on the package fixmath by Walter Schmidt to change the default mathematics layout to the “ISO” math style:

  • Capital Greek letters are typeset in italic shape by default.

  • Both, Greek and Latin letters change shape if a different math alphabet is used.

Caution!

Be careful with Greek letters in the argument of \mathit, \mathrm, \mathbf, \mathsf, and \mathtt. By default, these math alphabets use text fonts. Fonts in OT1 text font encoding have capital (but not small) Greek letters at the expected places, T1 encoded text fonts have no Greek letters at all.

See the examples section on how to get upright small Greek letters in mathematical context.

1.2 New math alphabets

Isomath defines the new math alphabets:

\mathbfit

boldface italic

vector and matrix symbols

\mathsfit

sans-serif italic

optional (see OMLmath*_ options)

\mathsfbfit

sans-serif bold italic

tensor symbols

For compatibility with earlier versions and related packages, the new math alphabets are also available under the aliases \mathbold, \mathsans, and \mathboldsans.

The rmdefault and sfdefault options set the font family used for these alphabets.

Caution!

Using the new math alphabets for numbers can result in upright old-style numbers instead of italic ones, because some italic math fonts (e. g., cmr, cmbr) contain old-style in place of italic digits.

1.3 Semantic markup

The following commands set the argument in an ISO-conforming math alphabet:

\vectorsym, \matrixsym

bold italic for Greek and Latin letters, bold upright for numbers

\tensorsym

sans-serif bold italic

2 Usage

Make sure that LaTeX can find isomath.sty and load it with:

\usepackage{isomath}

Optionally redefine the standard vector macro \vec:

\renewcommand{\vec}{\vectorsym}

(see also Options, Examples, and isomath-test.tex).

2.1 Options

2.1.1 rmdefault

Family for serif math fonts (\mathrm, \mathbf, \mathit, \mathbfit). The default is to use the corresponding text font family (the value of \rmdefault). The font must be available in OML font encoding (cf. Table 3).

2.1.2 sfdefault

Family for sans-serif math fonts. The default is cmbr because most sans-serif fonts define the Computer Roman font cmm as OML substitution (see Table 4).

There are only few sans serif fonts in OML font encoding:

Name

Package

Comment

cmbr

cmbright

Computer Modern Bright, bitmap, slightly lighter than cmss (Type 1 fonts with hfbright)

fav

arev

Arev (Vera Sans), large x-height

hvm

hvmath

Helvetica Math, commercial, free bitmap version

iwona

iwona

Iwona, humanistic sans serif, some shapes very similar to roman

jkpss

kpfonts

Kepler Sans, quite light

llcmss

lxfonts

LX Fonts, “slide fonts”, very wide, large x-height

2.1.3 scaled

To improve the chances of finding a matching sans serif math font, the fonts fav, iwona, jkpss, and llcmss can be scaled with the scaled option (cf. Examples). For other fonts, the option is ignored.

2.1.4 reuseMathAlphabets

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.1

1

To access the upright shapes, the corresponding \textbf and \textsf commands might be used. Watch for side-effects, as these commands switch to text mode so that the font settings in the embedding text apply.

2.1.5 OMLmathrm, OMLmathbf, OMLmathsf, OMLmathsfit, OMLmathtt

The OMLmath* options bind the corresponding \math* command to an OML-encoded font.

The \mathsfit alphabet is not required for ISO conforming mathematical layout and therefore only defined if the OMLmathsfit argument is used.

The predefined math alphabets \mathrm, \mathbf, and \mathtt use OT1 encoded text fonts with ligatures and accents in place of the small Greek letters. The OMLmath* options enable the use of small Greek letters in math alphabet commands, e. g. \mathrm{\pi}, if the corresponding font is available in OML font encoding. Table 3 lists font families supporting the OML encoding.

Caution!

If no matching OML encoded font is found, LaTeX's substitute mechanism selects a font with different font attributes (for all letters, not only Greek). Currently, only the mathdesign package provides upright fonts in OML encoding. Many font packages define an italic font as OML substitute for roman fonts.

With some packages, these options can result in a “too many math alphabets used in version normal” error.

2.2 Examples

  • Use scaled arev fonts for the sans serif math alphabets (adapt the scaling factor to your needs):

    \usepackage[sfdefault=fav,scaled=0.875]{isomath}
    
  • Define the \mathsfit sans-serif italic math alphabet:

    \usepackage[OMLmathsfit]{isomath}
    
  • The \mathbfit and \mathsfbfit alphabets do not have a different weight in the bold math version because the number of LaTeX math fonts providing extrabold or ultrabold series is negligible.

    As a workaround, use the heavier arev font, scaled to 0,875, in the bold version of \mathsfbfit:

    \usepackage{isomath}
    \DeclareFontShape{OML}{fav}{bx}{it}{<-> s * [0.875] zavmbi7m}{}
    \SetMathAlphabet{\mathsfbfit}{bold}{OML}{fav}{bx}{it}
    

See also the isomath-test.tex test document.

2.2.1 How to get upright small Greek letters

Of the following methods, only the first requires isomath:

  1. Use isomath and the mathdesign package:

    \usepackage[utopia]{mathdesign}
    \usepackage[OMLmathrm,OMLmathbf]{isomath}
    

    Now, e. g., \mathrm{\pi} and \mathbf{\pi} work as expected.

  2. To get upright small Greek letters without affecting other fonts, set the math alphabet manually to one of the three mathdesign fonts, e. g.:

    \SetMathAlphabet{\mathbf}{normal}{OML}{mdput}{b}{n}
    

    (check if the letter shapes match with the rest of the document).

  3. Use a package that provides macros for upright Greek letters in math mode:

    fourier

    \otheralpha ... \otherOmega

    kpfonts

    \alphaup ... \Omegaup

    mathdesign

    \alphaup ... \Omegaup

    upgreek

    \upalpha ... \upOmega

  4. Use an upright text character (requires a matching LGR-encoded Greek text font). The following lines redefine \pi to set the mathematical constant pi upright:

    \usepackage[LGR,T1]{fontenc}
    \usepackage[greek,british]{babel}
    \usepackage{amsmath}
    \let\mathpi\pi
    \renewcommand{\pi}{\text{\textrm{\greektext p }}}
    
  5. Use the text character with the alphabeta package from the lgrx bundle:

    \usepackage{amsmath}
    \usepackage{alphabeta}
    

    and in the body

    $ u = 2 \text{\pi} r $
    

4 Background

This section discusses LaTeX math font selection, the OML font encoding, and the relation of LaTeX and Unicode mathematical typesetting.

4.1 Math font selection

There are three complementary methods to set font attributes in LaTeX math mode: LaTeX 2e font selection [fntguide] describes math alphabets and math versions, several extension packages provide alternative math styles.

4.1.1 Math alphabets

TeX's math alphabets correspond to the mathematical alphanumeric symbols block in Unicode. Both are “to be used for mathematical variables where style variations are important semantically”. The font guide [fntguide] defines in section 3:

Some math fonts are selected explicitly by one-argument commands such as \mathsf{max} or \mathbf{vec}; such fonts are called math alphabets.

Math fonts [...] have the same five attributes as text fonts: encoding, family, series, shape and size. However, there are no commands that allow the attributes to be individually changed. Instead, the conversion from math fonts to these five attributes is controlled by the math version.

The predefined math alphabets are:

\mathnormal

default2

\mathrm

roman3

\mathbf

bold roman

\mathsf

sans serif

\mathit

text italic

\mathtt

typewriter

\mathcal

calligraphic

2

\mathnormal is used by default for alphanumeric characters in math mode. It sets the letter shape according to character class and math style. (Table 1 shows the default letter shapes for common math styles).

3

The specifier “roman” is ambiguous: roman shape stands for upright, while roman type stands for serif (as opposed to sans serif).

Many packages define additional math alphabets (cf. Table 6).

In contrast to the similar named text commands, math alphabets are not orthogonal, e. g., the code $\mathit{\mathbf{a}}$ sets the letter a in upright bold type.

4.1.2 Math versions

Math versions specify the mapping from commands for mathematical symbols and math alphabets to a set of mathematical fonts4. They are intended for mathematical content in a special context like a bold section heading. Selecting a math version resembles the individual selection of text font attributes.

Example:

Some alternatives to set the letter a in a bold upright sans-serif font:

Text

Math

\textbf{\textsf{a}}

$\bm{\mathsf{a}}$

\bfseries \textsf{a}

\mathversion{bold} $\mathsf{a}$

\bfseries \sffamily a

$\mathsfbf{a}$

The predefined math versions are normal and bold with the following defaults for non-specified font attributes:

attribute

normal

bold

type

serif

serif

weight

medium

bold

shape

upright

upright

Packages can define additional math versions, e. g., the kpfonts package defines a sans math version (another sans math version example is available from a comp.text.tex post`) and the wrisym package defines a mono math version.

Math versions can only be changed outside of math mode. The commands \boldsymbol (amsmath) and \bm (bm) behave like “in-line math versions”: they typeset their argument using the fonts of the bold math version but can be used inside math mode.

4

The number of mathematical symbols exceeds the maximal number of characters in a TeX font file by an order of magnitude: Unicode defines about 2500 mathematical characters [tr25], font files used by 8-bit TeX engines are limited to 256 characters. The standard math fonts adhere to the original limit of 128 characters. Grouping math fonts with common characteristics in math versions simplifies the setting of font attributes for mathematical expressions. TeX limits the number of (symbol + alphanumeric) fonts per math version to 16.

4.1.3 Math styles

A math style is a document-level feature that determines the default letter shape in math mode (i. e. the shape attribute of letters in the \mathnormal math alphabet).5 LaTeX defaults to the “TeX” math style (without naming it such). Alternative math styles are introduced by extension packages (Table 2).

5

The math-style option of unicode-math changes also the shape attribute of other math alphabets (see also section the unicode-math package).

Default letter shapes for common math styles

math style

latin

Latin

greek

Greek

TeX

it

it

it

up

ISO

it

it

it

it

French

it

up

up

up

upright

up

up

up

up

Packages providing alternative math styles

math style

Package

Option(s)

ISO

fixmath

 

isomath

 

kpfonts

slantedGreeks

lucimatx

math-style=iso

mathdesign

greekuppercase=italicized

mathpazo

slantedGreek

mathptmx

slantedGreek

unicode-math

math-style=ISO

French

fourier

upright

kpfonts

frenchstyle (or upright)

lucimatx

math-style=french

mathdesign

uppercase=upright, greeklowercase=upright

unicode-math

math-style=french

upright

eulervm

 

lucimatx

math-style=upright

unicode-math

math-style=upright

4.2 OML font encoding

The equal treatment of Latin and Greek letters in the “ISO” math style is best achieved with a font that contains all required letters in one file.

There is only one established LaTeX font encoding that contains Latin and Greek letters, the OML font encoding. The standard Greek font encoding T7 is just a “reserved name” and the de-facto standard Greek text font encoding LGR has no Latin letters. Unfortunately, OML support is limited to a few (mostly italic) fonts.

4.2.1 Discussion

The LaTeX font encodings guide [encguide] names the OML encoding TeX math italic and defines:

The OML encoding contains italic Latin and Greek letters for use in mathematical formulae (typically used for variables) together with some symbols.

The reference to italic shape is odd:

  • No other font encoding is specific to a font shape.

  • The different font selection and the semantic of font features in mathematical formulae do not interfere with the font encoding: 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.

This seems to be more a remnant of pre-NFSS times than a necessary restriction – there is only one OML encoded font in Knuth's Computer Modern fonts: Computer Modern Math Italic (cmmi).

Proposals:

  • Drop the italic from the definition. Optionally add an explanation:

    The OML encoding contains Latin and Greek letters for use in mathematical formulae (typically used for variables) together with some symbols. It first appeared in the Computer Modern Math Italic (cmmi) font.

  • The name TeX math italic can be interpreted as “the encoding of Computer Modern Math Italic” rather than “an 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.

4.2.2 OML Support

Unfortunately, support for the OML encoding is missing for many font families even if the text font defines Greek letters. Supported font families can be found searching for oml*.fd files and grepping for DeclareFont.*OML in *.sty files.

Table 3 lists the findings for a selection of TeXLive 2012 + some additionally installed font packages.

  • If there is an alias (substitution) from the text font to a math-variant, only the text font is listed.

  • Many text fonts define substitutions also for upright shape, however mapping to an italic variant of the OML encoded font. These are not listed as supporting m/n or bx/n here.

Table 4 lists some fonts that define cmm as OML substitution. With isomath, a better matching substitution can be set using the rmdefault or sfdefault options.

Font families supporting the OML encoding

Name

Family (package)

m/it

bx/it

m/n

bx/n

antt

Antykwa Torunska (anttor)

   

cmr

Computer Modern

   

ccr

Concrete Roman (concmath)

   

cmbr

CM Bright (cmbright)

   

hlh

Lucida

   

hfor

CM with old-style digits

   

iwona

Iwona (sans serif) (iwona)

   

iwonal

Iwona light

   

iwonac

Iwona condensed

   

iwonalc

Iwona light condensed

   

jkp

Kepler Serif (kpfonts)

   

jkpw

Kepler Serif wide

   

jkpvos

Kepler Serif oldstyle

   

jkpvosw

Kepler Serif oldstyle wide

   

jkpl

Kepler Serif light

   

jkplw

Kepler Serif light wide

   

jkplvos

Kepler Serif light oldstyle

   

jkplvosw

Kepler Serif light os wide

   

jkpss

Kepler Sans (kpfonts)

   

jkpssvos

Kepler Sans oldstyle

   

jtm

expanded Times (jamtimes)

   

llcmm

LX Fonts (sans serif) (lxfonts)

   

lmr

Latin Modern Roman (lmodern)

   

mak

Kerkis (kerkis)

     

kurier

Kurier (sans serif) (kurier)

   

kurierc

Kurier condensed

   

kurierl

Kurier light

   

kurierlc

Kurier light condensed

   

mdbch

Math Design Charter (mathdesign)

mdput

Math Design Utopia

mdugm

Math Design Garamond

neohellenic

Neohellenic (gfsneohellenic)

     

ntxmi

Times (newtx)

   

nxlmi

Libertine (newtx)

   

plcm

CM (PLaTeX)

     

ptmom

Times (Omega or MB-Times)

   

ptmomu

Times (Omega or MB-Times)

   

ptmcm

Times (mathptmx)

     

pxr

Palatino (pxfonts)

   

qpl

Palatino/Pagella (qpxmath)

   

qtm

Times/Termes (qtxmath)

   

txr

Times (txfonts)

   

udidot

Didot (gfsdidot)

     

ywclm

(greektex)

   

zavm

Arev (Vera Sans-Serif)

   

zplm

Palatino (mathpazo)

   

zpple

Palatino

   

ztmcm

Times (mathptmx)

     

zer

Computer Modern (zefonts)

   
Non-CM fonts with cmm as OML substitution

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 Century Schoolbook (psnfss)

uni

Universal (universa)

uhv

Helvetica (helvetic)

upl

Palatino (palatino)

utm

Times (times)

uzc

Zapf Chancery (zapfchan)

4.3 Unicode mathematical typesetting

This section compares math font selection in LaTeX and Unicode. It suggests a set of 14 math alphabet commands that covers all Unicode mathematical alphanumeric symbols and discusses compatibility issues between math typesetting with traditional (8-bit) TeX engines versus the unicode-math package for Unicode-enabled TeX engines (XeTeX, LuaTeX).

The technical report [tr25] presents an in-depth discussion of the mathematical character repertoire of the Unicode Standard as well as mathematical notation in general.

4.3.1 Unicode mathematical alphabets

Chapter 2 Mathematical Character Repertoire of [tr25] lists 14 Mathematical Alphabets in Table 2.1. These mathematical alphabets are a superset of the predefined math alphabets in the LaTeX core.

Unicode assigns code points to most letters of the mathematical alphabets in the mathematical alphanumeric symbols Unicode block. The plain (upright) letters have been unified with the existing characters in the Basic Latin and Greek blocks.

Table 5 maps the 14 Unicode mathematical alphabets to LaTeX commands according to the naming scheme below. Table 6 lists the status of LaTeX support for the mathematical alphanumeric symbols.

4.3.1.1 Naming scheme

The naming scheme is an extension of the predefined math alphabet commands with the established short-cuts:

bf

bold

it

italic

cal

script (calligraphic)

frak

fraktur

bb

double-struck (blackboard bold)

sf

sans serif

combined to commands in the form \math<type><weight><shape>.

The <type>, <weight>, and <shape> specifiers are optional (defaults depend on the math version). Their order matches the names of Unicode Mathematical Alphanumeric Symbols.

Examples:

\mathbf{d}     % MATHEMATICAL BOLD SMALL D
\mathsfbfit{d} % MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL D.
Mapping Unicode mathematical alphanumeric symbols to LaTeX math alphabets.

serifs

weight

shape

symbols

math alphabet

serif

medium

upright

Latin/Greek/digits6

\mathrm

bold

 

Latin/Greek/digits

\mathbf

 

italic

Latin/Greek

\mathit

bold

italic

Latin/Greek

\mathbfit

 

script

Latin

\mathcal

bold

script

Latin

\mathbfcal

 

fraktur

Latin

\mathfrak

 

double-struck

Latin/digits

\mathbb

bold

fraktur

Latin

\mathbffrak

sans serif

   

Latin/digits

\mathsf

sans serif

bold

 

Latin/Greek/digits

\mathsfbf

sans serif

 

italic

Latin

\mathsfit

sans serif

bold

italic

Latin/Greek

\mathsfbfit

 

monospace

Latin/digits

\mathtt

6
(1, 2)

plain standard characters outside the mathematical alphanumeric symbols Unicode block.

4.3.1.2 LaTeX support

Most commonly used math alphabets are supported either by the TeX kernel or additional packages. Full support is only provided by the unicode-math package.

LaTeX support for mathematical alphanumeric symbols.

style

math alphabet

package, comment

plain6

\mathrm

predefined7

\mathup

unicode-math, kpfonts

bf

\mathbf

predefined7

it

\mathit

predefined7

bf it

\mathbfit

isomath8

\mathbold

fixmath, mathpazo, mathptmx, tmmath8

\boldsymbol

amsmath

\bm

bm

cal

\mathcal

predefined9

\mathscr

mathrsfs, euscript, mathdesign

bf cal

\mathbfscr

unicode-math

frak

\mathfrak

amssymb, amsfonts, eufrak

bf frak

\mathbffrak

unicode-math

bb

\mathbb

amssymb, bbold, mathbbol, mbboard, mathpazo, sbbm

\mathbbm

bbm

\mathds

dsfont (doublestoke)

sf

\mathsf

predefined7

sf bf

\mathbfsfup

unicode-math

sf it

\mathsfit

isomath8

sf bf it

\mathsfbfit

isomath8

\mathbold

cmbright, hvmath

\mathbfsfit

unicode-math

tt

\mathtt

predefined7

7
(1, 2, 3, 4, 5)

no small Greek, full Greek with OMLmath* options and OML-encoded fonts

8
(1, 2, 3, 4)

Some italic math fonts (e. g., cmr, cmbr) have old-style numbers in place of italic digits.

9

formal script with calrsfs, eucal, fourier, small Latin letters only with urwchancal

4.3.2 The unicode-math package

Users of UTF-8 enabled TeX engines (XeTeX, LuaTeX) can typeset mathematics with the experimental unicode-math package by Will Robertson. It provides a LaTeX interface to OpenType fonts with math support, e. g., Asana Math, Cambria Math, New Euler or XITS, with commands to access the complete mathematical character repertoire of the Unicode Standard.

LaTeX math font selection methods with unicode-math:

  • Math alphabets map to a range of the mathematical alphanumeric symbols block in the current font (or a substitution defined with the range math font option).

    Some command names differ from the predefined math alphabets or the above naming scheme:

    LaTeX

    unicode-math

    \mathbf

    \mathbfup

    \mathsf

    \mathsfup

    \mathsfbf

    \mathbfsfup

    \mathsfbfit

    \mathbfsfit

    With unicode-math, \mathbf, \mathsf, and \mathsfbf behave similar to “in-line math versions”: they consider the math style for upright vs. italic shape. Compatibility can be achieved via the options bold-style=upright and sans-style=upright.

    \mathbfsfit reverses the order of the sf and bf selectors, so that, e. g., the Unicode character MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL A is selected by the non-mnemonic \mathbfsfit{A}.

  • Math versions can be set up using the syntax \setmathfont[version=<version name>,<font features>]{<font name>}

  • Several math styles are supported with the math-style package option that accepts the values TeX, ISO, french, upright, and literal.

4.4 Conclusions and outlook

It is hoped, that in the future more font 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.

Upright small Greek letters in \mathrm would enable the specification of the constant pi, Myons, Pions, alpha-particles, photons, and neutrinos with math alphabets. (With mathdesign fonts, this is already possible today.)

With the development of the unicode-math package, an interesting alternative for ISO-conforming math typesetting became available to users of Unicode-enabled TeX engines (XeTeX or LuaTeX).

5 References

[ISO-80000-2]

Quantities and units – Part 2: Mathematical signs and symbols to be used in the natural sciences and technology: http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=31887.

[ISO-31]

Quantities and units, Superseded by [ISO-80000].

[typefaces]

National Institute of Standards and Technology (NIST), Typefaces for Symbols in Scientific Manuscripts: http://physics.nist.gov/cuu/pdf/typefaces.pdf.

[checklist]

National Institute of Standards and Technology (NIST), SI Unit rules and style conventions Check List for Reviewing Manuscripts: http://physics.nist.gov/cuu/Units/checklist.html.

[fonts_for_symbols]

International Union of Pure and Applied Chemistry (IUPAC), 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]

Bureau international des poids et mesures (BIPM), The International System of Units (SI): http://www.bipm.org/en/si/si_brochure/.

[Green-Book]

International Union of Pure and Applied Chemistry (IUPAC), Quantities, Units and Symbols in Physical Chemistry, 3rd edition, RSC Publishing, Cambridge 2007: [ISBN 0 85404 433 7; ISBN-13 978 0 85404 433 7].

[Red-Book]

International Union of Pure and Applied Physics (IUPAP), Symbols, Units, Nomenclature and Fundamental Constants in Physics: http://metrology.wordpress.com/measurement-process-index/iupap-red-book/index-iupap-red-book/.

[becc97]

Claudio Beccari, Typesetting mathematics for science and technology according to ISO 31 XI, TUGboat, Volume 18, 1997, No. 1: http://www.tug.org/TUGboat/tb18-1/tb54becc.pdf.

[encguide]

Frank Mittelbach, Robin Fairbairns, Werner Lemberg, LaTeX3 Project Team, LaTeX font encodings: http://mirror.ctan.org/macros/latex/doc/encguide.pdf.

[fntguide]
(1, 2)

LaTeX3 Project Team, LaTeX 2e font selection: http://mirror.ctan.org/macros/latex/doc/fntguide.pdf.

[tr25]
(1, 2, 3)

Barbara Beeton, Asmus Freytag, Murray Sargent III, Unicode Support for Mathematics, Unicode Technical Report #25: http://www.unicode.org/reports/tr25/.

[beeton:2000]

Barbara Beeton: Unicode and math, a combination whose time has come – Finally!, TUGBoat, 21#3, 2000: http://www.tug.org/TUGboat/Articles/tb21-3/tb68beet.pdf.

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