path: root/Master/texmf-dist/doc/latex/isomath/isomath.txt

.. -*- rst-mode -*-

isomath: Math for scientists
****************************

:Author:    Günter Milde
:Date:      2011-01-14
:Copyright: © 2008, 2011 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 sets up an “ISO math style” allowing the
           use of Greek and Latin letters as symbols for scalars,
           vectors, matrices, and tensors in the typefaces recommended
           for scientific papers by the International Standard
           ISO 80000-2.

.. contents::
.. sectnum::


Features
--------

.. How do you write the stress tensor ``$\sigma$`` in a
   `sans-serif bold italic` typeface, as recommended by [typefaces]_?

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

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

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

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

The traditional TeX `math style`_ deviates from this rules in some
points:

* capital Greek letters default to upright shape,

* small Greek letters are excluded from font changes with the `math
  alphabets`_.

* The ``\vec`` command produces an arrow accent.

The `isomath` package implements an `ISO math style`_ and provides
`new math alphabets`_ with bold italic and sans-serif bold italic
typeshape that can be used for vector and tensor symbols.


.. _`equal treatment of Latin and Greek`:

ISO math style
~~~~~~~~~~~~~~

The required package fixmath_ changes the default math layout to the
“ISO” `math style`_:

+ Uppercase Greek letters are typeset italic by default.

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

However, fixmath works only for the Computer Modern font family.
With `isomath`,

+ the used math fonts are configurable (using the rmdefault_ and
  sfdefault_ options), and

+ upright Greek letters can be made available through the common
  ``\math*`` alphabets via the `OMLmath*`_ options if the
  corresponding fonts support the `OML font encoding`_.

.. Caution::

  Using Greek letters in standard `math alphabets`_, e. g.,
  ``\mathrm{\pi}``, can lead to garbage, as the standard math
  alphabets are usually taken from text fonts that have ligatures and
  non-alpha symbols in place of the small Greek letters.
  Do not use small Greek letters in the standard math alphabet commands
  ``mathit``, ``mathrm``, ``mathbf``, ``mathsf``, and ``mathtt``
  unless you use the `OMLmath*`_ options.

  Some packages provide alternative macros or options for upright
  Greek letters (cf. `Table 6`_).


New math alphabets
~~~~~~~~~~~~~~~~~~
`Isomath` defines three new `math alphabets`_:

  .. class:: borderless

  ===============  ======================  =================================
  ``\mathbfit``    boldface italic         vector and matrix symbols
  ``\mathsfit``    sans-serif italic       optional (see OMLmath*_ options)
  ``\mathsfbfit``  sans-serif bold italic  tensor symbols
  ===============  ======================  =================================

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) have old-style numbers in place of italic
  digits.

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

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

  .. class:: borderless

  ==========================  ========================================
  ``\vectorsym, \matrixsym``  bold italic for Greek and Latin letters,
                              bold upright for numbers

  ``\tensorsym``              sans-serif bold italic
  ==========================  ========================================


Usage
-----

Make sure that LaTeX can find ``isomath.sty`` and load it with
``\usepackage`` (see also Options_ and Examples_).

Options
~~~~~~~

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`_).


sfdefault
'''''''''
Family for sans-serif math fonts. The default is ``cmbr`` because many
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`_:

.. class:: borderless

========== =========== ===================================================
Name       Package     Comment
========== =========== ===================================================
``cmbr``   cmbright_   `Computer Modern Bright`, bitmap, slightly lighter
                       than cmss (Type 1 fonts with hfbright_)
``fav``    arev_       `Arev` (`Vera Sans`) with math extension,
                       large x-height
``iwona``  iwona_      Humanistic Sans Serif,
                       some shapes very similar to roman
``hvm``    hvmath_     `Helvetica Math`, commercial, free bitmap version
``llcmss`` lxfonts_    `LX Fonts`, very wide, eccentric, large x-height,
                       new in 2008
========== =========== ===================================================


scaled
''''''
To improve the chances of configuring a matching sans serif math font,
the fonts, ``fav``, ``llcmss``, and ``iwona`` can be scaled with the
``scaled`` option (cf. Examples_).


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. [#]_

.. [#] 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, so watch for
   side-effects.

.. _OMLmath*:

OMLmathrm, OMLmathbf, OMLmathsf, OMLmathsfit, OMLmathtt
'''''''''''''''''''''''''''''''''''''''''''''''''''''''

With Greek letters defined as ``\mathalpha``, the letter fonts are
expected to be in `OML font encoding`_.  The predefined
`math alphabets`_, however, use OT1 encoded text fonts. These fonts
have ligatures and accents in place of the small Greek letters.
The ``\mathsfit`` alphabet is not required for ISO conforming math.

The ``OMLmath*`` options bind the corresponding ``\math*`` command to an
OML-encoded font.
This enables use of small Greek letters in `math alphabet`_ commands,
e. g., ``\mathrm{\pi}`` *if an OML encoded font is available*.
`Table 3`_ lists font families supporting the OML encoding.

.. caution::

  If no matching OML encoded font is found, LaTeX's substitute
  mechanism kicks in and 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.


Examples
~~~~~~~~

* Redefine the standard ``\vec`` command to set its argument in an
  ISO-conforming math alphabet.::

    \usepackage{isomath}
    \renewcommand{\vec}{\vectorsym}

* Use scaled arev_ fonts for the sans serif 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.

How to get upright small Greek letters
''''''''''''''''''''''''''''''''''''''

Of the following methods, only the first requires `isomath`:

a) Use `isomath` and the mathdesign_ package::

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

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

b) 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).

c) Use a package that provides macros for upright Greek letters
   in math:
   
     .. class:: borderless
     
     =============  =====================================
     fourier_       ``\otheralpha ... \otherOmega``           
     kpfonts_       ``\alphaup ... \Omegaup``            
     mathdesign_    ``\alphaup ... \Omegaup``            
     upgreek_       ``\upalpha ... \upOmega``            
     =============  =====================================

d) 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 }}}



Related packages
----------------

Requirements
~~~~~~~~~~~~

fixmath_
  by Walter Schmidt defines Greek letters as alphabetic symbols.

kvoptions_
  by Heiko Oberdiek facilitates the setup of package options
  and provides a key=value interface (based on keyval_).


Recommendations
~~~~~~~~~~~~~~~

cmbright_
  by Walter Schmidt provides sans serif and sans-serif bold fonts
  for the ``\mathsfit`` and ``\mathsfbfit`` alphabets that match
  with Computer Modern and derivatives. Free Type 1 versions of the
  fonts are provided by hfbright_.

arev_
  by Stephen Hartke provides the not-so-light `Arev` sans serif font
  with letters that are clearly distinguishable from the roman or
  italic counterparts (important if used to distinguish vectors and
  tensors).

  `Arev` has a large x-height. For many fonts, either small or capital
  letters will not match in size.


Alternatives
~~~~~~~~~~~~

See `Table 2`_ for other packages that implement the “ISO” `math
style`_ and `Table 6`_ for packages that provide bold italic
math fonts.

`“In-line math versions”`_
  can be used as ISO-conforming replacement for ``\vec``:

  * ``\boldsymbol`` from `amsbsy`_ (part of `amsmath`_, the
    near-indispensable adjunct to serious mathematical typesetting in
    LaTeX),

  * ``\bm`` from the `bm`_ package. Combining `bm` and `isomath` may
    lead to the `too many math alphabets used in version normal`_ error.

``\text``
  from `amsmath`_ can be used to get, e. g., upright or sans-serif
  bold italic Greek symbols from a text font into a formula (see
  `How to get upright small Greek letters`_).

unicode-math_
  for XeTeX and LuaTeX allows mathematical typesetting using OpenType
  math fonts. It supports the “ISO” `math style`_ and all mathematical
  characters in the Unicode standard.

  unicode-math cannot be used together with `isomath`. It can, however,
  replace all of isomath's functionality. See the discussion of `the
  unicode-math package`_ below.


Conflicts
~~~~~~~~~

“_`too many math alphabets used in version normal`”
  This error occurs if the combination of packages tries to load more
  than 16 fonts into the ``normal`` `math version`_.

  `Isomath` can reduce the number of math alphabet definitions with the
  reuseMathAlphabets_ option (see there for side-effects).

  Examples for problematic combinations:

  + The `kpfonts`_, `pxfonts`_, and `txfonts`_ packages define many
    additional math alphabets.

  + The `bm`_ package normally allocates several symbol fonts for bold
    and heavy fonts. Their number can be customized by defining
    ``\bmmax`` and ``\hmmax`` before loading the package.

fourier_
  provides upright and italic Greek letters, but uses non-standard
  math font encodings. It cannot be used with `isomath`.

  However, it is possible to use the non-alphanumeric symbols from
  `fourier`_ together with math alphabets from another package, e.g
  `mathdesign`_::

         \usepackage{fourier}
         \usepackage[OMLmathbf,rmdefault=mdput,
                     sfdefault=arev,scaled=0.85]{isomath}


Background
----------

This section discusses LaTeX `math font selection`_, suitable
`math letter fonts`_ for the ISO math style, and the relation of LaTeX and
`Unicode mathematical typesetting`_.


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`_ (cf. `Table 2`_).

.. _math alphabet:

Math alphabets
''''''''''''''

Math alphabets are a counterpart 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:

    .. class:: borderless

    =================  ===============
    ``\mathnormal``     default [#mathnormal]_
    ``\mathrm``         roman [#roman]_
    ``\mathbf``         bold roman
    ``\mathsf``         sans serif
    ``\mathit``         text italic
    ``\mathtt``         typewriter
    ``\mathcal``        calligraphic
    =================  ===============

.. [#mathnormal] ``\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).

.. [#roman] 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.


.. _math version:

Math versions
'''''''''''''

The number of mathematical symbols exceeds the maximal number of
characters in a TeX font file by an order of magnitude.  [#max]_
Grouping math fonts with common characteristics in math versions
simplifies the setting of font attributes for mathematical expressions.

*Math versions* set up “math symbol fonts” for non-alphanumeric
symbols and bind the `math alphabet`_ commands to fonts using default
values for non-specified font attributes. TeX limits the number of
(symbol + alphanumeric) fonts per math version to 16.

The predefined math versions are ``normal`` and ``bold`` with the
defaults:

  .. class:: borderless

  ========  ==========  ========
  ..        ``normal``  ``bold``
  *type*    serif       serif
  *weight*  medium      bold
  *shape*   upright     upright
  ========  ==========  ========

Packages can define additional math versions, e. g., the wrisym_ package
defines a ``mono`` math version. A ``sans`` math version example is
available from a `comp.text.tex post
<http://newsgroups.derkeiler.com/Archive/Comp/comp.text.tex/2007-09/msg00181.html>`__

Math versions are intended for mathematical content in a special
context, e. g., a bold section heading.
Setting a math version resembles the individual selection of text
font attributes (bold, sans-serif, monospaced).

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.

Example: four ways to set the letter ``a`` in a bold
sans-serif font::

  % Text                 Math:
  \textbf{\textsf{a}}    $\bm{\mathsf{a}}$
  \bfseries \textsf{a}   \mathversion{bold} $\mathsf{a}$

.. [#max] Unicode provides about 2500 math characters. Font files used
   by 8-bit TeX engines can hold up to 256 characters. The standard
   math fonts adhere to the original limit of 128 characters.

.. _math style:

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`_).

.. _Table 1:

.. table:: 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
  ============  =======  =======  =======  =======

LaTeX defaults to the “TeX” math style (without naming it such).
Alternative math styles are introduced by extension packages
(`Table 2`_).

.. _Table 2:

.. table:: Packages providing 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
  ============  =============  ==================================


Math letter fonts
~~~~~~~~~~~~~~~~~

The equal treatment of Latin and Greek letters in the `ISO math
style`_ is simplest 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.

OML font encoding
'''''''''''''''''

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 formulas (typically used for variables) together with some
  symbols.

The reference to *italic* shape is odd:

* No other font encoding is specific to the font shape.

* The different font selection and the semantic of font features in
  math 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 formulas (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.


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 2009 + 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 3:

.. table:: Font families supporting the OML encoding

   ============= =========================== ======= ======== ====== =======
   Name          Family                      m/it    bx/it    m/n    bx/n
   ============= =========================== ======= ======== ====== =======
   aer           AE (Almost European)           ✓      ✓
   antt          Antykwa Torunska               ✓      ✓
   cmr           Computer Modern Roman          ✓      ✓
   ccr           Concrete                       ✓      ✓
   cmbr          Computer Modern Bright         ✓      ✓
   hlh           Lucida                         ✓      ✓
   hfor          CM with old-style digits       ✓      ✓
   iwona         Iwona (sans serif)             ✓      ✓
   jkp           Kepler Serif                   ✓      ✓
   jkpl          Kepler Serif                   ✓      ✓
   jkpvos        Kepler Serif                   ✓      ✓
   jkplvos       Kepler Serif                   ✓      ✓
   llcmm         LX Fonts (sans serif)          ✓      ✓
   lmr           Latin Modern Roman             ✓      ✓
   mak           Kerkis                         ✓
   kurier        Kurier                         ✓      ✓
   mdbch         Math Design Charter            ✓      ✓         ✓     ✓
   mdput         Math Design Utopia             ✓      ✓         ✓     ✓
   mdugm         Math Design Garamond           ✓      ✓         ✓     ✓
   neohellenic   GFS Neohellenic                ✓
   plcm          CM (PLaTeX)                    ✓
   ptmom         Times (Omega or MB-Times)      ✓      ✓
   ptmomu        Times (Omega or MB-Times)      ✓      ✓
   ptmcm         Times (psfont)                 ✓
   pxr           Palatino (pxfonts)             ✓      ✓
   qpl           Palatino/Pagella (qpxmath)     ✓      ✓
   qtm           Times/Termes (qtxmath)         ✓      ✓
   txr           Times (txfonts)                ✓      ✓
   udidot        Didot (gfsdidot)               ✓
   ywclm         (greektex)                     ✓      ✓
   zavm          Arev (Vera Sans-Serif)         ✓      ✓
   zesfcm        (efont)                        ✓
   zplm          Palatino (mathpazo)            ✓      ✓
   zpple         Palatino                       ✓      ✓
   ztmcm         Times (mathptmv)               ✓
   zer           Computer Modern (zefonts)      ✓      ✓
   ============= =========================== ======= ======== ====== =======


`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.

.. _Table 4:

.. table:: 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 Courier (nctrsbk)
   uni           Universal (universa)
   uhv           Helvetica (helvetic)
   upl           Palatino (palatino)
   utm           Times (times)
   uzc           Zapf Chancery (zapfchan)
   ============= ===============================


Unicode mathematical typesetting
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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

This section compares `math font selection`_ in LaTeX and Unicode.
It suggests a set of 14 math alphabets 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).

.. _mathematical alphanumeric symbols:

Unicode math 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 assignes code points to most letters of the mathematical
alphabets in the `mathematical alphanumeric symbols Unicode block`_.
The plain (upright, serifed) 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. Full support is
provided by `the unicode-math package`_.

.. _table 5:

.. table:: Mapping Unicode `mathematical alphanumeric symbols`_ to LaTeX
   math alphabets.

   ==========  ========  =============  ==================  ===============
   serifs      weight    shape          symbols             math alphabet
   ==========  ========  =============  ==================  ===============
   *serif*     *medium*  *upright*      Latin/Greek/digits  ``\mathrm``
                                        [#up]_
   ..          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``
   ==========  ========  =============  ==================  ===============

.. [#up] plain standard characters outside the
   `mathematical alphanumeric symbols` Unicode block.

Naming scheme
`````````````

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

  .. class:: borderless

  =====  ================================
  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.


.. _Table 6:

.. table:: LaTeX support for `mathematical alphanumeric symbols`_.

   ============  ========================= ===========================
   style         math alphabet             package, comment
   ============  ========================= ===========================
   plain [#up]_  ``\mathrm``               predefined [#no-g]_
   ..            ``\mathup``               unicode-math_
      bf         ``\mathbf``               predefined  [#no-g]_
         it      ``\mathit``               predefined  [#no-g]_
      bf it      ``\mathbfit``             isomath [#digits]_
      ..         ``\mathbold``             fixmath_, mathpazo_,
                                           mathptmx_, tmmath_
                                           [#digits]_
      ..         ``\boldsymbol``           amsmath_
      ..         ``\bm``                   bm_
         cal     ``\mathcal``              predefined [#script]_
         ..      ``\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_
         ..      ``\mathbbm``              bbm_
         ..      ``\mathds``               dsfont (doublestoke_)
   sf            ``\mathsf``               predefined  [#no-g]_
   sf bf         ``\mathbfsfup``           unicode-math_
   sf    it      ``\mathsfit``             isomath [#digits]_
   sf bf it      ``\mathsfbfit``           isomath [#digits]_
   ..            ``\mathbold``             cmbright_, hvmath_
   ..            ``\mathbfsfit``           unicode-math_
         tt      ``\mathtt``               predefined  [#no-g]_
   ============  ========================= ===========================

.. [#no-g] no small Greek, full Greek with `OMLmath*`_ options.
.. [#digits] Some italic math fonts (e. g., cmr, cmbr) have old-style
             numbers in place of italic digits.
.. [#script] no small Latin, formal script with calrsfs_, eucal_, fourier_


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 mathematics 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`_
  are not directly supported but easy to emulate.

  As Unicode fonts can hold all math symbols in a single font file, a
  single ``\setmathfont[<font features>]{<font name>}`` can replace
  the ``\mathversion{<mathversion>}`` command if a complete OpenType
  math font in the desired version is available.


  However, complete OpenType math fonts are rare. Therefore
  unicode-math supports using multiple fonts with the ``range``
  option.  This way one can emulate, e. g., the ``bold`` math version
  via::

     \renewcommand{\boldmath}{%
       \setmathfont{XITS Bold}%
       \setmathfont[range={"1D400-"1F020}]{XITS Math}%
       \setmathfont[range=\mathup->\mathbfup]{XITS Math}%
       \setmathfont[range=\mathsfit->\mathbfsfit]{XITS Math}%
       % ...
     }

  It would be nice if unicode-math could provide a ``\newmathversion``
  command similar to the ``\newfontfamily`` in fontspec_ for such setups.

  For alphanumerical characters, the ``\mathbf``, ``\mathsf``, and
  ``\mathsfbf`` behave like `“in-line math versions”`_.

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


Conclusions and outlook
~~~~~~~~~~~~~~~~~~~~~~~

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 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).


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/.

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

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

.. [tr25] 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.

.. see also
   [koma-mail] Custom font substitution: http://www.komascript.de/node/823.


.. Links
   =====

.. _BIPM:  http://www.bipm.org/
.. _IUPAC: http://iupac.org/
.. _IUPAP: http://www.iupap.org/
.. _LaTeX Project Public License: http://www.latex-project.org/lppl.txt
.. _Jens-Peer Kuska: http://phong.informatik.uni-leipzig.de/~kuska/
.. _NIST:  http://physics.nist.gov/
.. _mathematical alphanumeric symbols unicode block:
    http://www.unicode.org/charts/PDF/U1D400.pdf
.. _amsbsy: http://mirror.ctan.org/help/Catalogue/entries/amsbsy.html
.. _amsfonts: http://mirror.ctan.org/help/Catalogue/entries/amsfonts.html
.. _amsmath: http://mirror.ctan.org/help/Catalogue/entries/amsmath.html
.. _amssymb: http://mirror.ctan.org/help/Catalogue/entries/amssymb.html
.. _arev: http://mirror.ctan.org/help/Catalogue/entries/arev.html
.. _Asana Math: http://mirror.ctan.org/help/Catalogue/entries/asana-math.html
.. _bm: http://mirror.ctan.org/help/Catalogue/entries/bm.html
.. _bbm: http://mirror.ctan.org/help/Catalogue/entries/bbm.html
.. _bbold: http://mirror.ctan.org/help/Catalogue/entries/bbold.html
.. _calrsfs: http://mirror.ctan.org/help/Catalogue/entries/calrsfs.html
.. _cmbright: http://mirror.ctan.org/help/Catalogue/entries/cmbright.html
.. _doublestoke: http://mirror.ctan.org/help/Catalogue/entries/doublestoke.html
.. _eucal: http://mirror.ctan.org/help/Catalogue/entries/eucal.html
.. _eufrak: http://mirror.ctan.org/help/Catalogue/entries/eufrak.html
.. _eulervm: http://mirror.ctan.org/help/Catalogue/entries/eulervm.html
.. _euscript: http://mirror.ctan.org/help/Catalogue/entries/euscript.html
.. _fixmath: http://mirror.ctan.org/help/Catalogue/entries/fixmath.html
.. _fix-cm: http://mirror.ctan.org/help/Catalogue/entries/fix-cm.html
.. _fourier: http://mirror.ctan.org/help/Catalogue/entries/fourier.html
.. _fontspec: http://mirror.ctan.org/help/Catalogue/entries/fontspec.html
.. _hvmath: http://mirror.ctan.org/help/Catalogue/entries/hvmath.html
.. _hfbright: http://mirror.ctan.org/help/Catalogue/entries/hfbright.html
.. _ifthen: http://mirror.ctan.org/help/Catalogue/entries/ifthen.html
.. _iwona: http://mirror.ctan.org/help/Catalogue/entries/iwona.html
.. _kpfonts: http://mirror.ctan.org/help/Catalogue/entries/kpfonts.html
.. _kvoptions: http://mirror.ctan.org/help/Catalogue/entries/kvoptions.html
.. _keyval: http://mirror.ctan.org/help/Catalogue/entries/keyval.html
.. _lxfonts: http://mirror.ctan.org/help/Catalogue/entries/lxfonts.html
.. _lucimatx: http://pctex.com/files/managed/b/bf/lucimatxAbbrev.pdf
.. _mathbbol: http://mirror.ctan.org/help/Catalogue/entries/mathbbol.html
.. _mbboard: http://mirror.ctan.org/help/Catalogue/entries/mbboard.html
.. _mathdesign: http://mirror.ctan.org/help/Catalogue/entries/mathdesign.html
.. _mathpazo: http://mirror.ctan.org/help/Catalogue/entries/mathpazo.html
.. _mathptmx: http://mirror.ctan.org/help/Catalogue/entries/mathptmx.html
.. _mathrsfs: http://mirror.ctan.org/help/Catalogue/entries/mathrsfs.html
.. _New Euler: https://github.com/khaledhosny/euler-otf
.. _pxfonts: http://mirror.ctan.org/help/Catalogue/entries/pxfonts.html
.. _sfmath: http://dtrx.de/od/tex/sfmath.html
.. _tmmath: http://mirror.ctan.org/help/Catalogue/entries/tmmath.html
.. _txfonts: http://mirror.ctan.org/help/Catalogue/entries/txfonts.html
.. _unicode-math:
    http://mirror.ctan.org/help/Catalogue/entries/unicode-math.html
.. _upgreek: http://mirror.ctan.org/help/Catalogue/entries/upgreek.html
.. _wrisym: http://phong.informatik.uni-leipzig.de/~kuska/wri_texmf_4.2.zip
.. _XITS: http://mirror.ctan.org/help/Catalogue/entries/xits.html