summaryrefslogtreecommitdiff
path: root/Master/texmf-dist/doc/latex/isomath/isomath.txt
diff options
context:
space:
mode:
authorKarl Berry <karl@freefriends.org>2012-09-12 22:14:06 +0000
committerKarl Berry <karl@freefriends.org>2012-09-12 22:14:06 +0000
commit60134622cf5eb833e549dd5dfefb08a674b5a78c (patch)
tree579dcaa6e820e1fba51249eb4c3c654c868c76b0 /Master/texmf-dist/doc/latex/isomath/isomath.txt
parent524f74405302fcc9daf66401d0da8485241764e9 (diff)
isomath (12sep12)
git-svn-id: svn://tug.org/texlive/trunk@27654 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/latex/isomath/isomath.txt')
-rw-r--r--Master/texmf-dist/doc/latex/isomath/isomath.txt722
1 files changed, 383 insertions, 339 deletions
diff --git a/Master/texmf-dist/doc/latex/isomath/isomath.txt b/Master/texmf-dist/doc/latex/isomath/isomath.txt
index 23100dcacfe..f91e12e6678 100644
--- a/Master/texmf-dist/doc/latex/isomath/isomath.txt
+++ b/Master/texmf-dist/doc/latex/isomath/isomath.txt
@@ -1,22 +1,26 @@
.. -*- rst-mode -*-
-isomath: Math for scientists
-****************************
+isomath
+*******
+Mathematical style for science and technology
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
:Author: Günter Milde
-:Date: 2011-01-14
-:Copyright: © 2008, 2011 Günter Milde
+:Date: 2012-09-10
+:Copyright: © 2008, 2012 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.
+: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::
+.. contents:: :depth: 2
.. sectnum::
@@ -24,121 +28,122 @@ 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
+ *sans-serif bold italic* typeface, as recommended by [typefaces]_?
+
+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]_.
+
+.. admonition:: 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.
+
+.. The recommendations in this standard are intended mainly for use in the
+ natural sciences and technology, but also apply to other areas where
+ mathematics is used.
+
+TeX's default mathematical style deviates from this rules in several
points:
-* capital Greek letters default to upright shape,
+* Capital Greek letters default to upright shape,
* small Greek letters are excluded from font changes with the `math
- alphabets`_.
+ alphabet`_ commands, and
-* The ``\vec`` command produces an arrow accent.
+* 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.
+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_).
-.. _`equal treatment of Latin and Greek`:
-ISO math style
-~~~~~~~~~~~~~~
+“ISO” math style
+~~~~~~~~~~~~~~~~
-The required package fixmath_ changes the default math layout to the
-“ISO” `math style`_:
+Isomath builds on the package fixmath_ by Walter Schmidt to change the
+default mathematics layout to the “ISO” `math style`_:
-+ Uppercase Greek letters are typeset italic by default.
++ Capital Greek letters are typeset in italic shape 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.
+ 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.
- Some packages provide alternative macros or options for upright
- Greek letters (cf. `Table 6`_).
+ See the examples_ section on `how to get upright small Greek letters`_ in
+ mathematical context.
New math alphabets
~~~~~~~~~~~~~~~~~~
-`Isomath` defines three new `math alphabets`_:
+`Isomath` defines the new `math alphabets`_:
- .. class:: borderless
+.. class:: borderless
- =============== ====================== =================================
- ``\mathbfit`` boldface italic vector and matrix symbols
- ``\mathsfit`` sans-serif italic optional (see OMLmath*_ options)
- ``\mathsfbfit`` sans-serif bold italic tensor symbols
- =============== ====================== =================================
+=============== ====================== =================================
+``\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) have old-style numbers in place of italic
- digits.
+ 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.
-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:
+The following commands set the argument in an ISO-conforming `math alphabet`_:
- .. class:: borderless
+.. class:: borderless
- ========================== ========================================
- ``\vectorsym, \matrixsym`` bold italic for Greek and Latin letters,
- bold upright for numbers
+========================== ========================================
+``\vectorsym, \matrixsym`` bold italic for Greek and Latin letters,
+ bold upright for numbers
- ``\tensorsym`` sans-serif bold italic
- ========================== ========================================
+``\tensorsym`` sans-serif bold italic
+========================== ========================================
Usage
-----
-Make sure that LaTeX can find ``isomath.sty`` and load it with
-``\usepackage`` (see also Options_ and Examples_).
+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_).
Options
~~~~~~~
@@ -153,7 +158,7 @@ family (the value of ``\rmdefault``). The font must be available in
sfdefault
'''''''''
-Family for sans-serif math fonts. The default is ``cmbr`` because many
+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`_).
@@ -161,26 +166,25 @@ 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
+``fav`` arev_ `Arev` (`Vera Sans`), large x-height
``hvm`` hvmath_ `Helvetica Math`, commercial, free bitmap version
-``llcmss`` lxfonts_ `LX Fonts`, very wide, eccentric, large x-height,
- new in 2008
-========== =========== ===================================================
+``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
+========== =========== =====================================================
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_).
+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.
reuseMathAlphabets
@@ -191,34 +195,35 @@ 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.
+ ``\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.
.. _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.
+
+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 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.
+ 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.
@@ -227,13 +232,7 @@ e. g., ``\mathrm{\pi}`` *if an OML encoded font is available*.
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
+* Use scaled arev_ fonts for the sans serif math alphabets
(adapt the scaling factor to your needs)::
\usepackage[sfdefault=fav,scaled=0.875]{isomath}
@@ -254,7 +253,8 @@ Examples
\DeclareFontShape{OML}{fav}{bx}{it}{<-> s * [0.875] zavmbi7m}{}
\SetMathAlphabet{\mathsfbfit}{bold}{OML}{fav}{bx}{it}
-See also the ``isomath-test.tex`` test document.
+See also the `isomath-test.tex`_ test document.
+
How to get upright small Greek letters
''''''''''''''''''''''''''''''''''''''
@@ -278,16 +278,16 @@ b) To get upright small Greek letters without affecting other fonts,
(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``
- ============= =====================================
+ in math mode:
+
+ .. 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
@@ -299,6 +299,15 @@ d) Use an upright text character (requires a matching LGR-encoded
\let\mathpi\pi
\renewcommand{\pi}{\text{\textrm{\greektext p }}}
+e) 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 $
Related packages
@@ -337,23 +346,26 @@ arev_
Alternatives
~~~~~~~~~~~~
-See `Table 2`_ for other packages that implement the “ISO” `math
-style`_ and `Table 6`_ for packages that provide bold italic
-math fonts.
+The TUGboat article by Claudio Beccari [becc97]_ discusses tricks and
+commands for physicists and engineers in order to satisfy the international
+regulations and to distinguish similar symbols with different meanings.
+
+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``:
+ * ``\bm`` from the `bm`_ package. Combining `bm` and `isomath` may
+ lead to the `too many math alphabets used in version normal`_ error.
+
* ``\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
+amsmath_
+ provides the command ``\text``, that 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_
@@ -361,7 +373,7 @@ unicode-math_
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,
+ `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.
@@ -379,10 +391,11 @@ Conflicts
Examples for problematic combinations:
+ The `kpfonts`_, `pxfonts`_, and `txfonts`_ packages define many
- additional math alphabets.
+ additional math alphabets (`kpfonts` works with `isomath`, if
+ it is loaded with ``\usepackage[nomathscript]{kpfonts}``).
+ The `bm`_ package normally allocates several symbol fonts for bold
- and heavy fonts. Their number can be customized by defining
+ and heavy fonts. Their number can be customised by defining
``\bmmax`` and ``\hmmax`` before loading the package.
fourier_
@@ -397,13 +410,19 @@ fourier_
\usepackage[OMLmathbf,rmdefault=mdput,
sfdefault=arev,scaled=0.85]{isomath}
+sansmath_
+ defines a ``sans`` `math version`_ using **text** fonts in OT1 or T1 font
+ encoding. As fixmath/isomath expect math fonts in `OML font encoding`_,
+ Greek letters will not work inside the ``sans`` math version defined by
+ sansmath.
+
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`_.
+This section discusses LaTeX `math font selection`_, the `OML font
+encoding`_, and the relation of LaTeX and `Unicode mathematical
+typesetting`_.
Math font selection
@@ -412,14 +431,14 @@ 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`_).
+provide alternative `math styles`_.
.. _math alphabet:
Math alphabets
''''''''''''''
-Math alphabets are a counterpart to the `mathematical alphanumeric
+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
@@ -437,17 +456,17 @@ section 3:
The _`predefined math alphabets` are:
- .. class:: borderless
+ .. class:: borderless
- ================= ===============
- ``\mathnormal`` default [#mathnormal]_
- ``\mathrm`` roman [#roman]_
- ``\mathbf`` bold roman
- ``\mathsf`` sans serif
- ``\mathit`` text italic
- ``\mathtt`` typewriter
- ``\mathcal`` calligraphic
- ================= ===============
+ ================= ===============
+ ``\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
@@ -470,53 +489,61 @@ letter ``a`` in **upright** bold type.
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* specify the mapping from commands for mathematical
+symbols and `math alphabets`_ to a set of mathematical fonts [#]_.
+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:
+
+ .. class:: borderless
+
+ ============================ ===================================
+ Text Math
+ ============================ ===================================
+ ``\textbf{\textsf{a}}`` ``$\bm{\mathsf{a}}$``
+ ``\bfseries \textsf{a}`` ``\mathversion{bold} $\mathsf{a}$``
+ ``\bfseries \sffamily a`` ``$\mathsfbf{a}$``
+ ============================ ===================================
-*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:
+following defaults for non-specified font attributes:
- .. class:: borderless
+.. class:: borderless
- ======== ========== ========
- .. ``normal`` ``bold``
- *type* serif serif
- *weight* medium bold
- *shape* upright upright
- ======== ========== ========
+========= ========== ========
+attribute ``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>`__
+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 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).
+__ http://newsgroups.derkeiler.com/Archive/Comp/comp.text.tex/2007-09/msg00181.html
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} $\mathsf{a}$
+.. [#] 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.
-.. [#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:
@@ -525,9 +552,16 @@ 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`_).
+``\mathnormal`` `math alphabet`_). [#]_
+LaTeX defaults to the “TeX” math style (without naming it such).
+Alternative math styles are introduced by extension packages
+(`Table 2`_).
+
+.. [#] The ``math-style`` option of unicode-math_ changes also the shape
+ attribute of other math alphabets (see also section
+ `the unicode-math package`_).
-.. _Table 1:
+.. _ Table 1:
.. table:: Default letter shapes for common math styles
@@ -540,13 +574,10 @@ letter shape in math mode (i. e. the shape attribute of letters in the
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
+.. table:: Packages providing alternative math styles
============ ============= ==================================
math style Package Option(s)
@@ -572,11 +603,11 @@ Alternative math styles are introduced by extension packages
============ ============= ==================================
-Math letter fonts
+OML font encoding
~~~~~~~~~~~~~~~~~
-The equal treatment of Latin and Greek letters in the `ISO math
-style`_ is simplest achieved with a font that contains all required
+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
@@ -585,22 +616,22 @@ 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
-'''''''''''''''''
+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 formulas (typically used for variables) together with some
+ 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 the font shape.
+* No other font encoding is specific to a font shape.
* The different font selection and the semantic of font features in
- math do not interfere with the font *encoding*: Both,
+ 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
@@ -615,7 +646,7 @@ 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
+ mathematical formulae (typically used for variables) together with
some symbols. It first appeared in the `Computer Modern Math
Italic` (cmmi) font.
@@ -635,7 +666,7 @@ 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
+`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
@@ -645,56 +676,69 @@ additionally installed font packages.
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.
+
.. _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) ✓ ✓
- ============= =========================== ======= ======== ====== =======
+ ============= ================================= ======= ======== ====== =======
+ 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_) ✓ ✓
+ ============= ================================= ======= ======== ====== =======
-`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
@@ -716,7 +760,7 @@ rmdefault_ or sfdefault_ options.
ubk Bookman (bookman)
ucr Courier (courier)
ucrs Courier
- unc New Courier (nctrsbk)
+ unc New Century Schoolbook (psnfss)
uni Universal (universa)
uhv Helvetica (helvetic)
upl Palatino (palatino)
@@ -728,35 +772,61 @@ rmdefault_ or sfdefault_ options.
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
-mathematics character repertoire of the Unicode Standard as well as
+mathematical 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
-''''''''''''''''''''''
+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 assignes code points to most letters of the mathematical
+Unicode assigns 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
+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. Full support is
-provided by `the unicode-math package`_.
+LaTeX support for the mathematical alphanumeric symbols.
+
+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 5:
@@ -786,33 +856,12 @@ provided by `the unicode-math package`_.
.. [#up] plain standard characters outside the
`mathematical alphanumeric symbols` Unicode block.
-Naming scheme
+LaTeX support
`````````````
-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.
+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`_.
.. _Table 6:
@@ -823,7 +872,7 @@ Examples::
style math alphabet package, comment
============ ========================= ===========================
plain [#up]_ ``\mathrm`` predefined [#no-g]_
- .. ``\mathup`` unicode-math_
+ .. ``\mathup`` unicode-math_, kpfonts_
bf ``\mathbf`` predefined [#no-g]_
it ``\mathit`` predefined [#no-g]_
bf it ``\mathbfit`` isomath [#digits]_
@@ -840,7 +889,7 @@ Examples::
bf frak ``\mathbffrak`` unicode-math_
bb ``\mathbb`` amssymb_, bbold_,
mathbbol_, mbboard_,
- mathpazo_
+ mathpazo_, sbbm_
.. ``\mathbbm`` bbm_
.. ``\mathds`` dsfont (doublestoke_)
sf ``\mathsf`` predefined [#no-g]_
@@ -852,10 +901,12 @@ Examples::
tt ``\mathtt`` predefined [#no-g]_
============ ========================= ===========================
-.. [#no-g] no small Greek, full Greek with `OMLmath*`_ options.
+.. [#no-g] no small Greek, full Greek with `OMLmath*`_ options and
+ OML-encoded fonts
.. [#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_
+.. [#script] formal script with calrsfs_, eucal_, fourier_,
+ small Latin letters only with urwchancal_
The unicode-math package
@@ -865,18 +916,19 @@ 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
+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).
+* `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`_:
+
+ .. class:: borderless
=============== ===============
LaTeX unicode-math
@@ -894,46 +946,21 @@ LaTeX `math font selection`_ methods with unicode-math:
``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.
-
+ so that, e. g., the Unicode character MATHEMATICAL SANS-SERIF BOLD
+ ITALIC CAPITAL A is selected by the non-mnemonic ``\mathbfsfit{A}``.
- 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::
+* `Math versions`_ can be set up using the syntax
+ ``\setmathfont[version=<version name>,<font features>]{<font name>}``
- \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``.
+* Several `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
+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.
@@ -942,9 +969,6 @@ 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_
@@ -991,6 +1015,10 @@ References
`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.
@@ -1026,6 +1054,7 @@ References
.. _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
+.. _anttor: http://mirror.ctan.org/help/Catalogue/entries/anttor.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
@@ -1033,7 +1062,9 @@ References
.. _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
+.. _concmath: http://mirror.ctan.org/help/Catalogue/entries/concmath.html
.. _doublestoke: http://mirror.ctan.org/help/Catalogue/entries/doublestoke.html
+.. _efont: http://mirror.ctan.org/help/Catalogue/entries/efont.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
@@ -1042,13 +1073,20 @@ References
.. _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
+.. _gfsdidot: http://mirror.ctan.org/help/Catalogue/entries/gfsdidot.html
+.. _gfsneohellenic: http://mirror.ctan.org/help/Catalogue/entries/gfsneohellenic.html
+.. _greektex: http://mirror.ctan.org/help/Catalogue/entries/greektex.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
+.. _jamtimes: http://mirror.ctan.org/help/Catalogue/entries/jamtimes.html
+.. _kerkis: http://mirror.ctan.org/help/Catalogue/entries/kerkis.html
+.. _keyval: http://mirror.ctan.org/help/Catalogue/entries/keyval.html
.. _kpfonts: http://mirror.ctan.org/help/Catalogue/entries/kpfonts.html
+.. _kurier: http://mirror.ctan.org/help/Catalogue/entries/kurier.html
.. _kvoptions: http://mirror.ctan.org/help/Catalogue/entries/kvoptions.html
-.. _keyval: http://mirror.ctan.org/help/Catalogue/entries/keyval.html
+.. _lgrx: http://mirror.ctan.org/help/Catalogue/entries/lgrx.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
@@ -1056,14 +1094,20 @@ References
.. _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
+.. _mathptmv: http://mirror.ctan.org/help/Catalogue/entries/mathptmv.html
.. _mathrsfs: http://mirror.ctan.org/help/Catalogue/entries/mathrsfs.html
+.. _newtx: http://mirror.ctan.org/help/Catalogue/entries/newtx.html
.. _New Euler: https://github.com/khaledhosny/euler-otf
.. _pxfonts: http://mirror.ctan.org/help/Catalogue/entries/pxfonts.html
+.. _sansmath: http://mirror.ctan.org/help/Catalogue/entries/sansmath.html
+.. _sbbm: http://mirror.ctan.org/help/Catalogue/entries/sbbm.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
+.. _urwchancal: http://mirror.ctan.org/help/Catalogue/entries/urwchancal.html
.. _wrisym: http://phong.informatik.uni-leipzig.de/~kuska/wri_texmf_4.2.zip
.. _XITS: http://mirror.ctan.org/help/Catalogue/entries/xits.html
+.. _zefonts: http://mirror.ctan.org/help/Catalogue/entries/zefonts.html