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author | Karl Berry <karl@freefriends.org> | 2011-02-05 00:20:35 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2011-02-05 00:20:35 +0000 |
commit | 1a813fddccf1088251a3bf66876370618b724a8a (patch) | |
tree | 3caaac2202bc3a7c791b38f1c119d065ebea48d6 /Master/texmf-dist/doc/latex/isomath/isomath.txt | |
parent | 4289e4647ab448dbce672649f32f107dda45c4aa (diff) |
isomath 0.5 (2feb11)
git-svn-id: svn://tug.org/texlive/trunk@21296 c570f23f-e606-0410-a88d-b1316a301751
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diff --git a/Master/texmf-dist/doc/latex/isomath/isomath.txt b/Master/texmf-dist/doc/latex/isomath/isomath.txt index ad3697083c4..23100dcacfe 100644 --- a/Master/texmf-dist/doc/latex/isomath/isomath.txt +++ b/Master/texmf-dist/doc/latex/isomath/isomath.txt @@ -4,148 +4,162 @@ isomath: Math for scientists **************************** :Author: Günter Milde -:Date: 2010-08-23 -:Copyright: © 2008, 2010 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 enables formatting Greek and Latin - letters as symbols for vectors, matrices, and tensors - in the typefaces recommended for scientific papers - by the International Standard ISO 31. +: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:: -Motivation ----------- + +Features +-------- .. How do you write the stress tensor ``$\sigma$`` in a - sans-serif bold italic typeface, as recommended by [typefaces]_? + `sans-serif bold italic` typeface, as recommended by [typefaces]_? -Scientific organisations like IUPAP_, IUPAC_, NIST_, BIPM_, and others -recommend typesetting math according to the International Standard ISO 31 -`Quantities and units` [ISO-31]_.\ [#]_ +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]_: -.. [#] Summaries of these rules are free available, see [typefaces]_, - [checklist]_, [fonts_for_symbols]_, and [SI-brochure]_. +* The overall rule is that symbols representing physical quantities + (or variables) are italic, but symbols representing units, or + labels, are roman. -The traditional `LaTeX math style` deviates in some points from this rules: +* Symbols for vectors are boldface italic, symbols for tensors are + sans-serif bold italic, and symbols for matrices are boldface + italic. -* The ``\vec`` command produces an array accent, while ISO 31 recommends - a bold italic typeface for vector symbols. +* The above rules apply equally to letter symbols from both the Greek + and the Latin alphabet. -* Greek letters are excluded from font changes with the math - alphabets, while the ISO 31 rules apply equally to letters from the - Greek and Latin alphabet. +The traditional TeX `math style`_ deviates from this rules in some +points: -* There is no provision for typesetting of Greek letters in bold italic - style recommended for vectors. +* capital Greek letters default to upright shape, -* There is no provision for typesetting letters in sans-serif bold italic - recommended for typesetting tensor symbols. +* small Greek letters are excluded from font changes with the `math + alphabets`_. -Some of these points are adressed by `related packages`_, however -there is currently no package (known to the author) that defines the -sans-serif bold italic math alphabet needed for tensor symbols. +* 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. -Features --------- .. _`equal treatment of Latin and Greek`: -Equal treatment of Latin and Greek letters -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +ISO math style +~~~~~~~~~~~~~~ -This feature is provided by the required package fixmath_ which -ensures that: +The required package fixmath_ changes the default math layout to the +“ISO” `math style`_: -+ Both, Greek and Latin letters change shape if a different - math alphabet is used. ++ Uppercase Greek letters are typeset italic by default. -+ By default, uppercase Greek letters are typeset in italic style. ++ Both, Greek and Latin letters change shape if a different + `math alphabet`_ is used. -However, `fixmath` works only for Computer Modern. With `isomath`, +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 + ``\math*`` alphabets via the `OMLmath*`_ options if the corresponding fonts support the `OML font encoding`_. -Caution: - Placing Greek letters in a ``\math*`` macro, e. g. - ``\mathrm{k\Omega}``, can lead to garbage, as the standard math +.. 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 Greek letters in the standard math alphabet commands + Do not use small Greek letters in the standard math alphabet commands ``mathit``, ``mathrm``, ``mathbf``, ``mathsf``, and ``mathtt`` - unless you use the OMLmath_ options.\ [#]_ + unless you use the `OMLmath*`_ options. - .. [#] Some packages provide ``\up*`` or ``\var*`` macros for - upright Greek letters so the above example could be written - ``\mathrm{k}\upOmega``. + Some packages provide alternative macros or options for upright + Greek letters (cf. `Table 6`_). New math alphabets ~~~~~~~~~~~~~~~~~~ -New math alphabets are defined: +`Isomath` defines three new `math alphabets`_: + + .. class:: borderless -:``\mathbold``: boldface italic (vector and matrix symbols), -:``\mathboldsans``: sans-serif bold italic (tensor symbols). -:``\mathsans``: sans-serif italic (optional), + =============== ====================== ================================= + ``\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 +The rmdefault_ and sfdefault_ options_ set the font family used for these alphabets. +.. Caution:: -Command aliases -~~~~~~~~~~~~~~~ -The command aliases ``\vectorsym``, ``\matrixsym``, and ``\tensorsym`` -allow semantic markup. They print the argument in an ISO-conforming -typeface. + 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``. -Font mappings -~~~~~~~~~~~~~ +Semantic markup +~~~~~~~~~~~~~~~ +The following commands set the argument in an ISO-conforming math alphabet: -Some font definitions are added for font families which have an OML -encoded counterpart but no substitution definition in their ``*.fd`` -files. + .. class:: borderless -Usage ------ + ========================== ======================================== + ``\vectorsym, \matrixsym`` bold italic for Greek and Latin letters, + bold upright for numbers -Make sure that LaTeX can find ``isomath.sty`` and insert the command:: + ``\tensorsym`` sans-serif bold italic + ========================== ======================================== - \usepackage{isomath} -in the document preamble (see also Examples_). +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 (roman and kursive). The default is to use the -corresponding text font family (the value of ``\rmdefault``). The font -must be available in `OML font encoding`_. +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 2`_). +(see `Table 4`_). -There are only few sans serif `fonts that support the OML -encoding`_: +There are only few sans serif fonts in `OML font encoding`_: -.. class:: booktab +.. class:: borderless ========== =========== =================================================== Name Package Comment @@ -153,27 +167,27 @@ 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-hight + 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, excentric, large x-hight, +``llcmss`` lxfonts_ `LX Fonts`, very wide, eccentric, large x-height, new in 2008 ========== =========== =================================================== scaled '''''' -As the choice of sans serif math fonts is very limited, -the fonts, ``fav``, ``llcmss``, and ``iwona`` can be scaled -with the ``scaled`` option (see examples_). +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 +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 @@ -181,63 +195,110 @@ option tells ``isomath`` to re-use the existing ``\mathbf`` and math-mode off and might use a different font, so watch for side-effects. -OMLmath -'''''''' +.. _OMLmath*: + +OMLmathrm, OMLmathbf, OMLmathsf, OMLmathsfit, OMLmathtt +''''''''''''''''''''''''''''''''''''''''''''''''''''''' -With Greek letters defined as ``\mathalpha``, the math alphabets are -expected to be in `OML font encoding`_. Unfortunately, the standard -math alphabets are usually taken from OT1 or T1 encoded fonts that -have ligatures and accents in place of the Greek letters. +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 following options cause isomath to (re)define math alphabets in OML -encoding:: +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. - OMLmathrm, OMLmathbf, OMLmathsf, OMLmathsans, OMLmathtt +.. caution:: -Setting these options enables access to small Greek letters in -different shapes with e.g. ``\mathrm{\pi}`` **if an OML encoded font -is available**. Currently, only the mathdesign_ package provides -upright `fonts that support the OML encoding`_. Many font packages -define an italic font as replacement for a roman font in OML encoding. + 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. -With some packages, these options can result in a “`too many math alphabets -used in version normal`_” error. Examples ~~~~~~~~ -* Use `isomath` with the default settings:: +* 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):: -* Define also a slanted sans-serif math alphabet:: + \usepackage[sfdefault=fav,scaled=0.875]{isomath} - \usepackage[OMLmathsans]{isomath} +* Define the ``\mathsfit`` sans-serif italic math alphabet:: -* Use the heavier `Arev` sans serif fonts:: + \usepackage[OMLmathsfit]{isomath} - \usepackage[sfdefault=fav,scaled=0.875]{isomath} - (Adapt the scaling factor to your needs.) +* 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. -* Redefine the standard ``\vec`` macro to typeset its argument in `bold - italic`:: + As a workaround, use the heavier arev_ font, scaled to 0,875, in the + bold version of ``\mathsfbfit``:: \usepackage{isomath} - \renewcommand{\vec}{\vectorsym} + \DeclareFontShape{OML}{fav}{bx}{it}{<-> s * [0.875] zavmbi7m}{} + \SetMathAlphabet{\mathsfbfit}{bold}{OML}{fav}{bx}{it} - (Use ``\bm`` or ``boldmath`` for for the zero and unit vectors, as - ``\vec{0}`` and ``\vec{1}`` will give undesired results.) +See also the ``isomath-test.tex`` test document. -* The mathdesign_ package provides an OML encoded *bold roman* font but does - not set it up for ``\mathbf``. To set it up, write e.g.:: +How to get upright small Greek letters +'''''''''''''''''''''''''''''''''''''' - \usepackage[charter]{mathdesign} - \usepackage[OMLmathbf]{isomath} +Of the following methods, only the first requires `isomath`: - Now, e.g. ``\mathbf{\pi}`` produces a bold upright pi symbol. +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 }}} -See also the ``isomath-test.tex`` test document. Related packages @@ -250,7 +311,7 @@ fixmath_ by Walter Schmidt defines Greek letters as alphabetic symbols. kvoptions_ - (in the oberdiek_ bundle) facilitates the setup of package options + by Heiko Oberdiek facilitates the setup of package options and provides a key=value interface (based on keyval_). @@ -258,65 +319,62 @@ Recommendations ~~~~~~~~~~~~~~~ cmbright_ - provides *sans serif* and *sans-serif bold* fonts for the - ``\mathsans`` and ``\mathboldsans`` alphabets that match with - Computer Modern and derivatives. Free Type 1 versions of the fonts - with hfbright_. + 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_ - provides *sans serif* somewhat heavier letters that are clearly - distinguishable from the roman or italic counterparts (important if - used to distinguish vectors and tensors). However, `Arev` has a - large x-hight, so for most default fonts, either small or capital + 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 ~~~~~~~~~~~~ -If the only requirement is a bold italic font for (Latin and Greek) vector -symbols, there are established alternatives to `isomath`: - -* Packages that support `equal treatment of Latin and Greek`_ and - provide the ``\mathbold`` alphabet (but not ``\mathsansbold``) in - `OML font encoding`_: +See `Table 2`_ for other packages that implement the “ISO” `math +style`_ and `Table 6`_ for packages that provide bold italic +math fonts. - Roman - * eulervm_ (Euler Math), - * fixmath_ (Computer Modern), - * mathpazo_ (Palatino), - * tmmath_ (TM-Math/Times). +`“In-line math versions”`_ + can be used as ISO-conforming replacement for ``\vec``: - Sans serif - * arev_ (Arev/Vera Sans), - * cmbright_ (CM Bright), - * hvmath_ (HV-Math/Helvetica), + * ``\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. -* Packages that provide commands which can be used as replacement for - ``\vec``: - - * `amsbsy`_ (part of `amsmath`_, the near-indispensable adjunct to serious - mathematical typesetting in LaTeX) defines ``\boldmath``, +``\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`_). - * `bm`_ defines a command ``\bm`` which makes its argument bold (more - careful than amsbsy's ``\boldmath``). Combining `bm` and `isomath` may - lead to the `too many math alphabets used in version normal`_ error. +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. -The ``\text`` macro from `amsmath`_ can be used to get e.g. upright or -sans-serif bold slanted Greek symbols from a text font into a formula. + 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`” - +“_`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. + than 16 fonts into the ``normal`` `math version`_. - It can be avoided with the reuseMathAlphabets_ option (see there - for side-effects). + `Isomath` can reduce the number of math alphabet definitions with the + reuseMathAlphabets_ option (see there for side-effects). Examples for problematic combinations: @@ -327,13 +385,13 @@ Conflicts and heavy fonts. Their number can be customized by defining ``\bmmax`` and ``\hmmax`` before loading the package. -* The `fourier`_ package for math typesetting with Utopia defines its own, - incompatible math font encodings. It cannot be used with ``isomath`` but - provides other means to typeset upright or italic Greek (see its - documentation). +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 symbols from `fourier`_ together - with math alphabets from another package, e.g `mathdesign`_:: + 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, @@ -343,43 +401,197 @@ Conflicts Background ---------- -Letter symbols -~~~~~~~~~~~~~~ +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`_. -IUPAC_'s [fonts_for_symbols]_ guide says: - 2. The overall rule is that symbols representing physical quantities (or - variables) are italic, but symbols representing units, or labels, are - roman. […] +Math font selection +~~~~~~~~~~~~~~~~~~~ - 3. The above rule applies equally to letter symbols from both the Greek - and the Latin alphabet, […]. +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`_). -In contrast, the standard LaTeX style treats Greek letter symbols +.. _math alphabet: -* as invariant operators, +Math alphabets +'''''''''''''' -* with lower case italic and upper case upright. +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: -A possible fix (established by fixmath_) is using a common font for -Greek and Latin letters. There is one established font encoding -providing Latin and Greek letters: the `OML font encoding`_. However, + Some math fonts are selected explicitly by one-argument commands + such as ``\mathsf{max}`` or ``\mathbf{vec}``; such fonts are called + *math alphabets*. -* support_ for OML is limited to a few (mostly italic) fonts. + 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 widely supported but non-standard `LGR` font encoding has Greek - but no Latin letters, while + The _`predefined math alphabets` are: -* the standard Greek font encoding `T7` is just a “reserved name”. + .. class:: borderless + ================= =============== + ``\mathnormal`` default [#mathnormal]_ + ``\mathrm`` roman [#roman]_ + ``\mathbf`` bold roman + ``\mathsf`` sans serif + ``\mathit`` text italic + ``\mathtt`` typewriter + ``\mathcal`` calligraphic + ================= =============== -OML font encoding +.. [#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 + The _`OML` encoding contains italic Latin and Greek letters for use in mathematical formulas (typically used for variables) together with some symbols. @@ -394,9 +606,9 @@ The reference to *italic* shape is odd: alphabets in roman {n} as well as italic {it} shape without conflicts. -This seems to be a remnant of pre-NFSS times – there is only one OML -encoded font in Knuth's Computer Modern fonts: `Computer Modern Math -Italic` (cmmi) – rather than a necessary restriction. +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: @@ -415,16 +627,16 @@ Proposals: Math Letters`. The latter would also explain the acronym OML. -Support -''''''' +OML Support +''''''''''' Unfortunately, support for the OML encoding is missing for many font -families even if the base font contains all Greek letters. - +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 1`_ lists the findings for a selection of TeXLive + some -additonally installed font packages. + +`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. @@ -433,57 +645,57 @@ additonally 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 2`_ 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 1: +.. _Table 3: -.. table:: _`Fonts that support the OML encoding` +.. table:: Font families supporting the OML encoding ============= =========================== ======= ======== ====== ======= Name Family m/it bx/it m/n bx/n ============= =========================== ======= ======== ====== ======= - aer AE (Almost European) x x - antt Antykwa Torunska x x - cmr Computer Modern Roman x x - ccr Concrete x x - cmbr Computer Modern Bright x x - hlh Lucida x x - hfor CM with old-style digits x x - iwona Iwona (sans serif) x x - jkp Kepler Serif x x - jkpl Kepler Serif x x - jkpvos Kepler Serif x x - jkplvos Kepler Serif x x - llcmm LXfonts (sans serif) x x - lmr Latin Modern Roman x x - mak Kerkis x - kurier Kurier x x - mdbch Math Design Charter x x x x - mdput Math Design Utopia x x x x - mdugm Math Design Garamond x x x x - neohellenic GFS Neohellenic x - plcm CM (PLaTeX) x - ptmom Times (Omega or MB-Times) x x - ptmomu Times (Omega or MB-Times) x x - ptmcm Times (psfont) x - pxr Palatino (pxfonts) x x - qpl Palatino/Pagella (qpxmath) x x - qtm Times/Termes (qtxmath) x x - txr Times (txfonts) x x - udidot Didot (gfsdidot) x - ywclm (greektex) x x - zavm Arev (Vera Sans-Serif) x x - zesfcm (efont) x - zplm Palatino (mathpazo) x x - zpple Palatino x x - ztmcm Times (mathptmx) x - zer Computer Modern (zefonts) x x + 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 2: +`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 @@ -513,189 +725,345 @@ rmdefault_ or sfdefault_ options. ============= =============================== -Math in Unicode -~~~~~~~~~~~~~~~ +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. -Basis for the definition of the Unicode block -`mathematical alphanumeric symbols`_, was the consideration outlined -in [beeton:2000]_: - - These alphabets are needed for proper composition - of mathematics: - - * lightface upright Latin, Greek and digits - * boldface upright Latin, Greek and digits - * lightface italic Latin, Greek and digits - * boldface italic Latin, Greek and digits - * script - * fraktur - * bold fraktur - * open-face (blackboard bold) including digits - * lightface upright sans serif Latin and digits - * lightface italic sans serif Latin - * boldface upright sans serif Latin, Greek, and digits - * boldface italic sans serif Latin and Greek - * monospace Latin and digits - - Except for the lightface upright letters and digits, - which are to be encoded using the base Unicodes - (ASCII for the Latin letters and digits), the - alphanumerics are to be placed in a tightly packed - block (U+D400–D7FF) in plane 1, so that they can - be used for math (most likely via entity names in - MathML), but will be very difficult to access for - other purposes. - -The technical report `Unicode Support for Mathematics` [tr25]_ lists -“alphanumeric symbols encountered in mathematics” in table 2: -`Mathematical Alphabets`. - -The Unicode block `mathematical alphanumeric symbols`_ provides style -variants for Latin and Greek letters and digits. It is labelled “to be -used for mathematical variables where style variations are important -semantically”. `Table 3`_ gives a survey of current LaTeX support. - -.. _table 3: - -.. table:: Styles in the `mathematical alphanumeric symbols`_ - Unicode block - :class: booktab - - ================= ======= ================= ========================== - Style Symbols LaTeX macro Package, Comment - [#]_ - ================= ======= ================= ========================== - bold LGD ``\mathbf`` no Greek - - italic LG ``\mathit`` no Greek - \ ``\mathnormal`` small Greek but - old-style digits (upright) - bold italic LG ``\mathbold`` fixmath and friends - \ ``\boldsymbol`` ams - script L ``\mathcal`` or only capital Latin - (calligraphic) ``\mathscr`` - bold script L - fraktur L ``\mathfrak`` eufrak - double-struck L D ``\mathbb`` bbold, mathbbol, - mbboard - \ ``\mathbbm`` bbm - \ ``\mathds`` dsfont - bold fraktur L - sans-serif L D ``\mathsf`` no Greek - sans-serif bold LGD - sans-serif italic L ``\mathsans`` isomath - sans bold italic LG ``\mathboldsans`` isomath - monospace L D ``\mathtt`` no Greek - ----------------- ------- ----------------- -------------------------- - *Not in the mathematical alphanumeric symbols block*: - ---------------------------------------------------------------------- - plain LGD ``\mathrm`` no Greek - \ ``\mathnormal`` capital Greek - ================= ======= ================= ========================== - -.. [#] LGD: **L**\ atin, **G**\ reek, **D**\ igits +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. +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. +Kerkis, GFS Neohellenic, LX Fonts and KP-Serif. -Alternatively, the T7 encoding could be used for math alphabets (if it ever -happens to materialise). +Alternatively, the T7 encoding could be used for math alphabets (if it +ever happens to materialise). -Upright small Greek letters in ``\mathrm`` would enable the specification of -the constant pi, Myons, Pions, alpha-particles, photons, and neutrinos -without special packages. (With mathdesign_, this is already possible -today.) +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-31] International Standard 31 `Quantities and units`, - (ISO 31-0:1992 to ISO 31-14:1992): - http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_tc_browse.htm?commid=46202 +.. [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] `Typefaces for Symbols in Scientific Manuscripts`: - http://physics.nist.gov/Document/typefaces.pdf +.. [typefaces] National Institute of Standards and Technology (NIST_), + `Typefaces for Symbols in Scientific Manuscripts`: + http://physics.nist.gov/cuu/pdf/typefaces.pdf. -.. [checklist] `SI Unit rules and style conventions` +.. [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 + http://physics.nist.gov/cuu/Units/checklist.html. -.. [fonts_for_symbols] `On the use of italic and roman fonts for symbols +.. [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 + 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]. -.. [SI-brochure] `The International System of Units (SI)`: - http://www.bipm.org/en/si/si_brochure/ +.. [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] `LaTeX font encodings`: - http://mirror.ctan.org/macros/latex/doc/encguide.pdf +.. [encguide] Frank Mittelbach, Robin Fairbairns, Werner Lemberg, + LaTeX3 Project Team, `LaTeX font encodings`: + http://mirror.ctan.org/macros/latex/doc/encguide.pdf. -.. [fntguide] `LaTeX 2e font selection`: - http://mirror.ctan.org/macros/latex/doc/fntguide.pdf +.. [fntguide] LaTeX3 Project Team, `LaTeX 2e font selection`: + http://mirror.ctan.org/macros/latex/doc/fntguide.pdf. -.. [tr25] `Unicode Support for Mathematics`, Unicode Technical Report #25: - http://www.unicode.org/reports/tr25/ +.. [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. available: + 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 - - [Green-Book] `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] + [koma-mail] Custom font substitution: http://www.komascript.de/node/823. .. Links ===== -.. Print external links as footnotes (currently errors with LaTeX) - .. target-notes:: - -.. _LaTeX Project Public License: http://www.latex-project.org/lppl.txt .. _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: +.. _mathematical alphanumeric symbols unicode block: http://www.unicode.org/charts/PDF/U1D400.pdf -.. _amsbsy: http://dante.ctan.org/CTAN/help/Catalogue/entries/amsbsy.html -.. _amsmath: http://dante.ctan.org/CTAN/help/Catalogue/entries/amsmath.html -.. _arev: http://dante.ctan.org/CTAN/help/Catalogue/entries/arev.html -.. _bm: http://dante.ctan.org/CTAN/help/Catalogue/entries/bm.html -.. _cmbright: http://dante.ctan.org/CTAN/help/Catalogue/entries/cmbright.html -.. _eulervm: http://dante.ctan.org/CTAN/help/Catalogue/entries/eulervm.html -.. _fixmath: http://dante.ctan.org/CTAN/help/Catalogue/entries/fixmath.html -.. _fix-cm: http://dante.ctan.org/CTAN/help/Catalogue/entries/fix-cm.html -.. _fourier: http://dante.ctan.org/CTAN/help/Catalogue/entries/fourier.html -.. _hvmath: http://dante.ctan.org/CTAN/help/Catalogue/entries/hvmath.html -.. _hfbright: http://dante.ctan.org/CTAN/help/Catalogue/entries/hfbright.html -.. _ifthen: http://dante.ctan.org/CTAN/help/Catalogue/entries/ifthen.html -.. _iwona: http://dante.ctan.org/CTAN/help/Catalogue/entries/iwona.html -.. _kpfonts: http://dante.ctan.org/CTAN/help/Catalogue/entries/kpfonts.html -.. _kvoptions: http://dante.ctan.org/CTAN/help/Catalogue/entries/kvoptions.html -.. _keyval: http://dante.ctan.org/CTAN/help/Catalogue/entries/keyval.html -.. _lxfonts: http://dante.ctan.org/CTAN/help/Catalogue/entries/lxfonts.html -.. _mathdesign: http://dante.ctan.org/CTAN/help/Catalogue/entries/mathdesign.html -.. _mathpazo: http://dante.ctan.org/CTAN/help/Catalogue/entries/mathpazo.html -.. _oberdiek: http://dante.ctan.org/CTAN/help/Catalogue/entries/oberdiek.html +.. _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 -.. _pxfonts: http://dante.ctan.org/CTAN/help/Catalogue/entries/pxfonts.html -.. _tmmath: http://dante.ctan.org/CTAN/help/Catalogue/entries/tmmath.html -.. _txfonts: http://dante.ctan.org/CTAN/help/Catalogue/entries/txfonts.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 |