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authorKarl Berry <karl@freefriends.org>2010-09-18 00:10:58 +0000
committerKarl Berry <karl@freefriends.org>2010-09-18 00:10:58 +0000
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+.. -*- rst-mode -*-
+
+isomath: Math for scientists
+****************************
+
+:Author: Günter Milde
+:Date: 2010-08-23
+:Copyright: © 2008, 2010 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.
+
+.. contents::
+.. sectnum::
+
+Motivation
+----------
+
+.. How do you write the stress tensor ``$\sigma$`` in a
+ 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]_.\ [#]_
+
+.. [#] Summaries of these rules are free available, see [typefaces]_,
+ [checklist]_, [fonts_for_symbols]_, and [SI-brochure]_.
+
+The traditional `LaTeX math style` deviates in some points from this rules:
+
+* The ``\vec`` command produces an array accent, while ISO 31 recommends
+ a bold italic typeface for vector symbols.
+
+* 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.
+
+* There is no provision for typesetting of Greek letters in bold italic
+ style recommended for vectors.
+
+* There is no provision for typesetting letters in sans-serif bold italic
+ recommended for typesetting tensor symbols.
+
+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.
+
+
+Features
+--------
+
+.. _`equal treatment of Latin and Greek`:
+
+Equal treatment of Latin and Greek letters
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+This feature is provided by the required package fixmath_ which
+ensures that:
+
++ Both, Greek and Latin letters change shape if a different
+ math alphabet is used.
+
++ By default, uppercase Greek letters are typeset in italic style.
+
+However, `fixmath` works only for Computer Modern. 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:
+ Placing Greek letters in a ``\math*`` macro, e. g.
+ ``\mathrm{k\Omega}``, 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
+ ``mathit``, ``mathrm``, ``mathbf``, ``mathsf``, and ``mathtt``
+ 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``.
+
+
+New math alphabets
+~~~~~~~~~~~~~~~~~~
+New math alphabets are defined:
+
+:``\mathbold``: boldface italic (vector and matrix symbols),
+:``\mathboldsans``: sans-serif bold italic (tensor symbols).
+:``\mathsans``: sans-serif italic (optional),
+
+The rmdefault_ and sfdefault_ options set the font family used for
+these alphabets.
+
+
+Command aliases
+~~~~~~~~~~~~~~~
+The command aliases ``\vectorsym``, ``\matrixsym``, and ``\tensorsym``
+allow semantic markup. They print the argument in an ISO-conforming
+typeface.
+
+
+Font mappings
+~~~~~~~~~~~~~
+
+Some font definitions are added for font families which have an OML
+encoded counterpart but no substitution definition in their ``*.fd``
+files.
+
+Usage
+-----
+
+Make sure that LaTeX can find ``isomath.sty`` and insert the command::
+
+ \usepackage{isomath}
+
+in the document preamble (see also 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`_.
+
+
+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`_).
+
+There are only few sans serif `fonts that support the OML
+encoding`_:
+
+.. class:: booktab
+
+========== =========== ===================================================
+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
+``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,
+ 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_).
+
+
+reuseMathAlphabets
+''''''''''''''''''
+The definition of new math alphabets can lead to a “`too many math
+alphabets used in version normal`_” error. As a workaround, this
+option tells ``isomath`` to re-use the existing ``\mathbf`` and
+``\mathsf`` alphabets for italic bold and sans-serif bold. [#]_
+
+.. [#] To access the upright shapes, the corresponding ``\textbf`` and
+ ``\textsf`` commands might be used. However, this toggles the
+ math-mode off and might use a different font, so watch for
+ side-effects.
+
+OMLmath
+''''''''
+
+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.
+
+The following options cause isomath to (re)define math alphabets in OML
+encoding::
+
+ OMLmathrm, OMLmathbf, OMLmathsf, OMLmathsans, OMLmathtt
+
+Setting these options enables access to small Greek letters in
+different shapes with e.g. ``\mathrm{\pi}`` **if an OML encoded font
+is available**. Currently, 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.
+
+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::
+
+ \usepackage{isomath}
+
+* Define also a slanted sans-serif math alphabet::
+
+ \usepackage[OMLmathsans]{isomath}
+
+* Use the heavier `Arev` sans serif fonts::
+
+ \usepackage[sfdefault=fav,scaled=0.875]{isomath}
+
+ (Adapt the scaling factor to your needs.)
+
+* Redefine the standard ``\vec`` macro to typeset its argument in `bold
+ italic`::
+
+ \usepackage{isomath}
+ \renewcommand{\vec}{\vectorsym}
+
+ (Use ``\bm`` or ``boldmath`` for for the zero and unit vectors, as
+ ``\vec{0}`` and ``\vec{1}`` will give undesired results.)
+
+* 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.::
+
+ \usepackage[charter]{mathdesign}
+ \usepackage[OMLmathbf]{isomath}
+
+ Now, e.g. ``\mathbf{\pi}`` produces a bold upright pi symbol.
+
+See also the ``isomath-test.tex`` test document.
+
+
+Related packages
+----------------
+
+Requirements
+~~~~~~~~~~~~
+
+fixmath_
+ by Walter Schmidt defines Greek letters as alphabetic symbols.
+
+kvoptions_
+ (in the oberdiek_ bundle) facilitates the setup of package options
+ and provides a key=value interface (based on keyval_).
+
+
+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_.
+
+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
+ 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`_:
+
+ Roman
+ * eulervm_ (Euler Math),
+ * fixmath_ (Computer Modern),
+ * mathpazo_ (Palatino),
+ * tmmath_ (TM-Math/Times).
+
+ Sans serif
+ * arev_ (Arev/Vera Sans),
+ * cmbright_ (CM Bright),
+ * hvmath_ (HV-Math/Helvetica),
+
+
+* 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``,
+
+ * `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.
+
+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.
+
+
+Conflicts
+~~~~~~~~~
+
+* “_`too many math alphabets used in version normal`”
+
+ This error occurs if the combination of packages tries to load more
+ than 16 fonts into the ‘normal’ math version.
+
+ It can be avoided with the reuseMathAlphabets_ option (see there
+ for side-effects).
+
+ Examples for problematic combinations:
+
+ + The `kpfonts`_, `pxfonts`_, and `txfonts`_ packages define many
+ additional math alphabets.
+
+ + The `bm`_ package normally allocates several symbol fonts for bold
+ and heavy fonts. Their number can be customized by defining
+ ``\bmmax`` and ``\hmmax`` before loading the package.
+
+* 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).
+
+ However, it is possible to use the symbols from `fourier`_ together
+ with math alphabets from another package, e.g `mathdesign`_::
+
+ \usepackage{fourier}
+ \usepackage[OMLmathbf,rmdefault=mdput,
+ sfdefault=arev,scaled=0.85]{isomath}
+
+
+Background
+----------
+
+Letter symbols
+~~~~~~~~~~~~~~
+
+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. […]
+
+ 3. The above rule applies equally to letter symbols from both the Greek
+ and the Latin alphabet, […].
+
+In contrast, the standard LaTeX style treats Greek letter symbols
+
+* as invariant operators,
+
+* with lower case italic and upper case upright.
+
+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,
+
+* support_ for OML is limited to a few (mostly italic) fonts.
+
+* The widely supported but non-standard `LGR` font encoding has Greek
+ but no Latin letters, while
+
+* the standard Greek font encoding `T7` is just a “reserved name”.
+
+
+OML font encoding
+~~~~~~~~~~~~~~~~~
+
+The `LaTeX font encodings` guide [encguide]_ names the OML encoding
+`TeX math italic` and defines:
+
+ The OML encoding contains italic Latin and Greek letters for use in
+ mathematical formulas (typically used for variables) together with some
+ symbols.
+
+The reference to *italic* shape is odd:
+
+* No other font encoding is specific to the font shape.
+
+* The different font selection and the semantic of font features in
+ math do not interfere with the font *encoding*: Both,
+ ``\DeclareSymbolFont`` and ``\DeclareMathAlphabet`` require a
+ shape argument. Thus it is possible to set up OML encoded math
+ alphabets in roman {n} as well as italic {it} shape without
+ conflicts.
+
+This seems to be 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.
+
+Proposals:
+
+* Drop the *italic* from the definition. Optionally add an explanation:
+
+ The OML encoding contains Latin and Greek letters for use in
+ mathematical formulas (typically used for variables) together with
+ some symbols. It first appeared in the `Computer Modern Math
+ Italic` (cmmi) font.
+
+* The name `TeX math italic` can be interpreted as “the encoding
+ **of** `Computer Modern Math Italic`” rather than “an encoding
+ **for** math italic” fonts.
+
+ A less confusing name would be `TeX math letters` or `Original/Old
+ Math Letters`. The latter would also explain the acronym OML.
+
+
+Support
+'''''''
+
+Unfortunately, support for the OML encoding is missing for many font
+families even if the base font contains all Greek letters.
+
+Supported font families can be found searching for ``oml*.fd`` files
+and grepping for ``DeclareFont.*OML`` in ``*.sty`` files.
+`Table 1`_ lists the findings for a selection of TeXLive + some
+additonally installed font packages.
+
+* If there is an alias (substitution) from the text font to a
+ math-variant, only the text font is listed.
+
+* Many text fonts define substitutions also for upright shape,
+ however mapping to an italic variant of the OML encoded font. These
+ are not listed as supporting ``m/n`` or ``bx/n`` here.
+
+`Table 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:: _`Fonts that support 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
+ ============= =========================== ======= ======== ====== =======
+
+
+.. _Table 2:
+
+.. table:: Non-CM fonts with ``cmm`` as OML substitution
+
+ ============= ===============================
+ Family Name
+ ============= ===============================
+ bch Charter (psnfss)
+ pag Avant Garde (psnfss)
+ pbk Bookman (psnfss)
+ pcr Courier (psnfss)
+ phv Helvetica (psnfss)
+ pnc New Century Schoolbook (psnfss)
+ ppl Palatino (psnfss)
+ ptm Times Roman (psnfss)
+ put Utopia (psnfss)
+ pzc Zapf Chancery (psnfss)
+ uag Avant Garde (avantgar)
+ ubk Bookman (bookman)
+ ucr Courier (courier)
+ ucrs Courier
+ unc New Courier (nctrsbk)
+ uni Universal (universa)
+ uhv Helvetica (helvetic)
+ upl Palatino (palatino)
+ utm Times (times)
+ uzc Zapf Chancery (zapfchan)
+ ============= ===============================
+
+
+Math in Unicode
+~~~~~~~~~~~~~~~
+
+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
+
+
+
+Conclusions and outlook
+~~~~~~~~~~~~~~~~~~~~~~~
+
+It is hoped, that in the future more fonts families will support the OML
+encoding in normal and bold weight as well as upright and italic shape.
+This would be a major step towards a LaTeX equivalent of the `Mathematical
+Alphanumeric Symbols`_ Unicode block.
+
+This should be (relatively) easy to achieve via virtual fonts when the
+glyphs for the Greek letters already exist. Examples are Latin Modern,
+Kerkis, GFS-Neohellenic, LX-Fonts and KP-Serif.
+
+Alternatively, the T7 encoding could be used for math alphabets (if it ever
+happens to materialise).
+
+Upright small Greek letters in ``\mathrm`` would enable the specification of
+the constant pi, Myons, Pions, alpha-particles, photons, and neutrinos
+without special packages. (With mathdesign_, this is already possible
+today.)
+
+
+
+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
+
+.. [typefaces] `Typefaces for Symbols in Scientific Manuscripts`:
+ http://physics.nist.gov/Document/typefaces.pdf
+
+.. [checklist] `SI Unit rules and style conventions`
+ Check List for Reviewing Manuscripts:
+ http://physics.nist.gov/cuu/Units/checklist.html
+
+.. [fonts_for_symbols] `On the use of italic and roman fonts for symbols
+ in scientific text`, (Revised December 1999):
+ http://old.iupac.org/standing/idcns/fonts_for_symbols.html
+
+.. [SI-brochure] `The International System of Units (SI)`:
+ http://www.bipm.org/en/si/si_brochure/
+
+.. [encguide] `LaTeX font encodings`:
+ http://mirror.ctan.org/macros/latex/doc/encguide.pdf
+
+.. [fntguide] `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/
+
+.. [beeton:2000] Barbara Beeton:
+ `Unicode and math, a combination whose time has come – Finally!`,
+ TUGBoat, 21#3, 2000. available:
+ 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]
+
+
+.. 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/
+.. _NIST: http://physics.nist.gov/
+.. _mathematical alphanumeric symbols:
+ 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
+.. _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