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+<title>isomath: Math for scientists</title>
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+<meta name="date" content="2011-01-14" />
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+/* sub, sup {font-size: 70%;} */ /* Mozilla default is `smaller` */
+
+
+/* Tables */
+/* ====== */
+
+/* margins and borders for "normal" tables */
+table {
+ margin-top: 0.5em ;
+ margin-bottom: 0.5em;
+ border-style: outset;
+ border-width: thin;
+ /* border-collapse: collapse; */
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+blockquote > table {
+ margin-top: 0em ;
+ margin-bottom: 0em;
+}
+
+td, th {
+ border-style: inset;
+ border-width: thin;
+ /* text-align: left; */
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+/* no borders for "borderless" tables */
+table.borderless, table.borderless * {
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+
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+
+
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+/* pre.literal-block, pre.doctest-block { */
+/* margin-top: 0em ; */
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+/* Table of Contents */
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+/* don't indent like a topic */
+div.topic.contents {
+ margin: 0;
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+/* div.topic.contents ul { */
+/* list-style: none; */
+/* } */
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+ padding: 0px 1em }
+
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+<style type="text/css">
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+:Copyright: 2008 G. Milde
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+
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+/* content: "⎘"; */
+/* font-size: x-small; */
+/* vertical-align: super; */
+/* } */
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+ margin-left: 1.2em;
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+dl.footnote > dt {
+ font-size: small;
+ vertical-align: super;
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+
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+ vertical-align: super;
+ }
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+ padding-top: 0.1ex;
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+
+/* no borders for "borderless" tables */
+table.booktabs.borderless, table.booktabs.borderless * {
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+</style>
+</head>
+<body>
+<div class="document" id="isomath-math-for-scientists">
+<h1 class="title">isomath: Math for scientists</h1>
+
+<dl class="docinfo simple">
+<dt class="author">Author</dt>
+<dd class="author">Günter Milde</dd>
+<dt class="date">Date</dt>
+<dd class="date">2011-01-14</dd>
+<dt class="copyright">Copyright</dt>
+<dd class="copyright">© 2008, 2011 Günter Milde</dd>
+<dt>Licence</dt>
+<dd><p>This work may be distributed and/or modified under the
+conditions of the <a class="reference external" href="http://www.latex-project.org/lppl.txt">LaTeX Project Public License</a>, either
+version&nbsp;1.3 of this license or (at your option) any later version.</p>
+</dd>
+</dl>
+<div class="abstract topic">
+<p class="topic-title first">Abstract</p>
+<p>The <cite>isomath</cite> 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&nbsp;80000-2.</p>
+</div>
+<!-- -*- rst-mode -*- -->
+<div class="contents topic" id="contents">
+<p class="topic-title first">Contents</p>
+<ul class="auto-toc simple">
+<li><p><a class="reference internal" href="#features" id="id30"><span class="sectnum">1</span> Features</a></p>
+<ul class="auto-toc">
+<li><p><a class="reference internal" href="#iso-math-style" id="id31"><span class="sectnum">1.1</span> ISO math style</a></p></li>
+<li><p><a class="reference internal" href="#new-math-alphabets" id="id32"><span class="sectnum">1.2</span> New math alphabets</a></p></li>
+<li><p><a class="reference internal" href="#semantic-markup" id="id33"><span class="sectnum">1.3</span> Semantic markup</a></p></li>
+</ul>
+</li>
+<li><p><a class="reference internal" href="#usage" id="id34"><span class="sectnum">2</span> Usage</a></p>
+<ul class="auto-toc">
+<li><p><a class="reference internal" href="#options" id="id35"><span class="sectnum">2.1</span> Options</a></p>
+<ul class="auto-toc">
+<li><p><a class="reference internal" href="#rmdefault" id="id36"><span class="sectnum">2.1.1</span> rmdefault</a></p></li>
+<li><p><a class="reference internal" href="#sfdefault" id="id37"><span class="sectnum">2.1.2</span> sfdefault</a></p></li>
+<li><p><a class="reference internal" href="#scaled" id="id38"><span class="sectnum">2.1.3</span> scaled</a></p></li>
+<li><p><a class="reference internal" href="#reusemathalphabets" id="id39"><span class="sectnum">2.1.4</span> reuseMathAlphabets</a></p></li>
+<li><p><a class="reference internal" href="#omlmathrm-omlmathbf-omlmathsf-omlmathsfit-omlmathtt" id="id40"><span class="sectnum">2.1.5</span> OMLmathrm, OMLmathbf, OMLmathsf, OMLmathsfit, OMLmathtt</a></p></li>
+</ul>
+</li>
+<li><p><a class="reference internal" href="#examples" id="id41"><span class="sectnum">2.2</span> Examples</a></p>
+<ul class="auto-toc">
+<li><p><a class="reference internal" href="#how-to-get-upright-small-greek-letters" id="id42"><span class="sectnum">2.2.1</span> How to get upright small Greek letters</a></p></li>
+</ul>
+</li>
+</ul>
+</li>
+<li><p><a class="reference internal" href="#related-packages" id="id43"><span class="sectnum">3</span> Related packages</a></p>
+<ul class="auto-toc">
+<li><p><a class="reference internal" href="#requirements" id="id44"><span class="sectnum">3.1</span> Requirements</a></p></li>
+<li><p><a class="reference internal" href="#recommendations" id="id45"><span class="sectnum">3.2</span> Recommendations</a></p></li>
+<li><p><a class="reference internal" href="#alternatives" id="id46"><span class="sectnum">3.3</span> Alternatives</a></p></li>
+<li><p><a class="reference internal" href="#conflicts" id="id47"><span class="sectnum">3.4</span> Conflicts</a></p></li>
+</ul>
+</li>
+<li><p><a class="reference internal" href="#background" id="id48"><span class="sectnum">4</span> Background</a></p>
+<ul class="auto-toc">
+<li><p><a class="reference internal" href="#math-font-selection" id="id49"><span class="sectnum">4.1</span> Math font selection</a></p>
+<ul class="auto-toc">
+<li><p><a class="reference internal" href="#math-alphabets" id="id50"><span class="sectnum">4.1.1</span> Math alphabets</a></p></li>
+<li><p><a class="reference internal" href="#math-versions" id="id51"><span class="sectnum">4.1.2</span> Math versions</a></p></li>
+<li><p><a class="reference internal" href="#math-styles" id="id52"><span class="sectnum">4.1.3</span> Math styles</a></p></li>
+</ul>
+</li>
+<li><p><a class="reference internal" href="#math-letter-fonts" id="id53"><span class="sectnum">4.2</span> Math letter fonts</a></p>
+<ul class="auto-toc">
+<li><p><a class="reference internal" href="#oml-font-encoding" id="id54"><span class="sectnum">4.2.1</span> OML font encoding</a></p></li>
+<li><p><a class="reference internal" href="#oml-support" id="id55"><span class="sectnum">4.2.2</span> OML Support</a></p></li>
+</ul>
+</li>
+<li><p><a class="reference internal" href="#unicode-mathematical-typesetting" id="id56"><span class="sectnum">4.3</span> Unicode mathematical typesetting</a></p>
+<ul class="auto-toc">
+<li><p><a class="reference internal" href="#unicode-math-alphabets" id="id57"><span class="sectnum">4.3.1</span> Unicode math alphabets</a></p>
+<ul class="auto-toc">
+<li><p><a class="reference internal" href="#naming-scheme" id="id58"><span class="sectnum">4.3.1.1</span> Naming scheme</a></p></li>
+</ul>
+</li>
+<li><p><a class="reference internal" href="#the-unicode-math-package" id="id59"><span class="sectnum">4.3.2</span> The unicode-math package</a></p></li>
+</ul>
+</li>
+<li><p><a class="reference internal" href="#conclusions-and-outlook" id="id60"><span class="sectnum">4.4</span> Conclusions and outlook</a></p></li>
+</ul>
+</li>
+<li><p><a class="reference internal" href="#references" id="id61"><span class="sectnum">5</span> References</a></p></li>
+</ul>
+</div>
+<div class="section" id="features">
+<h1><a class="toc-backref" href="#id30"><span class="sectnum">1</span> Features</a></h1>
+<!-- How do you write the stress tensor ``$\sigma$`` in a
+`sans-serif bold italic` typeface, as recommended by [typefaces]_? -->
+<p>Leading international scientific organisations recommend math layout
+rules in line with the International Standard <a class="citation-reference" href="#iso-80000-2" id="id1">[ISO-80000-2]</a> in their
+style guides, e. g., <a class="citation-reference" href="#typefaces" id="id2">[typefaces]</a>, <a class="citation-reference" href="#checklist" id="id3">[checklist]</a>, <a class="citation-reference" href="#si" id="id4">[SI]</a>, <a class="citation-reference" href="#fonts-for-symbols" id="id5">[fonts_for_symbols]</a>,
+<a class="citation-reference" href="#red-book" id="id6">[Red-Book]</a>, <a class="citation-reference" href="#green-book" id="id7">[Green-Book]</a>:</p>
+<ul class="simple">
+<li><p>The overall rule is that symbols representing physical quantities
+(or variables) are italic, but symbols representing units, or
+labels, are roman.</p></li>
+<li><p>Symbols for vectors are boldface italic, symbols for tensors are
+sans-serif bold italic, and symbols for matrices are boldface
+italic.</p></li>
+<li><p>The above rules apply equally to letter symbols from both the Greek
+and the Latin alphabet.</p></li>
+</ul>
+<p>The traditional TeX <a class="reference internal" href="#math-style">math style</a> deviates from this rules in some
+points:</p>
+<ul class="simple">
+<li><p>capital Greek letters default to upright shape,</p></li>
+<li><p>small Greek letters are excluded from font changes with the <a class="reference internal" href="#math-alphabets">math
+alphabets</a>.</p></li>
+<li><p>The <tt class="literal">\vec</tt> command produces an arrow accent.</p></li>
+</ul>
+<p>The <cite>isomath</cite> package implements an <a class="reference internal" href="#iso-math-style">ISO math style</a> and provides
+<a class="reference internal" href="#new-math-alphabets">new math alphabets</a> with bold italic and sans-serif bold italic
+typeshape that can be used for vector and tensor symbols.</p>
+<div class="section" id="iso-math-style">
+<span id="equal-treatment-of-latin-and-greek"></span><h2><a class="toc-backref" href="#id31"><span class="sectnum">1.1</span> ISO math style</a></h2>
+<p>The required package <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/fixmath.html">fixmath</a> changes the default math layout to the
+“ISO” <a class="reference internal" href="#math-style">math style</a>:</p>
+<ul class="simple">
+<li><p>Uppercase Greek letters are typeset italic by default.</p></li>
+<li><p>Both, Greek and Latin letters change shape if a different
+<a class="reference internal" href="#math-alphabet">math alphabet</a> is used.</p></li>
+</ul>
+<p>However, fixmath works only for the Computer Modern font family.
+With <cite>isomath</cite>,</p>
+<ul class="simple">
+<li><p>the used math fonts are configurable (using the <a class="reference internal" href="#rmdefault">rmdefault</a> and
+<a class="reference internal" href="#sfdefault">sfdefault</a> options), and</p></li>
+<li><p>upright Greek letters can be made available through the common
+<tt class="literal">\math*</tt> alphabets via the <a class="reference internal" href="#omlmath">OMLmath*</a> options if the
+corresponding fonts support the <a class="reference internal" href="#oml-font-encoding">OML font encoding</a>.</p></li>
+</ul>
+<div class="caution">
+<p class="admonition-title">Caution!</p>
+<p>Using Greek letters in standard <a class="reference internal" href="#math-alphabets">math alphabets</a>, e. g.,
+<tt class="literal"><span class="pre">\mathrm{\pi}</span></tt>, 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
+<tt class="literal">mathit</tt>, <tt class="literal">mathrm</tt>, <tt class="literal">mathbf</tt>, <tt class="literal">mathsf</tt>, and <tt class="literal">mathtt</tt>
+unless you use the <a class="reference internal" href="#omlmath">OMLmath*</a> options.</p>
+<p>Some packages provide alternative macros or options for upright
+Greek letters (cf.&nbsp;<a class="reference internal" href="#table-6">Table&nbsp;6</a>).</p>
+</div>
+</div>
+<div class="section" id="new-math-alphabets">
+<h2><a class="toc-backref" href="#id32"><span class="sectnum">1.2</span> New math alphabets</a></h2>
+<p><cite>Isomath</cite> defines three new <a class="reference internal" href="#math-alphabets">math alphabets</a>:</p>
+<blockquote>
+<table class="borderless booktabs numbered align-left">
+<colgroup>
+<col width="21%" />
+<col width="31%" />
+<col width="47%" />
+</colgroup>
+<tbody valign="top">
+<tr><td><p><tt class="literal">\mathbfit</tt></p></td>
+<td><p>boldface italic</p></td>
+<td><p>vector and matrix symbols</p></td>
+</tr>
+<tr><td><p><tt class="literal">\mathsfit</tt></p></td>
+<td><p>sans-serif italic</p></td>
+<td><p>optional (see OMLmath*_ options)</p></td>
+</tr>
+<tr><td><p><tt class="literal">\mathsfbfit</tt></p></td>
+<td><p>sans-serif bold italic</p></td>
+<td><p>tensor symbols</p></td>
+</tr>
+</tbody>
+</table>
+</blockquote>
+<p>The <a class="reference internal" href="#rmdefault">rmdefault</a> and <a class="reference internal" href="#sfdefault">sfdefault</a> <a class="reference internal" href="#options">options</a> set the font family used for
+these alphabets.</p>
+<div class="caution">
+<p class="admonition-title">Caution!</p>
+<p>Using the new math alphabets for numbers can result in <span class="target" id="upright-old-style-numbers">upright
+old-style numbers</span> instead of italic ones, because some italic math
+fonts (e. g., cmr, cmbr) have old-style numbers in place of italic
+digits.</p>
+</div>
+<p>For compatibility with earlier versions and <a class="reference internal" href="#related-packages">related packages</a>, the
+new math alphabets are also available under the aliases
+<tt class="literal">\mathbold</tt>, <tt class="literal">\mathsans</tt>, and <tt class="literal">\mathboldsans</tt>.</p>
+</div>
+<div class="section" id="semantic-markup">
+<h2><a class="toc-backref" href="#id33"><span class="sectnum">1.3</span> Semantic markup</a></h2>
+<p>The following commands set the argument in an ISO-conforming math alphabet:</p>
+<blockquote>
+<table class="borderless booktabs numbered align-left">
+<colgroup>
+<col width="39%" />
+<col width="61%" />
+</colgroup>
+<tbody valign="top">
+<tr><td><p><tt class="literal">\vectorsym, \matrixsym</tt></p></td>
+<td><p>bold&nbsp;italic for Greek and Latin letters,
+bold&nbsp;upright for numbers</p></td>
+</tr>
+<tr><td><p><tt class="literal">\tensorsym</tt></p></td>
+<td><p>sans-serif bold italic</p></td>
+</tr>
+</tbody>
+</table>
+</blockquote>
+</div>
+</div>
+<div class="section" id="usage">
+<h1><a class="toc-backref" href="#id34"><span class="sectnum">2</span> Usage</a></h1>
+<p>Make sure that LaTeX can find <tt class="literal">isomath.sty</tt> and load it with
+<tt class="literal">\usepackage</tt> (see also <a class="reference internal" href="#options">Options</a> and <a class="reference internal" href="#examples">Examples</a>).</p>
+<div class="section" id="options">
+<h2><a class="toc-backref" href="#id35"><span class="sectnum">2.1</span> Options</a></h2>
+<div class="section" id="rmdefault">
+<h3><a class="toc-backref" href="#id36"><span class="sectnum">2.1.1</span> rmdefault</a></h3>
+<p>Family for serif math fonts (<tt class="literal">\mathrm</tt>, <tt class="literal">\mathbf</tt>, <tt class="literal">\mathit</tt>,
+<tt class="literal">\mathbfit</tt>). The default is to use the corresponding text font
+family (the value of <tt class="literal">\rmdefault</tt>). The font must be available in
+<a class="reference internal" href="#oml-font-encoding">OML font encoding</a> (cf. <a class="reference internal" href="#table-3">Table&nbsp;3</a>).</p>
+</div>
+<div class="section" id="sfdefault">
+<h3><a class="toc-backref" href="#id37"><span class="sectnum">2.1.2</span> sfdefault</a></h3>
+<p>Family for sans-serif math fonts. The default is <tt class="literal">cmbr</tt> because many
+sans-serif fonts define the Computer Roman font <cite>cmm</cite> as OML substitution
+(see <a class="reference internal" href="#table-4">Table&nbsp;4</a>).</p>
+<p>There are only few sans serif fonts in <a class="reference internal" href="#oml-font-encoding">OML font encoding</a>:</p>
+<table class="borderless booktabs numbered align-left">
+<colgroup>
+<col width="14%" />
+<col width="15%" />
+<col width="71%" />
+</colgroup>
+<thead valign="bottom">
+<tr><th class="head"><p>Name</p></th>
+<th class="head"><p>Package</p></th>
+<th class="head"><p>Comment</p></th>
+</tr>
+</thead>
+<tbody valign="top">
+<tr><td><p><tt class="literal">cmbr</tt></p></td>
+<td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/cmbright.html">cmbright</a></p></td>
+<td><p><cite>Computer Modern Bright</cite>, bitmap, slightly lighter
+than cmss (Type 1 fonts with <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/hfbright.html">hfbright</a>)</p></td>
+</tr>
+<tr><td><p><tt class="literal">fav</tt></p></td>
+<td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/arev.html">arev</a></p></td>
+<td><p><cite>Arev</cite> (<cite>Vera Sans</cite>) with math extension,
+large x-height</p></td>
+</tr>
+<tr><td><p><tt class="literal">iwona</tt></p></td>
+<td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/iwona.html">iwona</a></p></td>
+<td><p>Humanistic Sans Serif,
+some shapes very similar to roman</p></td>
+</tr>
+<tr><td><p><tt class="literal">hvm</tt></p></td>
+<td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/hvmath.html">hvmath</a></p></td>
+<td><p><cite>Helvetica Math</cite>, commercial, free bitmap version</p></td>
+</tr>
+<tr><td><p><tt class="literal">llcmss</tt></p></td>
+<td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/lxfonts.html">lxfonts</a></p></td>
+<td><p><cite>LX Fonts</cite>, very wide, eccentric, large x-height,
+new in 2008</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="section" id="scaled">
+<h3><a class="toc-backref" href="#id38"><span class="sectnum">2.1.3</span> scaled</a></h3>
+<p>To improve the chances of configuring a matching sans serif math font,
+the fonts, <tt class="literal">fav</tt>, <tt class="literal">llcmss</tt>, and <tt class="literal">iwona</tt> can be scaled with the
+<tt class="literal">scaled</tt> option (cf. <a class="reference internal" href="#examples">Examples</a>).</p>
+</div>
+<div class="section" id="reusemathalphabets">
+<h3><a class="toc-backref" href="#id39"><span class="sectnum">2.1.4</span> reuseMathAlphabets</a></h3>
+<p>The definition of new math alphabets can lead to a “<a class="reference internal" href="#too-many-math-alphabets-used-in-version-normal">too many math
+alphabets used in version normal</a>” error. As a workaround, this
+option tells <cite>isomath</cite> to re-use the existing <tt class="literal">\mathbf</tt> and
+<tt class="literal">\mathsf</tt> alphabets for italic bold and sans-serif bold.<a class="footnote-reference" href="#id9" id="id8"><sup>1</sup></a></p>
+<dl class="footnote"><dt class="label"><a class="fn-backref" href="#id8">1</a></dt>
+<dd id="id9">
+<p class="first last">To access the upright shapes, the corresponding <tt class="literal">\textbf</tt> and
+<tt class="literal">\textsf</tt> commands might be used. However, this toggles the
+math-mode off and might use a different font, so watch for
+side-effects.</p>
+</dd>
+</dl>
+</div>
+<div class="section" id="omlmathrm-omlmathbf-omlmathsf-omlmathsfit-omlmathtt">
+<span id="omlmath"></span><h3><a class="toc-backref" href="#id40"><span class="sectnum">2.1.5</span> OMLmathrm, OMLmathbf, OMLmathsf, OMLmathsfit, OMLmathtt</a></h3>
+<p>With Greek letters defined as <tt class="literal">\mathalpha</tt>, the letter fonts are
+expected to be in <a class="reference internal" href="#oml-font-encoding">OML font encoding</a>. The predefined
+<a class="reference internal" href="#math-alphabets">math alphabets</a>, however, use OT1 encoded text fonts. These fonts
+have ligatures and accents in place of the small Greek letters.
+The <tt class="literal">\mathsfit</tt> alphabet is not required for ISO conforming math.</p>
+<p>The <tt class="literal">OMLmath*</tt> options bind the corresponding <tt class="literal">\math*</tt> command to an
+OML-encoded font.
+This enables use of small Greek letters in <a class="reference internal" href="#math-alphabet">math alphabet</a> commands,
+e. g., <tt class="literal"><span class="pre">\mathrm{\pi}</span></tt> <em>if an OML encoded font is available</em>.
+<a class="reference internal" href="#table-3">Table&nbsp;3</a> lists font families supporting the OML encoding.</p>
+<div class="caution">
+<p class="admonition-title">Caution!</p>
+<p>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 <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/mathdesign.html">mathdesign</a>
+package provides upright fonts in OML encoding. Many font packages
+define an <em>italic</em> font as OML substitute for roman fonts.</p>
+<p>With some packages, these options can result in a “<a class="reference internal" href="#too-many-math-alphabets-used-in-version-normal">too many math
+alphabets used in version normal</a>” error.</p>
+</div>
+</div>
+</div>
+<div class="section" id="examples">
+<h2><a class="toc-backref" href="#id41"><span class="sectnum">2.2</span> Examples</a></h2>
+<ul>
+<li><p>Redefine the standard <tt class="literal">\vec</tt> command to set its argument in an
+ISO-conforming math alphabet.:</p>
+<pre class="literal-block">\usepackage{isomath}
+\renewcommand{\vec}{\vectorsym}
+</pre>
+</li>
+<li><p>Use scaled <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/arev.html">arev</a> fonts for the sans serif alphabets
+(adapt the scaling factor to your needs):</p>
+<pre class="literal-block">\usepackage[sfdefault=fav,scaled=0.875]{isomath}
+</pre>
+</li>
+<li><p>Define the <tt class="literal">\mathsfit</tt> sans-serif italic math alphabet:</p>
+<pre class="literal-block">\usepackage[OMLmathsfit]{isomath}
+</pre>
+</li>
+<li><p>The <tt class="literal">\mathbfit</tt> and <tt class="literal">\mathsfbfit</tt> alphabets do not have a different
+weight in the <tt class="literal">bold</tt> <a class="reference internal" href="#math-version">math version</a> because the number of LaTeX math
+fonts providing <cite>extrabold</cite> or <cite>ultrabold</cite> series is negligible.</p>
+<p>As a workaround, use the heavier <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/arev.html">arev</a> font, scaled to 0,875, in the
+bold version of <tt class="literal">\mathsfbfit</tt>:</p>
+<pre class="literal-block">\usepackage{isomath}
+\DeclareFontShape{OML}{fav}{bx}{it}{&lt;-&gt; s * [0.875] zavmbi7m}{}
+\SetMathAlphabet{\mathsfbfit}{bold}{OML}{fav}{bx}{it}
+</pre>
+</li>
+</ul>
+<p>See also the <tt class="literal"><span class="pre">isomath-test.tex</span></tt> test document.</p>
+<div class="section" id="how-to-get-upright-small-greek-letters">
+<h3><a class="toc-backref" href="#id42"><span class="sectnum">2.2.1</span> How to get upright small Greek letters</a></h3>
+<p>Of the following methods, only the first requires <cite>isomath</cite>:</p>
+<ol class="loweralpha">
+<li><p>Use <cite>isomath</cite> and the <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/mathdesign.html">mathdesign</a> package:</p>
+<pre class="literal-block">\usepackage[utopia]{mathdesign}
+\usepackage[OMLmathrm,OMLmathbf]{isomath}
+</pre>
+<p>Now, e. g., <tt class="literal"><span class="pre">\mathrm{\pi}</span></tt> and <tt class="literal"><span class="pre">\mathbf{\pi}</span></tt> work as
+expected.</p>
+</li>
+<li><p>To get upright small Greek letters without affecting other fonts,
+set the math alphabet manually to one of the three <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/mathdesign.html">mathdesign</a>
+fonts, e. g.:</p>
+<pre class="literal-block">\SetMathAlphabet{\mathbf}{normal}{OML}{mdput}{b}{n}
+</pre>
+<p>(check if the letter shapes match with the rest of the document).</p>
+</li>
+<li><p>Use a package that provides macros for upright Greek letters
+in math:</p>
+<blockquote>
+<table class="borderless booktabs numbered align-left">
+<colgroup>
+<col width="26%" />
+<col width="74%" />
+</colgroup>
+<tbody valign="top">
+<tr><td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/fourier.html">fourier</a></p></td>
+<td><p><tt class="literal">\otheralpha ... \otherOmega</tt></p></td>
+</tr>
+<tr><td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/kpfonts.html">kpfonts</a></p></td>
+<td><p><tt class="literal">\alphaup ... \Omegaup</tt></p></td>
+</tr>
+<tr><td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/mathdesign.html">mathdesign</a></p></td>
+<td><p><tt class="literal">\alphaup ... \Omegaup</tt></p></td>
+</tr>
+<tr><td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/upgreek.html">upgreek</a></p></td>
+<td><p><tt class="literal">\upalpha ... \upOmega</tt></p></td>
+</tr>
+</tbody>
+</table>
+</blockquote>
+</li>
+<li><p>Use an upright text character (requires a matching LGR-encoded
+Greek text font). The following lines redefine <tt class="literal">\pi</tt> to set
+the mathematical constant pi upright:</p>
+<pre class="literal-block">\usepackage[LGR,T1]{fontenc}
+\usepackage[greek,british]{babel}
+\usepackage{amsmath}
+\let\mathpi\pi
+\renewcommand{\pi}{\text{\textrm{\greektext p }}}
+</pre>
+</li>
+</ol>
+</div>
+</div>
+</div>
+<div class="section" id="related-packages">
+<h1><a class="toc-backref" href="#id43"><span class="sectnum">3</span> Related packages</a></h1>
+<div class="section" id="requirements">
+<h2><a class="toc-backref" href="#id44"><span class="sectnum">3.1</span> Requirements</a></h2>
+<dl class="docutils">
+<dt><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/fixmath.html">fixmath</a></dt>
+<dd><p>by Walter Schmidt defines Greek letters as alphabetic symbols.</p>
+</dd>
+<dt><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/kvoptions.html">kvoptions</a></dt>
+<dd><p>by Heiko Oberdiek facilitates the setup of package options
+and provides a key=value interface (based on <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/keyval.html">keyval</a>).</p>
+</dd>
+</dl>
+</div>
+<div class="section" id="recommendations">
+<h2><a class="toc-backref" href="#id45"><span class="sectnum">3.2</span> Recommendations</a></h2>
+<dl class="docutils">
+<dt><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/cmbright.html">cmbright</a></dt>
+<dd><p>by Walter Schmidt provides sans serif and sans-serif bold fonts
+for the <tt class="literal">\mathsfit</tt> and <tt class="literal">\mathsfbfit</tt> alphabets that match
+with Computer Modern and derivatives. Free Type 1 versions of the
+fonts are provided by <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/hfbright.html">hfbright</a>.</p>
+</dd>
+<dt><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/arev.html">arev</a></dt>
+<dd><p>by Stephen Hartke provides the not-so-light <cite>Arev</cite> sans serif font
+with letters that are clearly distinguishable from the roman or
+italic counterparts (important if used to distinguish vectors and
+tensors).</p>
+<p><cite>Arev</cite> has a large x-height. For many fonts, either small or capital
+letters will not match in size.</p>
+</dd>
+</dl>
+</div>
+<div class="section" id="alternatives">
+<h2><a class="toc-backref" href="#id46"><span class="sectnum">3.3</span> Alternatives</a></h2>
+<p>See <a class="reference internal" href="#table-2">Table&nbsp;2</a> for other packages that implement the “ISO” <a class="reference internal" href="#math-style">math
+style</a> and <a class="reference internal" href="#table-6">Table&nbsp;6</a> for packages that provide bold italic
+math fonts.</p>
+<dl class="docutils">
+<dt><a class="reference internal" href="#in-line-math-versions">“In-line math versions”</a></dt>
+<dd><p>can be used as ISO-conforming replacement for <tt class="literal">\vec</tt>:</p>
+<ul class="simple">
+<li><p><tt class="literal">\boldsymbol</tt> from <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/amsbsy.html">amsbsy</a> (part of <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/amsmath.html">amsmath</a>, the
+near-indispensable adjunct to serious mathematical typesetting in
+LaTeX),</p></li>
+<li><p><tt class="literal">\bm</tt> from the <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/bm.html">bm</a> package. Combining <cite>bm</cite> and <cite>isomath</cite> may
+lead to the <a class="reference internal" href="#too-many-math-alphabets-used-in-version-normal">too many math alphabets used in version normal</a> error.</p></li>
+</ul>
+</dd>
+<dt><tt class="literal">\text</tt></dt>
+<dd><p>from <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/amsmath.html">amsmath</a> can be used to get, e. g., upright or sans-serif
+bold italic Greek symbols from a text font into a formula (see
+<a class="reference internal" href="#how-to-get-upright-small-greek-letters">How to get upright small Greek letters</a>).</p>
+</dd>
+<dt><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/unicode-math.html">unicode-math</a></dt>
+<dd><p>for XeTeX and LuaTeX allows mathematical typesetting using OpenType
+math fonts. It supports the “ISO” <a class="reference internal" href="#math-style">math style</a> and all mathematical
+characters in the Unicode standard.</p>
+<p>unicode-math cannot be used together with <cite>isomath</cite>. It can, however,
+replace all of isomath's functionality. See the discussion of <a class="reference internal" href="#the-unicode-math-package">the
+unicode-math package</a> below.</p>
+</dd>
+</dl>
+</div>
+<div class="section" id="conflicts">
+<h2><a class="toc-backref" href="#id47"><span class="sectnum">3.4</span> Conflicts</a></h2>
+<dl class="docutils">
+<dt>“<span class="target" id="too-many-math-alphabets-used-in-version-normal">too many math alphabets used in version normal</span>”</dt>
+<dd><p>This error occurs if the combination of packages tries to load more
+than 16 fonts into the <tt class="literal">normal</tt> <a class="reference internal" href="#math-version">math version</a>.</p>
+<p><cite>Isomath</cite> can reduce the number of math alphabet definitions with the
+<a class="reference internal" href="#reusemathalphabets">reuseMathAlphabets</a> option (see there for side-effects).</p>
+<p>Examples for problematic combinations:</p>
+<ul class="simple">
+<li><p>The <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/kpfonts.html">kpfonts</a>, <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/pxfonts.html">pxfonts</a>, and <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/txfonts.html">txfonts</a> packages define many
+additional math alphabets.</p></li>
+<li><p>The <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/bm.html">bm</a> package normally allocates several symbol fonts for bold
+and heavy fonts. Their number can be customized by defining
+<tt class="literal">\bmmax</tt> and <tt class="literal">\hmmax</tt> before loading the package.</p></li>
+</ul>
+</dd>
+<dt><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/fourier.html">fourier</a></dt>
+<dd><p>provides upright and italic Greek letters, but uses non-standard
+math font encodings. It cannot be used with <cite>isomath</cite>.</p>
+<p>However, it is possible to use the non-alphanumeric symbols from
+<a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/fourier.html">fourier</a> together with math alphabets from another package, e.g
+<a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/mathdesign.html">mathdesign</a>:</p>
+<pre class="literal-block">\usepackage{fourier}
+\usepackage[OMLmathbf,rmdefault=mdput,
+ sfdefault=arev,scaled=0.85]{isomath}
+</pre>
+</dd>
+</dl>
+</div>
+</div>
+<div class="section" id="background">
+<h1><a class="toc-backref" href="#id48"><span class="sectnum">4</span> Background</a></h1>
+<p>This section discusses LaTeX <a class="reference internal" href="#math-font-selection">math font selection</a>, suitable
+<a class="reference internal" href="#math-letter-fonts">math letter fonts</a> for the ISO math style, and the relation of LaTeX and
+<a class="reference internal" href="#unicode-mathematical-typesetting">Unicode mathematical typesetting</a>.</p>
+<div class="section" id="math-font-selection">
+<h2><a class="toc-backref" href="#id49"><span class="sectnum">4.1</span> Math font selection</a></h2>
+<p>There are three complementary methods to set font attributes in LaTeX
+math mode: <cite>LaTeX 2e font selection</cite> <a class="citation-reference" href="#fntguide" id="id10">[fntguide]</a> describes <a class="reference internal" href="#math-alphabets">math
+alphabets</a> and <a class="reference internal" href="#math-versions">math versions</a>, several extension packages
+provide alternative <a class="reference internal" href="#math-styles">math styles</a> (cf. <a class="reference internal" href="#table-2">Table&nbsp;2</a>).</p>
+<div class="section" id="math-alphabets">
+<span id="math-alphabet"></span><h3><a class="toc-backref" href="#id50"><span class="sectnum">4.1.1</span> Math alphabets</a></h3>
+<p>Math alphabets are a counterpart to the <a class="reference internal" href="#mathematical-alphanumeric-symbols">mathematical alphanumeric
+symbols</a> block in Unicode. Both are “to be used for mathematical
+variables where style variations are important semantically”.
+The font guide <a class="citation-reference" href="#fntguide" id="id11">[fntguide]</a> defines in
+section&nbsp;3:</p>
+<blockquote>
+<p>Some math fonts are selected explicitly by one-argument commands
+such as <tt class="literal">\mathsf{max}</tt> or <tt class="literal">\mathbf{vec}</tt>; such fonts are called
+<em>math alphabets</em>.</p>
+<p>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 <a class="reference internal" href="#math-version">math version</a>.</p>
+<p>The <span class="target" id="predefined-math-alphabets">predefined math alphabets</span> are:</p>
+<blockquote>
+<table class="borderless booktabs numbered align-left">
+<colgroup>
+<col width="43%" />
+<col width="58%" />
+</colgroup>
+<tbody valign="top">
+<tr><td><p><tt class="literal">\mathnormal</tt></p></td>
+<td><p>default<a class="footnote-reference" href="#mathnormal" id="id12"><sup>2</sup></a></p></td>
+</tr>
+<tr><td><p><tt class="literal">\mathrm</tt></p></td>
+<td><p>roman<a class="footnote-reference" href="#roman" id="id13"><sup>3</sup></a></p></td>
+</tr>
+<tr><td><p><tt class="literal">\mathbf</tt></p></td>
+<td><p>bold roman</p></td>
+</tr>
+<tr><td><p><tt class="literal">\mathsf</tt></p></td>
+<td><p>sans serif</p></td>
+</tr>
+<tr><td><p><tt class="literal">\mathit</tt></p></td>
+<td><p>text italic</p></td>
+</tr>
+<tr><td><p><tt class="literal">\mathtt</tt></p></td>
+<td><p>typewriter</p></td>
+</tr>
+<tr><td><p><tt class="literal">\mathcal</tt></p></td>
+<td><p>calligraphic</p></td>
+</tr>
+</tbody>
+</table>
+</blockquote>
+</blockquote>
+<dl class="footnote"><dt class="label"><a class="fn-backref" href="#id12">2</a></dt>
+<dd id="mathnormal">
+<p class="first last"><tt class="literal">\mathnormal</tt> is used by default for alphanumeric
+characters in math mode. It sets the letter shape according to
+character class and <a class="reference internal" href="#math-style">math style</a>. (<a class="reference internal" href="#table-1">Table&nbsp;1</a> shows the default
+letter shapes for common math styles).</p>
+</dd>
+<dt class="label"><a class="fn-backref" href="#id13">3</a></dt>
+<dd id="roman">
+<p class="first last">The specifier “roman” is ambiguous: roman shape
+stands for <em>upright</em>, while roman type stands for <em>serif</em> (as
+opposed to sans serif).</p>
+</dd>
+</dl>
+<p>Many packages define additional math alphabets (cf. <a class="reference internal" href="#table-6">Table&nbsp;6</a>).</p>
+<p>In contrast to the similar named text commands, math alphabets are
+<em>not</em> orthogonal, e. g., the code <tt class="literal"><span class="pre">$\mathit{\mathbf{a}}$</span></tt> sets the
+letter <tt class="literal">a</tt> in <strong>upright</strong> bold type.</p>
+</div>
+<div class="section" id="math-versions">
+<span id="math-version"></span><h3><a class="toc-backref" href="#id51"><span class="sectnum">4.1.2</span> Math versions</a></h3>
+<p>The number of mathematical symbols exceeds the maximal number of
+characters in a TeX font file by an order of magnitude.<a class="footnote-reference" href="#max" id="id14"><sup>4</sup></a>
+Grouping math fonts with common characteristics in math versions
+simplifies the setting of font attributes for mathematical expressions.</p>
+<p><em>Math versions</em> set up “math symbol fonts” for non-alphanumeric
+symbols and bind the <a class="reference internal" href="#math-alphabet">math alphabet</a> commands to fonts using default
+values for non-specified font attributes. TeX limits the number of
+(symbol + alphanumeric) fonts per math version to 16.</p>
+<p>The predefined math versions are <tt class="literal">normal</tt> and <tt class="literal">bold</tt> with the
+defaults:</p>
+<blockquote>
+<table class="borderless booktabs numbered align-left">
+<colgroup>
+<col width="31%" />
+<col width="38%" />
+<col width="31%" />
+</colgroup>
+<tbody valign="top">
+<tr><td><!-- -->
+</td>
+<td><p><tt class="literal">normal</tt></p></td>
+<td><p><tt class="literal">bold</tt></p></td>
+</tr>
+<tr><td><p><em>type</em></p></td>
+<td><p>serif</p></td>
+<td><p>serif</p></td>
+</tr>
+<tr><td><p><em>weight</em></p></td>
+<td><p>medium</p></td>
+<td><p>bold</p></td>
+</tr>
+<tr><td><p><em>shape</em></p></td>
+<td><p>upright</p></td>
+<td><p>upright</p></td>
+</tr>
+</tbody>
+</table>
+</blockquote>
+<p>Packages can define additional math versions, e. g., the <a class="reference external" href="http://phong.informatik.uni-leipzig.de/~kuska/wri_texmf_4.2.zip">wrisym</a> package
+defines a <tt class="literal">mono</tt> math version. A <tt class="literal">sans</tt> math version example is
+available from a <a class="reference external" href="http://newsgroups.derkeiler.com/Archive/Comp/comp.text.tex/2007-09/msg00181.html">comp.text.tex post</a></p>
+<p>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).</p>
+<p>Math versions can only be changed outside of math mode. The commands
+<tt class="literal">\boldsymbol</tt> (<a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/amsmath.html">amsmath</a>) and <tt class="literal">\bm</tt> (<a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/bm.html">bm</a>) behave like <span class="target" id="in-line-math-versions">“in-line
+math versions”</span>: they typeset their argument using the fonts of the
+<tt class="literal">bold</tt> math version but can be used inside math mode.</p>
+<p>Example: four ways to set the letter <tt class="literal">a</tt> in a bold
+sans-serif font:</p>
+<pre class="literal-block">% Text Math:
+\textbf{\textsf{a}} $\bm{\mathsf{a}}$
+\bfseries \textsf{a} \mathversion{bold} $\mathsf{a}$
+</pre>
+<dl class="footnote"><dt class="label"><a class="fn-backref" href="#id14">4</a></dt>
+<dd id="max">
+<p class="first last">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.</p>
+</dd>
+</dl>
+</div>
+<div class="section" id="math-styles">
+<span id="math-style"></span><h3><a class="toc-backref" href="#id52"><span class="sectnum">4.1.3</span> Math styles</a></h3>
+<p>A <em>math style</em> is a document-level feature that determines the default
+letter shape in math mode (i. e. the shape attribute of letters in the
+<tt class="literal">\mathnormal</tt> <a class="reference internal" href="#math-alphabet">math alphabet</a>).</p>
+<table class="booktabs numbered align-left" id="table-1">
+<caption>Default letter shapes for common math styles</caption>
+<colgroup>
+<col width="30%" />
+<col width="18%" />
+<col width="18%" />
+<col width="18%" />
+<col width="18%" />
+</colgroup>
+<thead valign="bottom">
+<tr><th class="head"><p>math style</p></th>
+<th class="head"><p>latin</p></th>
+<th class="head"><p>Latin</p></th>
+<th class="head"><p>greek</p></th>
+<th class="head"><p>Greek</p></th>
+</tr>
+</thead>
+<tbody valign="top">
+<tr><td><p>TeX</p></td>
+<td><p>it</p></td>
+<td><p>it</p></td>
+<td><p>it</p></td>
+<td><p>up</p></td>
+</tr>
+<tr><td><p>ISO</p></td>
+<td><p>it</p></td>
+<td><p>it</p></td>
+<td><p>it</p></td>
+<td><p>it</p></td>
+</tr>
+<tr><td><p>French</p></td>
+<td><p>it</p></td>
+<td><p>up</p></td>
+<td><p>up</p></td>
+<td><p>up</p></td>
+</tr>
+<tr><td><p>upright</p></td>
+<td><p>up</p></td>
+<td><p>up</p></td>
+<td><p>up</p></td>
+<td><p>up</p></td>
+</tr>
+</tbody>
+</table>
+<p>LaTeX defaults to the “TeX” math style (without naming it such).
+Alternative math styles are introduced by extension packages
+(<a class="reference internal" href="#table-2">Table&nbsp;2</a>).</p>
+<table class="booktabs numbered align-left" id="table-2">
+<caption>Packages providing math styles</caption>
+<colgroup>
+<col width="18%" />
+<col width="20%" />
+<col width="62%" />
+</colgroup>
+<thead valign="bottom">
+<tr><th class="head"><p>math style</p></th>
+<th class="head"><p>Package</p></th>
+<th class="head"><p>Option(s)</p></th>
+</tr>
+</thead>
+<tbody valign="top">
+<tr><td><p>ISO</p></td>
+<td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/fixmath.html">fixmath</a></p></td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><!-- -->
+</td>
+<td><p>isomath</p></td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><!-- -->
+</td>
+<td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/kpfonts.html">kpfonts</a></p></td>
+<td><p>slantedGreeks</p></td>
+</tr>
+<tr><td><!-- -->
+</td>
+<td><p><a class="reference external" href="http://pctex.com/files/managed/b/bf/lucimatxAbbrev.pdf">lucimatx</a></p></td>
+<td><p>math-style=iso</p></td>
+</tr>
+<tr><td><!-- -->
+</td>
+<td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/mathdesign.html">mathdesign</a></p></td>
+<td><p>greekuppercase=italicized</p></td>
+</tr>
+<tr><td><!-- -->
+</td>
+<td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/mathpazo.html">mathpazo</a></p></td>
+<td><p>slantedGreek</p></td>
+</tr>
+<tr><td><!-- -->
+</td>
+<td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/mathptmx.html">mathptmx</a></p></td>
+<td><p>slantedGreek</p></td>
+</tr>
+<tr><td><!-- -->
+</td>
+<td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/unicode-math.html">unicode-math</a></p></td>
+<td><p>math-style=ISO</p></td>
+</tr>
+<tr><td><p>French</p></td>
+<td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/fourier.html">fourier</a></p></td>
+<td><p>upright</p></td>
+</tr>
+<tr><td><!-- -->
+</td>
+<td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/kpfonts.html">kpfonts</a></p></td>
+<td><p>frenchstyle (or upright)</p></td>
+</tr>
+<tr><td><!-- -->
+</td>
+<td><p><a class="reference external" href="http://pctex.com/files/managed/b/bf/lucimatxAbbrev.pdf">lucimatx</a></p></td>
+<td><p>math-style=french</p></td>
+</tr>
+<tr><td><!-- -->
+</td>
+<td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/mathdesign.html">mathdesign</a></p></td>
+<td><p>uppercase=upright, greeklowercase=upright</p></td>
+</tr>
+<tr><td><!-- -->
+</td>
+<td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/unicode-math.html">unicode-math</a></p></td>
+<td><p>math-style=french</p></td>
+</tr>
+<tr><td><p>upright</p></td>
+<td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/eulervm.html">eulervm</a></p></td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><!-- -->
+</td>
+<td><p><a class="reference external" href="http://pctex.com/files/managed/b/bf/lucimatxAbbrev.pdf">lucimatx</a></p></td>
+<td><p>math-style=upright</p></td>
+</tr>
+<tr><td><!-- -->
+</td>
+<td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/unicode-math.html">unicode-math</a></p></td>
+<td><p>math-style=upright</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+</div>
+<div class="section" id="math-letter-fonts">
+<h2><a class="toc-backref" href="#id53"><span class="sectnum">4.2</span> Math letter fonts</a></h2>
+<p>The equal treatment of Latin and Greek letters in the <a class="reference internal" href="#iso-math-style">ISO math
+style</a> is simplest achieved with a font that contains all required
+letters in one file.</p>
+<p>There is only one established LaTeX font encoding that contains Latin and
+Greek letters, the <a class="reference internal" href="#oml-font-encoding">OML font encoding</a>. The standard Greek font
+encoding <cite>T7</cite> is just a “reserved name” and the de-facto standard
+Greek text font encoding <cite>LGR</cite> has no Latin letters. Unfortunately,
+<a class="reference internal" href="#oml-support">OML support</a> is limited to a few (mostly italic) fonts.</p>
+<div class="section" id="oml-font-encoding">
+<h3><a class="toc-backref" href="#id54"><span class="sectnum">4.2.1</span> OML font encoding</a></h3>
+<p>The <cite>LaTeX font encodings</cite> guide <a class="citation-reference" href="#encguide" id="id15">[encguide]</a> names the OML encoding
+<cite>TeX math italic</cite> and defines:</p>
+<blockquote>
+<p>The <span class="target" id="oml">OML</span> encoding contains italic Latin and Greek letters for use in
+mathematical formulas (typically used for variables) together with some
+symbols.</p>
+</blockquote>
+<p>The reference to <em>italic</em> shape is odd:</p>
+<ul class="simple">
+<li><p>No other font encoding is specific to the font shape.</p></li>
+<li><p>The different font selection and the semantic of font features in
+math do not interfere with the font <em>encoding</em>: Both,
+<tt class="literal">\DeclareSymbolFont</tt> and <tt class="literal">\DeclareMathAlphabet</tt> 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.</p></li>
+</ul>
+<p>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: <cite>Computer Modern Math Italic</cite> (cmmi).</p>
+<p>Proposals:</p>
+<ul>
+<li><p>Drop the <em>italic</em> from the definition. Optionally add an explanation:</p>
+<blockquote>
+<p>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 <cite>Computer Modern Math
+Italic</cite> (cmmi) font.</p>
+</blockquote>
+</li>
+<li><p>The name <cite>TeX math italic</cite> can be interpreted as “the encoding
+<strong>of</strong> <cite>Computer Modern Math Italic</cite>” rather than “an encoding
+<strong>for</strong> math italic” fonts.</p>
+<p>A less confusing name would be <cite>TeX math letters</cite> or <cite>Original/Old
+Math Letters</cite>. The latter would also explain the acronym OML.</p>
+</li>
+</ul>
+</div>
+<div class="section" id="oml-support">
+<h3><a class="toc-backref" href="#id55"><span class="sectnum">4.2.2</span> OML Support</a></h3>
+<p>Unfortunately, support for the OML encoding is missing for many font
+families even if the text font defines Greek letters.
+Supported font families can be found searching for <tt class="literal"><span class="pre">oml*.fd</span></tt> files
+and grepping for <tt class="literal"><span class="pre">DeclareFont.*OML</span></tt> in <tt class="literal">*.sty</tt> files.</p>
+<p><a class="reference internal" href="#table-3">Table&nbsp;3</a> lists the findings for a selection of TeXLive&nbsp;2009 + some
+additionally installed font packages.</p>
+<ul class="simple">
+<li><p>If there is an alias (substitution) from the text font to a
+math-variant, only the text font is listed.</p></li>
+<li><p>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 <tt class="literal">m/n</tt> or <tt class="literal">bx/n</tt> here.</p></li>
+</ul>
+<table class="booktabs numbered align-left" id="table-3">
+<caption>Font families supporting the OML encoding</caption>
+<colgroup>
+<col width="19%" />
+<col width="40%" />
+<col width="10%" />
+<col width="12%" />
+<col width="9%" />
+<col width="10%" />
+</colgroup>
+<thead valign="bottom">
+<tr><th class="head"><p>Name</p></th>
+<th class="head"><p>Family</p></th>
+<th class="head"><p>m/it</p></th>
+<th class="head"><p>bx/it</p></th>
+<th class="head"><p>m/n</p></th>
+<th class="head"><p>bx/n</p></th>
+</tr>
+</thead>
+<tbody valign="top">
+<tr><td><p>aer</p></td>
+<td><p>AE (Almost European)</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><p>antt</p></td>
+<td><p>Antykwa Torunska</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><p>cmr</p></td>
+<td><p>Computer Modern Roman</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><p>ccr</p></td>
+<td><p>Concrete</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><p>cmbr</p></td>
+<td><p>Computer Modern Bright</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><p>hlh</p></td>
+<td><p>Lucida</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><p>hfor</p></td>
+<td><p>CM with old-style digits</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><p>iwona</p></td>
+<td><p>Iwona (sans serif)</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><p>jkp</p></td>
+<td><p>Kepler Serif</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><p>jkpl</p></td>
+<td><p>Kepler Serif</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><p>jkpvos</p></td>
+<td><p>Kepler Serif</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><p>jkplvos</p></td>
+<td><p>Kepler Serif</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><p>llcmm</p></td>
+<td><p>LX Fonts (sans serif)</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><p>lmr</p></td>
+<td><p>Latin Modern Roman</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><p>mak</p></td>
+<td><p>Kerkis</p></td>
+<td><p>✓</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><p>kurier</p></td>
+<td><p>Kurier</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><p>mdbch</p></td>
+<td><p>Math Design Charter</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+</tr>
+<tr><td><p>mdput</p></td>
+<td><p>Math Design Utopia</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+</tr>
+<tr><td><p>mdugm</p></td>
+<td><p>Math Design Garamond</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+</tr>
+<tr><td><p>neohellenic</p></td>
+<td><p>GFS Neohellenic</p></td>
+<td><p>✓</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><p>plcm</p></td>
+<td><p>CM (PLaTeX)</p></td>
+<td><p>✓</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><p>ptmom</p></td>
+<td><p>Times (Omega or MB-Times)</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><p>ptmomu</p></td>
+<td><p>Times (Omega or MB-Times)</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><p>ptmcm</p></td>
+<td><p>Times (psfont)</p></td>
+<td><p>✓</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><p>pxr</p></td>
+<td><p>Palatino (pxfonts)</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><p>qpl</p></td>
+<td><p>Palatino/Pagella (qpxmath)</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><p>qtm</p></td>
+<td><p>Times/Termes (qtxmath)</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><p>txr</p></td>
+<td><p>Times (txfonts)</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><p>udidot</p></td>
+<td><p>Didot (gfsdidot)</p></td>
+<td><p>✓</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><p>ywclm</p></td>
+<td><p>(greektex)</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><p>zavm</p></td>
+<td><p>Arev (Vera Sans-Serif)</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><p>zesfcm</p></td>
+<td><p>(efont)</p></td>
+<td><p>✓</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><p>zplm</p></td>
+<td><p>Palatino (mathpazo)</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><p>zpple</p></td>
+<td><p>Palatino</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><p>ztmcm</p></td>
+<td><p>Times (mathptmv)</p></td>
+<td><p>✓</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+<tr><td><p>zer</p></td>
+<td><p>Computer Modern (zefonts)</p></td>
+<td><p>✓</p></td>
+<td><p>✓</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+</tbody>
+</table>
+<p><a class="reference internal" href="#table-4">Table&nbsp;4</a> lists some fonts that define <tt class="literal">cmm</tt> as OML substitution.
+With <cite>isomath</cite>, a better matching substitution can be set using the
+<a class="reference internal" href="#rmdefault">rmdefault</a> or <a class="reference internal" href="#sfdefault">sfdefault</a> options.</p>
+<table class="booktabs numbered align-left" id="table-4">
+<caption>Non-CM fonts with <tt class="literal">cmm</tt> as OML substitution</caption>
+<colgroup>
+<col width="30%" />
+<col width="70%" />
+</colgroup>
+<thead valign="bottom">
+<tr><th class="head"><p>Family</p></th>
+<th class="head"><p>Name</p></th>
+</tr>
+</thead>
+<tbody valign="top">
+<tr><td><p>bch</p></td>
+<td><p>Charter (psnfss)</p></td>
+</tr>
+<tr><td><p>pag</p></td>
+<td><p>Avant Garde (psnfss)</p></td>
+</tr>
+<tr><td><p>pbk</p></td>
+<td><p>Bookman (psnfss)</p></td>
+</tr>
+<tr><td><p>pcr</p></td>
+<td><p>Courier (psnfss)</p></td>
+</tr>
+<tr><td><p>phv</p></td>
+<td><p>Helvetica (psnfss)</p></td>
+</tr>
+<tr><td><p>pnc</p></td>
+<td><p>New Century Schoolbook (psnfss)</p></td>
+</tr>
+<tr><td><p>ppl</p></td>
+<td><p>Palatino (psnfss)</p></td>
+</tr>
+<tr><td><p>ptm</p></td>
+<td><p>Times Roman (psnfss)</p></td>
+</tr>
+<tr><td><p>put</p></td>
+<td><p>Utopia (psnfss)</p></td>
+</tr>
+<tr><td><p>pzc</p></td>
+<td><p>Zapf Chancery (psnfss)</p></td>
+</tr>
+<tr><td><p>uag</p></td>
+<td><p>Avant Garde (avantgar)</p></td>
+</tr>
+<tr><td><p>ubk</p></td>
+<td><p>Bookman (bookman)</p></td>
+</tr>
+<tr><td><p>ucr</p></td>
+<td><p>Courier (courier)</p></td>
+</tr>
+<tr><td><p>ucrs</p></td>
+<td><p>Courier</p></td>
+</tr>
+<tr><td><p>unc</p></td>
+<td><p>New Courier (nctrsbk)</p></td>
+</tr>
+<tr><td><p>uni</p></td>
+<td><p>Universal (universa)</p></td>
+</tr>
+<tr><td><p>uhv</p></td>
+<td><p>Helvetica (helvetic)</p></td>
+</tr>
+<tr><td><p>upl</p></td>
+<td><p>Palatino (palatino)</p></td>
+</tr>
+<tr><td><p>utm</p></td>
+<td><p>Times (times)</p></td>
+</tr>
+<tr><td><p>uzc</p></td>
+<td><p>Zapf Chancery (zapfchan)</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+</div>
+<div class="section" id="unicode-mathematical-typesetting">
+<h2><a class="toc-backref" href="#id56"><span class="sectnum">4.3</span> Unicode mathematical typesetting</a></h2>
+<p>The technical report <a class="citation-reference" href="#tr25" id="id16">[tr25]</a> presents an in-depth discussion of the
+mathematics character repertoire of the Unicode Standard as well as
+mathematical notation in general.</p>
+<p>This section compares <a class="reference internal" href="#math-font-selection">math font selection</a> in LaTeX and Unicode.
+It suggests a set of 14 math alphabets that covers all Unicode
+<a class="reference internal" href="#mathematical-alphanumeric-symbols">mathematical alphanumeric symbols</a> and discusses compatibility
+issues between math typesetting with traditional (8-bit) TeX engines
+versus <a class="reference internal" href="#the-unicode-math-package">the unicode-math package</a> for Unicode-enabled TeX engines
+(XeTeX, LuaTeX).</p>
+<div class="section" id="unicode-math-alphabets">
+<span id="mathematical-alphanumeric-symbols"></span><h3><a class="toc-backref" href="#id57"><span class="sectnum">4.3.1</span> Unicode math alphabets</a></h3>
+<p>Chapter 2 <cite>Mathematical Character Repertoire</cite> of <a class="citation-reference" href="#tr25" id="id17">[tr25]</a> lists 14
+<cite>Mathematical Alphabets</cite> in Table 2.1. These mathematical alphabets are a
+superset of the predefined <a class="reference internal" href="#math-alphabets">math alphabets</a> in the LaTeX core.</p>
+<p>Unicode assignes code points to most letters of the mathematical
+alphabets in the <a class="reference external" href="http://www.unicode.org/charts/PDF/U1D400.pdf">mathematical alphanumeric symbols Unicode block</a>.
+The plain (upright, serifed) letters have been unified with the
+existing characters in the Basic Latin and Greek blocks.</p>
+<p><a class="reference internal" href="#table-5">Table&nbsp;5</a> maps the 14 Unicode mathematical alphabets to LaTeX commands
+according to the <a class="reference internal" href="#naming-scheme">naming scheme</a> below. <a class="reference internal" href="#table-6">Table&nbsp;6</a> lists the status of
+LaTeX support for the mathematical alphanumeric symbols. Full support is
+provided by <a class="reference internal" href="#the-unicode-math-package">the unicode-math package</a>.</p>
+<table class="booktabs numbered align-left" id="table-5">
+<caption>Mapping Unicode <a class="reference internal" href="#mathematical-alphanumeric-symbols">mathematical alphanumeric symbols</a> to LaTeX
+math alphabets.</caption>
+<colgroup>
+<col width="16%" />
+<col width="13%" />
+<col width="20%" />
+<col width="28%" />
+<col width="23%" />
+</colgroup>
+<thead valign="bottom">
+<tr><th class="head"><p>serifs</p></th>
+<th class="head"><p>weight</p></th>
+<th class="head"><p>shape</p></th>
+<th class="head"><p>symbols</p></th>
+<th class="head"><p>math alphabet</p></th>
+</tr>
+</thead>
+<tbody valign="top">
+<tr><td><p><em>serif</em></p></td>
+<td><p><em>medium</em></p></td>
+<td><p><em>upright</em></p></td>
+<td><p>Latin/Greek/digits<a class="footnote-reference" href="#up" id="id18"><sup>5</sup></a></p></td>
+<td><p><tt class="literal">\mathrm</tt></p></td>
+</tr>
+<tr><td><!-- -->
+</td>
+<td><p>bold</p></td>
+<td>&nbsp;</td>
+<td><p>Latin/Greek/digits</p></td>
+<td><p><tt class="literal">\mathbf</tt></p></td>
+</tr>
+<tr><td><!-- -->
+</td>
+<td>&nbsp;</td>
+<td><p>italic</p></td>
+<td><p>Latin/Greek</p></td>
+<td><p><tt class="literal">\mathit</tt></p></td>
+</tr>
+<tr><td><!-- -->
+</td>
+<td><p>bold</p></td>
+<td><p>italic</p></td>
+<td><p>Latin/Greek</p></td>
+<td><p><tt class="literal">\mathbfit</tt></p></td>
+</tr>
+<tr><td><!-- -->
+</td>
+<td>&nbsp;</td>
+<td><p>script</p></td>
+<td><p>Latin</p></td>
+<td><p><tt class="literal">\mathcal</tt></p></td>
+</tr>
+<tr><td><!-- -->
+</td>
+<td><p>bold</p></td>
+<td><p>script</p></td>
+<td><p>Latin</p></td>
+<td><p><tt class="literal">\mathbfcal</tt></p></td>
+</tr>
+<tr><td><!-- -->
+</td>
+<td>&nbsp;</td>
+<td><p>fraktur</p></td>
+<td><p>Latin</p></td>
+<td><p><tt class="literal">\mathfrak</tt></p></td>
+</tr>
+<tr><td><!-- -->
+</td>
+<td>&nbsp;</td>
+<td><p>double-struck</p></td>
+<td><p>Latin/digits</p></td>
+<td><p><tt class="literal">\mathbb</tt></p></td>
+</tr>
+<tr><td><!-- -->
+</td>
+<td><p>bold</p></td>
+<td><p>fraktur</p></td>
+<td><p>Latin</p></td>
+<td><p><tt class="literal">\mathbffrak</tt></p></td>
+</tr>
+<tr><td><p>sans serif</p></td>
+<td>&nbsp;</td>
+<td>&nbsp;</td>
+<td><p>Latin/digits</p></td>
+<td><p><tt class="literal">\mathsf</tt></p></td>
+</tr>
+<tr><td><p>sans serif</p></td>
+<td><p>bold</p></td>
+<td>&nbsp;</td>
+<td><p>Latin/Greek/digits</p></td>
+<td><p><tt class="literal">\mathsfbf</tt></p></td>
+</tr>
+<tr><td><p>sans serif</p></td>
+<td>&nbsp;</td>
+<td><p>italic</p></td>
+<td><p>Latin</p></td>
+<td><p><tt class="literal">\mathsfit</tt></p></td>
+</tr>
+<tr><td><p>sans serif</p></td>
+<td><p>bold</p></td>
+<td><p>italic</p></td>
+<td><p>Latin/Greek</p></td>
+<td><p><tt class="literal">\mathsfbfit</tt></p></td>
+</tr>
+<tr><td><!-- -->
+</td>
+<td>&nbsp;</td>
+<td><p>monospace</p></td>
+<td><p>Latin/digits</p></td>
+<td><p><tt class="literal">\mathtt</tt></p></td>
+</tr>
+</tbody>
+</table>
+<dl class="footnote"><dt class="label">5</dt>
+<dd id="up">
+<em>(<a class="fn-backref" href="#id18">1</a>, <a class="fn-backref" href="#id19">2</a>)</em> <p class="last">plain standard characters outside the
+<cite>mathematical alphanumeric symbols</cite> Unicode block.</p>
+</dd>
+</dl>
+<div class="section" id="naming-scheme">
+<h4><a class="toc-backref" href="#id58"><span class="sectnum">4.3.1.1</span> Naming scheme</a></h4>
+<p>The naming scheme is an extension of the predefined <a class="reference internal" href="#math-alphabet">math alphabet</a>
+commands with the short-cuts</p>
+<blockquote>
+<table class="borderless booktabs numbered align-left">
+<colgroup>
+<col width="14%" />
+<col width="86%" />
+</colgroup>
+<tbody valign="top">
+<tr><td><p>bf</p></td>
+<td><p>bold,</p></td>
+</tr>
+<tr><td><p>it</p></td>
+<td><p>italic,</p></td>
+</tr>
+<tr><td><p>cal</p></td>
+<td><p>script (calligraphic),</p></td>
+</tr>
+<tr><td><p>frak</p></td>
+<td><p>fraktur,</p></td>
+</tr>
+<tr><td><p>bb</p></td>
+<td><p>double-struck (blackboard bold),</p></td>
+</tr>
+<tr><td><p>sf</p></td>
+<td><p>sans serif</p></td>
+</tr>
+</tbody>
+</table>
+</blockquote>
+<p>combined to commands in the form <tt class="literal"><span class="pre">\math&lt;type&gt;&lt;weight&gt;&lt;shape&gt;</span></tt>.</p>
+<p>The &lt;<em>type</em>&gt;, &lt;<em>weight</em>&gt;, and &lt;<em>shape</em>&gt; specifiers are optional
+(defaults depend on the <a class="reference internal" href="#math-version">math version</a>). Their order matches the
+names of Unicode <a class="reference internal" href="#mathematical-alphanumeric-symbols">Mathematical Alphanumeric Symbols</a>.</p>
+<p>Examples:</p>
+<pre class="literal-block">\mathbf{d} % MATHEMATICAL BOLD SMALL D
+\mathsfbfit{d} % MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL D.
+</pre>
+<table class="booktabs numbered align-left" id="table-6">
+<caption>LaTeX support for <a class="reference internal" href="#mathematical-alphanumeric-symbols">mathematical alphanumeric symbols</a>.</caption>
+<colgroup>
+<col width="18%" />
+<col width="38%" />
+<col width="43%" />
+</colgroup>
+<thead valign="bottom">
+<tr><th class="head"><p>style</p></th>
+<th class="head"><p>math alphabet</p></th>
+<th class="head"><p>package, comment</p></th>
+</tr>
+</thead>
+<tbody valign="top">
+<tr><td><p>plain<a class="footnote-reference" href="#up" id="id19"><sup>5</sup></a></p></td>
+<td><p><tt class="literal">\mathrm</tt></p></td>
+<td><p>predefined<a class="footnote-reference" href="#no-g" id="id20"><sup>6</sup></a></p></td>
+</tr>
+<tr><td><!-- -->
+</td>
+<td><p><tt class="literal">\mathup</tt></p></td>
+<td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/unicode-math.html">unicode-math</a></p></td>
+</tr>
+<tr><td><p>bf</p></td>
+<td><p><tt class="literal">\mathbf</tt></p></td>
+<td><p>predefined<a class="footnote-reference" href="#no-g" id="id21"><sup>6</sup></a></p></td>
+</tr>
+<tr><td><p>it</p></td>
+<td><p><tt class="literal">\mathit</tt></p></td>
+<td><p>predefined<a class="footnote-reference" href="#no-g" id="id22"><sup>6</sup></a></p></td>
+</tr>
+<tr><td><p>bf it</p></td>
+<td><p><tt class="literal">\mathbfit</tt></p></td>
+<td><p>isomath<a class="footnote-reference" href="#digits" id="id23"><sup>7</sup></a></p></td>
+</tr>
+<tr><td><!-- -->
+</td>
+<td><p><tt class="literal">\mathbold</tt></p></td>
+<td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/fixmath.html">fixmath</a>, <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/mathpazo.html">mathpazo</a>,
+<a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/mathptmx.html">mathptmx</a>, <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/tmmath.html">tmmath</a><a class="footnote-reference" href="#digits" id="id24"><sup>7</sup></a></p></td>
+</tr>
+<tr><td><!-- -->
+</td>
+<td><p><tt class="literal">\boldsymbol</tt></p></td>
+<td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/amsmath.html">amsmath</a></p></td>
+</tr>
+<tr><td><!-- -->
+</td>
+<td><p><tt class="literal">\bm</tt></p></td>
+<td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/bm.html">bm</a></p></td>
+</tr>
+<tr><td><p>cal</p></td>
+<td><p><tt class="literal">\mathcal</tt></p></td>
+<td><p>predefined<a class="footnote-reference" href="#script" id="id25"><sup>8</sup></a></p></td>
+</tr>
+<tr><td><!-- -->
+</td>
+<td><p><tt class="literal">\mathscr</tt></p></td>
+<td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/mathrsfs.html">mathrsfs</a>, <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/euscript.html">euscript</a>,
+<a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/mathdesign.html">mathdesign</a></p></td>
+</tr>
+<tr><td><p>bf cal</p></td>
+<td><p><tt class="literal">\mathbfscr</tt></p></td>
+<td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/unicode-math.html">unicode-math</a></p></td>
+</tr>
+<tr><td><p>frak</p></td>
+<td><p><tt class="literal">\mathfrak</tt></p></td>
+<td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/amssymb.html">amssymb</a>, <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/amsfonts.html">amsfonts</a>, <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/eufrak.html">eufrak</a></p></td>
+</tr>
+<tr><td><p>bf frak</p></td>
+<td><p><tt class="literal">\mathbffrak</tt></p></td>
+<td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/unicode-math.html">unicode-math</a></p></td>
+</tr>
+<tr><td><p>bb</p></td>
+<td><p><tt class="literal">\mathbb</tt></p></td>
+<td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/amssymb.html">amssymb</a>, <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/bbold.html">bbold</a>,
+<a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/mathbbol.html">mathbbol</a>, <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/mbboard.html">mbboard</a>,
+<a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/mathpazo.html">mathpazo</a></p></td>
+</tr>
+<tr><td><!-- -->
+</td>
+<td><p><tt class="literal">\mathbbm</tt></p></td>
+<td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/bbm.html">bbm</a></p></td>
+</tr>
+<tr><td><!-- -->
+</td>
+<td><p><tt class="literal">\mathds</tt></p></td>
+<td><p>dsfont (<a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/doublestoke.html">doublestoke</a>)</p></td>
+</tr>
+<tr><td><p>sf</p></td>
+<td><p><tt class="literal">\mathsf</tt></p></td>
+<td><p>predefined<a class="footnote-reference" href="#no-g" id="id26"><sup>6</sup></a></p></td>
+</tr>
+<tr><td><p>sf bf</p></td>
+<td><p><tt class="literal">\mathbfsfup</tt></p></td>
+<td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/unicode-math.html">unicode-math</a></p></td>
+</tr>
+<tr><td><p>sf it</p></td>
+<td><p><tt class="literal">\mathsfit</tt></p></td>
+<td><p>isomath<a class="footnote-reference" href="#digits" id="id27"><sup>7</sup></a></p></td>
+</tr>
+<tr><td><p>sf bf it</p></td>
+<td><p><tt class="literal">\mathsfbfit</tt></p></td>
+<td><p>isomath<a class="footnote-reference" href="#digits" id="id28"><sup>7</sup></a></p></td>
+</tr>
+<tr><td><!-- -->
+</td>
+<td><p><tt class="literal">\mathbold</tt></p></td>
+<td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/cmbright.html">cmbright</a>, <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/hvmath.html">hvmath</a></p></td>
+</tr>
+<tr><td><!-- -->
+</td>
+<td><p><tt class="literal">\mathbfsfit</tt></p></td>
+<td><p><a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/unicode-math.html">unicode-math</a></p></td>
+</tr>
+<tr><td><p>tt</p></td>
+<td><p><tt class="literal">\mathtt</tt></p></td>
+<td><p>predefined<a class="footnote-reference" href="#no-g" id="id29"><sup>6</sup></a></p></td>
+</tr>
+</tbody>
+</table>
+<dl class="footnote"><dt class="label">6</dt>
+<dd id="no-g">
+<em>(<a class="fn-backref" href="#id20">1</a>, <a class="fn-backref" href="#id21">2</a>, <a class="fn-backref" href="#id22">3</a>, <a class="fn-backref" href="#id26">4</a>, <a class="fn-backref" href="#id29">5</a>)</em> <p class="last">no small Greek, full Greek with <a class="reference internal" href="#omlmath">OMLmath*</a> options.</p>
+</dd>
+<dt class="label">7</dt>
+<dd id="digits">
+<em>(<a class="fn-backref" href="#id23">1</a>, <a class="fn-backref" href="#id24">2</a>, <a class="fn-backref" href="#id27">3</a>, <a class="fn-backref" href="#id28">4</a>)</em> <p class="last">Some italic math fonts (e. g., cmr, cmbr) have old-style
+numbers in place of italic digits.</p>
+</dd>
+<dt class="label"><a class="fn-backref" href="#id25">8</a></dt>
+<dd id="script">
+<p class="first last">no small Latin, formal script with <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/calrsfs.html">calrsfs</a>, <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/eucal.html">eucal</a>, <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/fourier.html">fourier</a></p>
+</dd>
+</dl>
+</div>
+</div>
+<div class="section" id="the-unicode-math-package">
+<h3><a class="toc-backref" href="#id59"><span class="sectnum">4.3.2</span> The unicode-math package</a></h3>
+<p>Users of UTF-8 enabled TeX engines (XeTeX, LuaTeX) can typeset
+mathematics with the experimental <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/unicode-math.html">unicode-math</a> package by Will
+Robertson. It provides a LaTeX interface to OpenType fonts with math
+support, e. g., <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/asana-math.html">Asana Math</a>, Cambria Math, <a class="reference external" href="https://github.com/khaledhosny/euler-otf">New Euler</a> or <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/xits.html">XITS</a>, with
+commands to access the complete mathematics character repertoire of the
+Unicode Standard</p>
+<p>LaTeX <a class="reference internal" href="#math-font-selection">math font selection</a> methods with unicode-math:</p>
+<dl class="docutils">
+<dt><a class="reference internal" href="#math-alphabets">math alphabets</a></dt>
+<dd><p>map to a range of the <a class="reference internal" href="#mathematical-alphanumeric-symbols">mathematical alphanumeric symbols</a> block in the
+current font (or a substitution defined with the <tt class="literal">range</tt> math font
+option).</p>
+<p>Some command names differ from the <a class="reference internal" href="#predefined-math-alphabets">predefined math alphabets</a> or the
+above <a class="reference internal" href="#naming-scheme">naming scheme</a>:</p>
+<table class="booktabs numbered align-left">
+<colgroup>
+<col width="50%" />
+<col width="50%" />
+</colgroup>
+<thead valign="bottom">
+<tr><th class="head"><p>LaTeX</p></th>
+<th class="head"><p>unicode-math</p></th>
+</tr>
+</thead>
+<tbody valign="top">
+<tr><td><p><tt class="literal">\mathbf</tt></p></td>
+<td><p><tt class="literal">\mathbfup</tt></p></td>
+</tr>
+<tr><td><p><tt class="literal">\mathsf</tt></p></td>
+<td><p><tt class="literal">\mathsfup</tt></p></td>
+</tr>
+<tr><td><p><tt class="literal">\mathsfbf</tt></p></td>
+<td><p><tt class="literal">\mathbfsfup</tt></p></td>
+</tr>
+<tr><td><p><tt class="literal">\mathsfbfit</tt></p></td>
+<td><p><tt class="literal">\mathbfsfit</tt></p></td>
+</tr>
+</tbody>
+</table>
+<p>With unicode-math, <tt class="literal">\mathbf</tt>, <tt class="literal">\mathsf</tt>, and <tt class="literal">\mathsfbf</tt>
+behave similar to <a class="reference internal" href="#in-line-math-versions">“in-line math versions”</a>: they consider the
+<a class="reference internal" href="#math-style">math style</a> for upright vs. italic shape. Compatibility can be
+achieved via the options <tt class="literal"><span class="pre">bold-style=upright</span></tt> and
+<tt class="literal"><span class="pre">sans-style=upright</span></tt>.</p>
+<p><tt class="literal">\mathbfsfit</tt> reverses the order of the <tt class="literal">sf</tt> and <tt class="literal">bf</tt> selectors,
+so that, e. g., the Unicode character <cite>MATHEMATICAL SANS-SERIF BOLD
+ITALIC CAPITAL A</cite> is selected by the non-mnemonic <tt class="literal">\mathbfsfit{A}</tt>.</p>
+</dd>
+<dt><a class="reference internal" href="#math-versions">math versions</a></dt>
+<dd><p>are not directly supported but easy to emulate.</p>
+<p>As Unicode fonts can hold all math symbols in a single font file, a
+single <tt class="literal"><span class="pre">\setmathfont[&lt;font</span> <span class="pre">features&gt;]{&lt;font</span> name&gt;}</tt> can replace
+the <tt class="literal"><span class="pre">\mathversion{&lt;mathversion&gt;}</span></tt> command if a complete OpenType
+math font in the desired version is available.</p>
+<p>However, complete OpenType math fonts are rare. Therefore
+unicode-math supports using multiple fonts with the <tt class="literal">range</tt>
+option. This way one can emulate, e. g., the <tt class="literal">bold</tt> math version
+via:</p>
+<pre class="literal-block">\renewcommand{\boldmath}{%
+ \setmathfont{XITS Bold}%
+ \setmathfont[range={&quot;1D400-&quot;1F020}]{XITS Math}%
+ \setmathfont[range=\mathup-&gt;\mathbfup]{XITS Math}%
+ \setmathfont[range=\mathsfit-&gt;\mathbfsfit]{XITS Math}%
+ % ...
+}
+</pre>
+<p>It would be nice if unicode-math could provide a <tt class="literal">\newmathversion</tt>
+command similar to the <tt class="literal">\newfontfamily</tt> in <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/fontspec.html">fontspec</a> for such setups.</p>
+<p>For alphanumerical characters, the <tt class="literal">\mathbf</tt>, <tt class="literal">\mathsf</tt>, and
+<tt class="literal">\mathsfbf</tt> behave like <a class="reference internal" href="#in-line-math-versions">“in-line math versions”</a>.</p>
+</dd>
+<dt><a class="reference internal" href="#math-styles">math styles</a></dt>
+<dd><p>are supported with the <tt class="literal"><span class="pre">math-style</span></tt> package option that accepts the
+values <tt class="literal">TeX</tt>, <tt class="literal">ISO</tt>, <tt class="literal">french</tt>, <tt class="literal">upright</tt>, and <tt class="literal">literal</tt>.</p>
+</dd>
+</dl>
+</div>
+</div>
+<div class="section" id="conclusions-and-outlook">
+<h2><a class="toc-backref" href="#id60"><span class="sectnum">4.4</span> Conclusions and outlook</a></h2>
+<p>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
+<a class="reference internal" href="#mathematical-alphanumeric-symbols">mathematical alphanumeric symbols</a> Unicode block.</p>
+<p>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.</p>
+<p>Alternatively, the T7 encoding could be used for math alphabets (if it
+ever happens to materialise).</p>
+<p>Upright small Greek letters in <tt class="literal">\mathrm</tt> would enable the
+specification of the constant pi, Myons, Pions, alpha-particles,
+photons, and neutrinos with <a class="reference internal" href="#math-alphabets">math alphabets</a>. (With <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/mathdesign.html">mathdesign</a>
+fonts, this is already possible today.)</p>
+<p>With the development of the <a class="reference external" href="http://mirror.ctan.org/help/Catalogue/entries/unicode-math.html">unicode-math</a> package, an interesting
+alternative for ISO-conforming math typesetting became available to
+users of Unicode-enabled TeX engines (XeTeX or LuaTeX).</p>
+</div>
+</div>
+<div class="section" id="references">
+<h1><a class="toc-backref" href="#id61"><span class="sectnum">5</span> References</a></h1>
+<dl class="citation"><dt class="label"><a class="fn-backref" href="#id1">[ISO-80000-2]</a></dt>
+<dd id="iso-80000-2">
+<p class="first last"><cite>Quantities and units – Part 2: Mathematical signs
+and symbols to be used in the natural sciences and technology</cite>:
+<a class="reference external" href="http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=31887">http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=31887</a>.</p>
+</dd>
+</dl>
+<dl class="citation"><dt class="label">[ISO-31]</dt>
+<dd id="iso-31">
+<p class="first last"><cite>Quantities and units</cite>, Superseded by [ISO-80000].</p>
+</dd>
+</dl>
+<dl class="citation"><dt class="label"><a class="fn-backref" href="#id2">[typefaces]</a></dt>
+<dd id="typefaces">
+<p class="first last">National Institute of Standards and Technology (<a class="reference external" href="http://physics.nist.gov/">NIST</a>),
+<cite>Typefaces for Symbols in Scientific Manuscripts</cite>:
+<a class="reference external" href="http://physics.nist.gov/cuu/pdf/typefaces.pdf">http://physics.nist.gov/cuu/pdf/typefaces.pdf</a>.</p>
+</dd>
+</dl>
+<dl class="citation"><dt class="label"><a class="fn-backref" href="#id3">[checklist]</a></dt>
+<dd id="checklist">
+<p class="first last">National Institute of Standards and Technology (<a class="reference external" href="http://physics.nist.gov/">NIST</a>),
+<cite>SI Unit rules and style conventions</cite>
+Check List for Reviewing Manuscripts:
+<a class="reference external" href="http://physics.nist.gov/cuu/Units/checklist.html">http://physics.nist.gov/cuu/Units/checklist.html</a>.</p>
+</dd>
+</dl>
+<dl class="citation"><dt class="label"><a class="fn-backref" href="#id5">[fonts_for_symbols]</a></dt>
+<dd id="fonts-for-symbols">
+<p class="first last">International Union of Pure and Applied
+Chemistry (<a class="reference external" href="http://iupac.org/">IUPAC</a>), <cite>On the use of italic and roman fonts for symbols
+in scientific text</cite>, (Revised December 1999):
+<a class="reference external" href="http://old.iupac.org/standing/idcns/fonts_for_symbols.html">http://old.iupac.org/standing/idcns/fonts_for_symbols.html</a>.</p>
+</dd>
+</dl>
+<dl class="citation"><dt class="label"><a class="fn-backref" href="#id4">[SI]</a></dt>
+<dd id="si">
+<p class="first last">Bureau international des poids et mesures (<a class="reference external" href="http://www.bipm.org/">BIPM</a>),
+<cite>The International System of Units (SI)</cite>:
+<a class="reference external" href="http://www.bipm.org/en/si/si_brochure/">http://www.bipm.org/en/si/si_brochure/</a>.</p>
+</dd>
+</dl>
+<dl class="citation"><dt class="label"><a class="fn-backref" href="#id7">[Green-Book]</a></dt>
+<dd id="green-book">
+<p class="first last">International Union of Pure and Applied Chemistry (<a class="reference external" href="http://iupac.org/">IUPAC</a>),
+<cite>Quantities, Units and Symbols in Physical Chemistry</cite>,
+3rd edition, RSC Publishing, Cambridge 2007:
+[ISBN 0 85404 433 7; ISBN-13 978 0 85404 433 7].</p>
+</dd>
+</dl>
+<dl class="citation"><dt class="label"><a class="fn-backref" href="#id6">[Red-Book]</a></dt>
+<dd id="red-book">
+<p class="first last">International Union of Pure and Applied Physics (<a class="reference external" href="http://www.iupap.org/">IUPAP</a>),
+<cite>Symbols, Units, Nomenclature and Fundamental Constants in Physics</cite>:
+<a class="reference external" href="http://metrology.wordpress.com/measurement-process-index/iupap-red-book/index-iupap-red-book/">http://metrology.wordpress.com/measurement-process-index/iupap-red-book/index-iupap-red-book/</a>.</p>
+</dd>
+</dl>
+<dl class="citation"><dt class="label"><a class="fn-backref" href="#id15">[encguide]</a></dt>
+<dd id="encguide">
+<p class="first last">Frank Mittelbach, Robin Fairbairns, Werner Lemberg,
+LaTeX3 Project Team, <cite>LaTeX font encodings</cite>:
+<a class="reference external" href="http://mirror.ctan.org/macros/latex/doc/encguide.pdf">http://mirror.ctan.org/macros/latex/doc/encguide.pdf</a>.</p>
+</dd>
+</dl>
+<dl class="citation"><dt class="label">[fntguide]</dt>
+<dd id="fntguide">
+<em>(<a class="fn-backref" href="#id10">1</a>, <a class="fn-backref" href="#id11">2</a>)</em> <p class="last">LaTeX3 Project Team, <cite>LaTeX 2e font selection</cite>:
+<a class="reference external" href="http://mirror.ctan.org/macros/latex/doc/fntguide.pdf">http://mirror.ctan.org/macros/latex/doc/fntguide.pdf</a>.</p>
+</dd>
+</dl>
+<dl class="citation"><dt class="label">[tr25]</dt>
+<dd id="tr25">
+<em>(<a class="fn-backref" href="#id16">1</a>, <a class="fn-backref" href="#id17">2</a>)</em> <p class="last">Barbara Beeton, Asmus Freytag, Murray Sargent III,
+<cite>Unicode Support for Mathematics</cite>, Unicode Technical Report #25:
+<a class="reference external" href="http://www.unicode.org/reports/tr25/">http://www.unicode.org/reports/tr25/</a>.</p>
+</dd>
+</dl>
+<dl class="citation"><dt class="label">[beeton:2000]</dt>
+<dd id="beeton-2000">
+<p class="first last">Barbara Beeton:
+<cite>Unicode and math, a combination whose time has come – Finally!</cite>,
+TUGBoat, 21#3, 2000:
+<a class="reference external" href="http://www.tug.org/TUGboat/Articles/tb21-3/tb68beet.pdf">http://www.tug.org/TUGboat/Articles/tb21-3/tb68beet.pdf</a>.</p>
+</dd>
+</dl>
+<!-- see also
+[koma-mail] Custom font substitution: http://www.komascript.de/node/823. -->
+<!-- Links
+===== -->
+</div>
+</div>
+</body>
+</html>