fundamentals.html

<section>
 <h2 id="fund">MathML Fundamentals</h2>

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 <section>
  <h3 id="fund_syntax">MathML Syntax and Grammar</h3>

  <section>
   <h4 id="fund_xmlgeneral">General Considerations</h4>

   <p>The basic &#x2018;syntax&#x2019; of MathML is
   defined using XML syntax,
   but other syntaxes that can encode labeled trees are possible. Notably the HTML parser
   may also be used with MathML.
   Upon this, we layer a &#x2018;grammar&#x2019;, being the rules for allowed elements,
   the order in which they can appear,
   and how they may be contained within each other,
   as well as additional syntactic rules for the values of attributes.
   These rules are defined by this specification,
   and formalized by a RelaxNG schema  [[RELAXNG-SCHEMA]] in <a href="#parsing"></a>.
   Derived schema in other formats, DTD (Document Type Definition)
   and  XML Schema [[XMLSchemas]] are also provided.
   </p>

   <p>MathML's character set consists of any
   Unicode characters [[Unicode]] allowed by the syntax being used. (See for example [[XML]] or [[HTML]].)
   The use of Unicode characters for mathematics is
   discussed in <a href="#chars"></a>.</p>

   <p>The following sections discuss the general aspects
   of the MathML grammar as well as describe the syntaxes used
   for attribute values.
   </p>

  </section>

  <section>
   <h4 id="interf_namespace">MathML and Namespaces</h4>

   <p>An XML namespace [[Namespaces]] is a collection of names identified by a URI.
   The URI for the MathML namespace is:</p>


    <pre>
     http://www.w3.org/1998/Math/MathML
    </pre>


   <p>To declare a namespace when using the XML serialisation of MathML,
   one uses an <code class="attribute">xmlns</code>
   attribute, or an attribute with an <code class="attribute">xmlns</code> prefix.</p>

   <div class="example ">
    <pre>
      &lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;
        &lt;mrow&gt;...&lt;/mrow&gt;
      &lt;/math&gt;
    </pre>
   </div>

   <p>When the <code class="attribute">xmlns</code> attribute is used as a
   prefix, it declares a prefix which can then be used to explicitly associate other
   elements
   and attributes with a particular namespace.
   When embedding MathML within HTML using XML syntax, one might use:
   </p>

   <div class="example ">
    <pre>
      &lt;body xmlns:m="http://www.w3.org/1998/Math/MathML"&gt;
        ...
        &lt;m:math&gt;&lt;m:mrow&gt;...&lt;/m:mrow&gt;&lt;/m:math&gt;
        ...
      &lt;/body&gt;
    </pre>
   </div>

   <p>HTML does not support namespace extensibility in the same way. The HTML parser
   has in-built knowledge of the HTML, SVG, and MathML namespaces. <code class="attribute">xmlns</code> attributes are
   just treated as normal attributes. Thus, when using the HTML serialisation of MathML,
   prefixed element names must not be used. <code class="attribute">xmlns</code>=<code class="attributevalue">http://www.w3.org/1998/Math/MathML</code>
   may be used on the <code class="element">math</code> element; it will be ignored by the HTML parser.

   If a MathML expression is likely to be in contexts where it may be parsed by an XML
   parser or an HTML parser, it SHOULD
   use the following form to ensure maximum compatibility:</p>

   <div class="example mathml-fragment">
    <pre>
      &lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;
        ...
      &lt;/math&gt;
    </pre>
   </div>

  </section>

  <section>
   <h4 id="fund_xmlsyntax">Children versus Arguments</h4>

   <p>There are presentation elements that conceptually accept only
   a single argument, but which for convenience have been written to accept any number
   of children;
   then we infer an <code class="element">mrow</code> containing those children which acts as
   the argument to the element in question; see <a href="#presm_inferredmrow"></a>.
   </p>

   <p>In the detailed discussions of element syntax given with each
   element throughout the MathML specification, the number of arguments required and
   their order, as well as other constraints on the content, are specified.
   This information is also tabulated
   for the presentation elements in <a href="#presm_reqarg"></a>.</p>

  </section>

  <section>
   <h4 id="fund_renderingmodel">MathML and Rendering</h4>
   <p>Web Platform implementations of [[MathML-Core]] should follow the
   detailed layout rules specified in that document.</p>

   <p>This document only recommends (i.e., does not require) specific
   ways of rendering Presentation MathML; this is in order to allow
   for medium-dependent rendering and for implementations not using
   the CSS based Web Platform.</p>

  </section>

  <section>
   <h4 id="fund_attval">MathML Attribute Values</h4>

   <p>MathML elements take attributes with values that further specialize
   the meaning or effect of the element. Attribute names are shown in a
   <code>monospaced</code> font throughout this document. The meanings of attributes and their
   allowed values are described within the specification of each element.
   The syntax notation explained in this section is used in specifying allowed values.
   </p>

   <section>
    <h5 id="fund_syntax_notation">Syntax notation used in the MathML specification</h5>

    <p>To  describe  the  MathML-specific  syntax  of
    attribute values, the  following conventions and notations are
    used for most attributes in the present document.</p>


    <table id="fund_table-attval" class="data">

     <thead>

      <tr>
       <th>Notation</th>
       <th>What it matches</th>
      </tr>
     </thead>

     <tbody
>

      <tr>
       <td id="type_unsigned-integer"><dfn><em>unsigned-integer</em></dfn></td>
       <td>As defined in [[MathML-Core]], an <a data-cite="CSS-VALUES-3#integer-value"><code>integer</code></a>, whose first character is neither
              U+002D HYPHEN-MINUS character (-) nor
              U+002B PLUS SIGN (+).</td>
      </tr>

      <tr>
       <td id="type_positive-integer"><dfn><em>positive-integer</em></dfn></td>
       <td>An [=unsigned-integer=] not consisting solely of "0"s (U+0030), representing a positive integer</td>
      </tr>

      <tr>
       <td id="type_integer"><dfn><em>integer</em></dfn></td>
       <td>an optional "-"  (U+002D), followed by an [=unsigned-integer=],
       and representing an integer
       </td>
      </tr>

      <tr>
       <td id="type_unsigned-number"><dfn><em>unsigned-number</em></dfn></td>
       <td>
         value as defined in
              [[CSS-VALUES-3]] <a data-cite="CSS-VALUES-3#number"><code>number</code></a>, whose first character is neither
              U+002D HYPHEN-MINUS character (-) nor
              U+002B PLUS SIGN (+),
              representing a non-negative terminating decimal number
       (a type of rational number)</td>
      </tr>

      <tr>
       <td id="type_number"><dfn><em>number</em></dfn></td>
       <td>
        an optional prefix of "-" (U+002D), followed by an <a href="#type_unsigned-number">unsigned number</a>,
       representing a terminating decimal number (a type of rational number)</td>
      </tr>

      <tr>
       <td id="type_character"><dfn><em>character</em></dfn></td>
       <td>a single non-whitespace character</td>
      </tr>

      <tr>
       <td id="type_string"><dfn><em>string</em></dfn></td>
       <td>an arbitrary, nonempty and finite, string of <em>character</em>s</td>
      </tr>

      <tr>
       <td id="type_length"><dfn><em>length</em></dfn></td>
       <td>a length, as explained below, <a href="#fund_units"></a></td>
      </tr>

      <tr>
       <td id="type_namedspace"><b><em>namedspace</em></b></td>
       <td>a named [=length=], [=namedspace=], as explained in <a href="#fund_units"></a></td>
      </tr>

      <tr>
       <td id="type_color"><dfn><em>color</em></dfn></td>
       <td>a color, using the syntax specified by [[CSS-Color-3]]</td>
      </tr>

      <tr>
       <td id="type_id"><dfn><em>id</em></dfn></td>
       <td>an identifier, unique within the document;
       must satisfy the NAME syntax of the XML recommendation [[XML]]</td>
      </tr>

      <tr>
       <td id="type_idref"><dfn><em>idref</em></dfn></td>
       <td>an identifier referring to another element within the document;
       must satisfy the NAME syntax of the XML recommendation [[XML]]</td>
      </tr>

      <tr>
       <td id="type_uri"><dfn><em>URI</em></dfn></td>
       <td>a Uniform Resource Identifier [[RFC3986]]. Note that the attribute value
       is typed in the schema as anyURI which allows any sequence of XML characters.
       Systems needing to use this string as a URI must encode the bytes of the UTF-8 encoding
       of any characters not allowed in URI using %HH encoding where HH are the byte value
       in hexadecimal.
       This ensures that such an attribute value may be interpreted as an IRI,
       or more generally a LEIRI; see  [[IRI]].</td>
      </tr>

      <tr>
       <td><em>italicized word</em></td>
       <td>values as explained in the text for each attribute; see <a href="#fund_defaults"></a></td>
      </tr>

      <tr>
       <td>"literal"</td>
       <td>quoted symbol, literally present in the attribute value (e.g. "+" or '+')</td>
      </tr>
     </tbody>
    </table>


    <p>The &#x2018;types&#x2019; described above, except for <em>string</em>,
    may be combined into composite patterns using the following operators. The whole
    attribute value must be delimited by single (') or double (") quotation marks in the
    marked up
    document.  Note that double quotation marks are often used in this specification to
    mark up
    literal expressions; an example is the "-" in line 5 of the table above.
    </p>

    <p>
     In the table
     below a form <em>f</em> means an instance of a type described in the table above.
     The combining operators are shown in order of precedence from highest
    to lowest:</p>

    <table id="fund_table_notn" class="data">

     <thead>

      <tr>
       <th>Notation</th>
       <th>What it matches</th>
      </tr>
     </thead>

     <tbody>

      <tr>
       <td><math class="doc" alttext="(f)"><mo>(</mo><mi>f</mi><mo>)</mo></math></td>
       <td>same <math class="doc" alttext="f"><mi>f</mi></math></td>
      </tr>

      <tr>
       <td><math class="doc" alttext="f?"><mi>f</mi><mo>?</mo></math></td>
       <td>an optional instance of <math class="doc" alttext="f"><mi>f</mi></math></td>
      </tr>

      <tr>
       <td><math class="doc" alttext="f*"><mi>f</mi><mo>*</mo></math></td>
       <td>zero or more instances of <math class="doc" alttext="f"><mi>f</mi></math>, with
       separating whitespace characters</td>
      </tr>

      <tr>
       <td><math class="doc" alttext="f+"><mi>f</mi><mo>+</mo></math></td>
       <td>one or more instances of <math class="doc" alttext="f"><mi>f</mi></math>, with
       separating whitespace characters</td>
      </tr>

      <tr>
       <td><math class="doc" alttext="f_1 f_2 ... f_n"><msub><mi>f</mi><mn>1</mn></msub><msub><mi>f</mi><mn>2</mn></msub> <mo>&#x22EF;</mo><msub><mi>f</mi><mi>n</mi></msub></math></td>
       <td>one instance of each form <math class="doc" alttext="f_i"><msub><mi>f</mi><mi>i</mi></msub></math>, in sequence,
       with no separating whitespace</td>
      </tr>

      <tr>
       <td><math class="doc" alttext="f_1, f_2, ..., f_n"><msub><mi>f</mi><mn>1</mn></msub><mo>,</mo><msub><mi>f</mi><mn>2</mn></msub><mo>,</mo> <mo>&#x2026;</mo><mo>,</mo><msub><mi>f</mi><mi>n</mi></msub></math></td>
       <td>one instance of each form <math class="doc" alttext="f_i"><msub><mi>f</mi><mi>i</mi></msub></math>, in sequence, with
       separating whitespace characters (but no commas)</td>
      </tr>

      <tr>
       <td style="white-space:nowrap"><math class="doc" alttext="f_1, f_2, ..., f_n"><msub><mi>f</mi><mn>1</mn></msub><mo>|</mo><msub><mi>f</mi><mn>2</mn></msub><mo>|</mo> <mo>&#x22EF;</mo><mo>|</mo><msub><mi>f</mi><mi>n</mi></msub></math></td>
       <td>any one of the specified forms <math class="doc" alttext="f_i"><msub><mi>f</mi><mi>i</mi></msub></math></td>
      </tr>
     </tbody>
    </table>

    <p>The notation we have chosen here is in the style of the syntactical notation of the
    RelaxNG
    used for MathML's basic schema, <a href="#parsing"></a>.
    </p>

    <p>Since some applications are inconsistent about normalization
    of whitespace, for maximum interoperability it is advisable to use only
    a single whitespace character for separating parts of a value.
    Moreover, leading and trailing whitespace in attribute values should be avoided.</p>

    <p>For most numerical attributes, only those in a subset of the
    expressible values are sensible; values outside this subset are not
    errors, unless otherwise specified, but rather are rounded up or down
    (at the discretion of the renderer) to the closest value within the
    allowed subset.  The set of allowed values may depend on the renderer,
    and is not specified by MathML.</p>

    <p>If a numerical value within an attribute value syntax description
    is declared to allow a minus sign ('-'), e.g., <code class="attribute">number</code> or
    <code class="attribute">integer</code>, it is not a syntax error when one is provided in
    cases where a negative value is not sensible. Instead, the value
    should be handled by the processing application as described in the
    preceding paragraph.  An explicit plus sign ('+') is not allowed as
    part of a numerical value except when it is specifically listed in the
    syntax (as a quoted '+' or "+"), and its presence can change the
    meaning of the attribute value (as documented with each attribute
    which permits it).</p>

   </section>

   <section>
    <h5 id="fund_units">Length Valued Attributes</h5>

    <p>Most presentation elements have attributes that accept values
    representing lengths to be used for size, spacing or similar properties.
    [[MathML-Core]] accepts lengths only in the
     <a id="type_unit" data-cite="CSS-VALUES-3#typedef-length-percentage"><code>&lt;length-percentage&gt;</code></a>
     syntax defined in [[CSS-VALUES-3]].
     MathML Full extends length syntax by accepting also a <dfn>namedspace</dfn>
     being one of:</p>
      <table class="data">
       <thead>
	<tr><th>Positive space</th><th>Negative space</th><th>Value</th></tr>
	</thead>
	<tbody>
	 <tr>
	  <td style="white-space:nowrap"><code class="attributevalue">veryverythinmathspace</code></td>
	  <td style="white-space:nowrap"><code class="attributevalue">negativeveryverythinmathspace</code></td>
	  <td>±1/18&#x2009;em</td>
	 </tr>
	 <tr>
	  <td style="white-space:nowrap"><code class="attributevalue">verythinmathspace</code></td>
	  <td style="white-space:nowrap"><code class="attributevalue">negativeverythinmathspace</code></td>
	  <td>±2/18&#x2009;em</td>
	 </tr>
	 <tr>
	  <td style="white-space:nowrap"><code class="attributevalue">thinmathspace</code></td>
	  <td style="white-space:nowrap"><code class="attributevalue">negativethinmathspace</code></td>
	  <td>±3/18&#x2009;em</td>
	 </tr>
	 <tr>
	  <td style="white-space:nowrap"><code class="attributevalue">mediummathspace</code></td>
	  <td style="white-space:nowrap"><code class="attributevalue">negativemediummathspace</code></td>
	  <td>±4/18&#x2009;em</td>
	 </tr>
	 <tr>
	  <td style="white-space:nowrap"><code class="attributevalue">thickmathspace</code></td>
	  <td style="white-space:nowrap"><code class="attributevalue">negativethickmathspace</code></td>
	  <td>±5/18&#x2009;em</td>
	 </tr>
	 <tr>
	  <td style="white-space:nowrap"><code class="attributevalue">verythickmathspace</code></td>
	  <td style="white-space:nowrap"><code class="attributevalue">negativeverythickmathspace</code></td>
	  <td>±6/18&#x2009;em</td>
	 </tr>
	 <tr>
	  <td style="white-space:nowrap"><code class="attributevalue">veryverythickmathspace</code></td>
	  <td style="white-space:nowrap"><code class="attributevalue">negativeveryverythickmathspace</code></td>
	  <td>±7/18&#x2009;em</td>
	 </tr>
	</tbody>
      </table>


    <p>In MathML&#160;3, the attributes on <a href="#presm_mpadded">mpadded</a>
     allowed three <dfn>pseudo-units</dfn>, <code>height</code>,
      <code>depth</code>, and <code>width</code> (taking the place of one of the usual CSS units)
      denoting the original dimensions of the content.
      It also allowed a deprecated usage with lengths specified as
     a number without a unit which was interpreted as a multiple of the
     reference value. These forms are considered invalid in MathML&#160;4.
    </p>

    <section>
     <h6 id="units_addl_notes">Additional notes about units</h6>


     <p>Two additional aspects of relative units must be clarified, however.
     First, some elements such as <a href="#presm_scrlim"></a> or <code class="element">mfrac</code>
     implicitly switch to smaller font sizes for some of their arguments.
     Similarly, <code class="element">mstyle</code> can be used to explicitly change
     the current font size. In such cases, the effective values of
     an <code>em</code> or <code>ex</code> inside those contexts will be
     different than outside. The second point is that the effective value
     of an <code>em</code> or <code>ex</code> used for an attribute value
     can be affected by changes to the current font size.
     Thus, attributes that affect the current font size,
     such as <code class="attribute">mathsize</code>
     and <code class="attribute">scriptlevel</code>, must be processed before
     evaluating other length valued attributes.
     </p>

    </section>
   </section>


   <section>
    <h5 id="fund_defaults">Default values of attributes</h5>

    <p>Default values for MathML attributes are, in general, given along with the
    detailed descriptions of specific elements in the text.  Default values
    shown in plain text in the tables of attributes for an element are literal,
    but when italicized are descriptions of how default values can be computed.</p>

    <p>Default values described as <em>inherited</em> are taken from the
    rendering environment, as described in <a href="#presm_mstyle"></a>,
    or in some cases (which are described individually) taken from the values of other
    attributes of surrounding elements, or from certain parts of those
    values. The value used will always be one which could have been specified
    explicitly, had it been known; it will never depend on the content or
    attributes of the same element, only on its environment. (What it means
    when used may, however, depend on those attributes or the content.)</p>

    <p>Default values described as <em>automatic</em> should be computed by
    a MathML renderer in a way which will produce a high-quality rendering; how
    to do this is not usually specified by the MathML specification. The value
    computed will always be one which could have been specified explicitly, had
    it been known, but it will usually depend on the element content and
    possibly on the context in which the element is rendered.</p>

    <p>Other italicized descriptions of default values which appear in the
    tables of attributes are explained individually for each attribute.</p>

    <p>The single or double quotes which are required around attribute values
    in an XML start tag are not shown in the tables of attribute value syntax
    for each element, but are around attribute values in examples in the
    text, so that the pieces of code shown are correct.</p>

    <p>Note that, in general, there is no mechanism in MathML to simulate the
    effect of not specifying attributes which are <em>inherited</em> or
    <em>automatic</em>.  Giving the words <q>inherited</q> or
    <q>automatic</q> explicitly will not work, and is not generally
    allowed.  Furthermore, the <code class="element">mstyle</code> element (<a href="#presm_mstyle"></a>)
    can even be used to change the default values of presentation attributes
    for its children.</p>

    <p>Note also that these defaults describe the
    behavior of MathML applications when an attribute is not supplied;
    they do not indicate a value that will be filled in by an XML parser,
    as is sometimes mandated by DTD-based specifications.</p>

    <p>In general, there are a number of
    properties of MathML rendering that may be thought of as overall
    properties of a document, or at least of sections of a large
    document.  Examples might be <code class="attribute">mathsize</code> (the math font
    size: see <a href="#presm_commatt"></a>), or the
    behavior in setting limits on operators such as integrals or sums
    (e.g., <code class="attribute">movablelimits</code> or <code class="attribute">displaystyle</code>), or
    upon breaking formulas over lines (e.g.
    <code class="attribute">linebreakstyle</code>); for such attributes see several
    elements in <a href="#presm_tokel"></a>.
    These may be thought to be inherited from some such
    containing scope. Just above we have mentioned the setting of default
    values of MathML attributes as <em>inherited</em> or
    <em>automatic</em>; there is a third source of global default values
    for behavior in rendering MathML, a MathML operator dictionary. A
    default example is provided in <a href="#oper-dict"></a>.
    This is also discussed in <a href="#presm_opdict"></a> and examples are given in
    <a href="#presm_mo_dict_attrs"></a>.</p>
   </section>

  </section>

  <section>
   <h4 id="fund_globatt">Attributes Shared by all MathML Elements</h4>

   <p>In addition to the attributes described specifically for each element,
   the attributes in the following table are allowed on every MathML element.
   Also allowed are attributes from the xml namespace, such as <code class="attribute">xml:lang</code>,
   and attributes from namespaces other than MathML,
   which are ignored by default.</p>

   <table class="attributes data">

    <thead>

     <tr>
      <th>Name</th>
      <th>values</th>
      <th>default</th>
     </tr>
    </thead>

    <tbody>

     <tr>
      <td rowspan="2" class="attname"><a class="coreyes" href="https://w3c.github.io/mathml-core/spec.html#dfn-id">id</a></td>
      <td><em>[=id=]</em></td>
      <td><em>none</em></td>
     </tr>

     <tr>
      <td colspan="2" class="attdesc">
       Establishes a unique identifier associated with the element
       to support linking, cross-references and parallel markup.
       See <code class="attribute">xref</code> and <a href="#mixing_parallel"></a>.
      </td>
     </tr>

     <tr>
      <td rowspan="2" class="attname"><span class="coreno">xref</span></td>
      <td><em>[=idref=]</em></td>
      <td><em>none</em></td>
     </tr>

     <tr>
      <td colspan="2" class="attdesc">
       References another element within the document.
       See <code class="attribute">id</code> and <a href="#mixing_parallel"></a>.
      </td>
     </tr>

     <tr>
      <td rowspan="2" class="attname"><a class="coreyes" href="https://w3c.github.io/mathml-core/spec.html#dfn-class">class</a></td>
      <td><em>[=string=]</em></td>
      <td><em>none</em></td>
     </tr>

     <tr>
      <td colspan="2" class="attdesc">
       Associates the element with a set of style classes for use with
       [[CSS21]].
       See <a href="#world-int-style"></a> for discussion of the interaction of MathML and CSS.
      </td>
     </tr>

     <tr>
      <td rowspan="2" class="attname"><a class="coreyes" href="https://w3c.github.io/mathml-core/spec.html#dfn-style">style</a></td>
      <td><em>[=string=]</em></td>
      <td><em>none</em></td>
     </tr>

     <tr>
      <td colspan="2" class="attdesc">
       Associates style information with the element for use with
       [[CSS21]].
       See <a href="#world-int-style"></a> for discussion of the interaction
       of MathML and CSS.
      </td>
     </tr>

     <tr>
      <td rowspan="2" class="attname"><span class="coreno">href</span></td>
      <td><a class="intref" href="#type_uri"><em>URI</em></a></td>
      <td><em>none</em></td>
     </tr>

     <tr>
      <td colspan="2" class="attdesc">
	Can be used to establish the element as a hyperlink to the specified <em>URI</em>.
      </td>
     </tr>
    </tbody>
   </table>

   
   <p id="presm_presatt_intent">All MathML presentation elements accept <code
   class="attribute">intent</code> and <code
   class="attribute">arg</code> attributes to support specifying
   <q>intent</q>. These are more fully described in
   [[[#mixing_intent]]].</p>
   <table class="attributes data">
 
    <thead>
 
     <tr>
      <th>Name</th>
      <th>values</th>
      <th>default</th>
     </tr>
    </thead>
 
    <tbody>
 
     <tr>
      <td rowspan="2" class="attname"><a class="coreyes" href="#parsing_rnc_core">intent</a></td>
      <td><a class="intref" href="#mixing_intent_grammar"><em>intent expression</em></a></td>
      <td><em>none</em></td>
     </tr>
     <tr>
      <td colspan="2" class="attdesc">The <code
      class="attribute">intent</code> attribute is more fully described
      in <a href="#mixing_intent"></a>. It may be used on presentation
      elements to give information about the intended meaning of the
      expression, mainly for guiding audio or braille accessible
      renderings.</td>
     </tr>
     <tr>
      <td rowspan="2" class="attname"><a class="coreyes" href="#parsing_rnc_core">arg</a></td>
      <td><a class="intref" href="#mixing_intent_grammar"><em>name</em></a></td>
      <td><em>none</em></td>
     </tr>
     <tr>
      <td colspan="2" class="attdesc">The <code
      class="attribute">arg</code> attribute is more fully described
      in <a href="#mixing_intent"></a>. It may be used to name an element to be referenced from an
      <code class="attribute">intent</code> expression on an ancestor element.</td>
     </tr>
    </tbody>
   </table>



   <p>See also <a href="#presm_commatt"></a> for a list of MathML attributes
   which can be used on most presentation token elements.
   </p>

  </section>

  <section>
   <h4 id="fund_collapse">Collapsing Whitespace in Input</h4>

   <p>In MathML, as in XML, <q>whitespace</q> means simple spaces,
   tabs, newlines, or carriage returns, i.e.,  characters with hexadecimal
   Unicode codes U+0020, U+0009, U+000A, or
   U+000D, respectively; see also the discussion of whitespace in Section 2.3 of
   [[XML]].</p>

   <p>MathML ignores whitespace occurring outside token elements.
   Non-whitespace characters are not allowed there. Whitespace occurring
   within the content of token elements, except for <a class="intref" href="#contm_cs"><code class="starttag">&lt;cs&gt;</code></a>, is normalized as follows. All whitespace at the beginning and end of the content is
   removed, and whitespace internal to content of the element is
   collapsed canonically, i.e.,  each sequence of 1 or more
   whitespace characters is replaced with one space character (U+0020, sometimes
   called a blank character).</p>

   <p>For example, <code>&lt;mo&gt; ( &lt;/mo&gt;</code> is equivalent to
   <code>&lt;mo&gt;(&lt;/mo&gt;</code>, and</p>

   <div class="example mathml mmlcore">
    <pre>
      &lt;mtext&gt;
     Theorem
     1:
      &lt;/mtext&gt;
    </pre>
   </div>
   <p>is equivalent to
   <code>&lt;mtext&gt;Theorem 1:&lt;/mtext&gt;</code>
   or
   <code>&lt;mtext&gt;Theorem&amp;#x20;1:&lt;/mtext&gt;</code>.</p>

   <p>Authors wishing to encode white space characters at the start or end of
   the content of a token, or in sequences other than a single space, without
   having them ignored, must use non-breaking space U+00A0 (or <code class="entity">nbsp</code>)
   or other non-marking characters that are not trimmed.
   For example, compare the above use of an <code class="element">mtext</code> element
   with</p>

   <div class="example mathml mmlcore">
    <pre>
      &lt;mtext&gt;
     &amp;#x00A0;&lt;!--nbsp--&gt;Theorem &amp;#x00A0;&lt;!--nbsp--&gt;1:
      &lt;/mtext&gt; </pre>
   </div>

   <p>When the first example is rendered, there is nothing before
   <q>Theorem</q>, one Unicode space character between <q>Theorem</q> and
   <q>1:</q>, and nothing after <q>1:</q>. In the
   second example, a single space character is to be rendered before
   <q>Theorem</q>; two spaces, one a Unicode space character and
   one a Unicode no-break space character, are to be rendered before
   <q>1:</q>; and there is nothing after the
   <q>1:</q>.</p>

   <p>Note that the value of the <code class="attribute">xml:space</code> attribute is not relevant
   in this situation since XML processors pass whitespace in tokens to a
   MathML processor; it is the requirements of MathML processing which specify that
   whitespace is trimmed and collapsed.</p>

   <p>For whitespace occurring outside the content of the token elements
   <code class="element">mi</code>, <code class="element">mn</code>, <code class="element">mo</code>, <code class="element">ms</code>, <code class="element">mtext</code>,
   <code class="element">ci</code>, <code class="element">cn</code>, <code class="element">cs</code>, <code class="element">csymbol</code> and <code class="element">annotation</code>,
   an <code class="element">mspace</code> element should be used, as opposed to an <code class="element">mtext</code> element containing
   only whitespace entities.</p>

  </section>

 </section>

 <section>
  <h3 id="interf_toplevel">The Top-Level
  <code class="defn starttag">&lt;math&gt;</code> Element</h3>

  <p>MathML specifies a single top-level or root <code class="element">math</code> element,
  which encapsulates each instance of
  MathML markup within a document.  All other MathML content must be
  contained in a <code class="element">math</code> element; in other words,
  every valid MathML expression is wrapped in outer
  <code class="starttag">&lt;math&gt;</code> tags. The <code class="element">math</code>
  element must always be the outermost element in a MathML expression;
  it is an error for one <code class="element">math</code> element to contain
  another.  These considerations also apply when sub-expressions are
  passed between applications, such as for cut-and-paste operations;
  see <a href="#world-int-transfers"></a>.</p>

  <p>The <code class="element">math</code> element can contain an arbitrary number
  of child elements. They render by default as if they
  were contained in an <code class="element">mrow</code> element.</p>

  <section>
   <h4 id="interf_toplevel_atts">Attributes</h4>

   <p>The <code class="element">math</code> element accepts any of the attributes that can be set on
   <a href="#presm_mstyle"></a>, including the common attributes
   specified in <a href="#fund_globatt"></a>.
   In particular, it accepts the <code class="attribute">dir</code> attribute for
   setting the overall directionality; the <code class="element">math</code> element is usually
   the most useful place to specify the directionality
   (see <a href="#presm_bidi"></a> for further discussion).
   Note that the <code class="attribute">dir</code> attribute defaults to <code class="attributevalue">ltr</code>
   on the <code class="element">math</code> element (but <em>inherits</em> on all other elements
   which accept the <code class="attribute">dir</code> attribute); this provides for backward
   compatibility with MathML 2.0 which had no notion of directionality.
   Also, it accepts the <code class="attribute">mathbackground</code> attribute in the same sense
   as <code class="element">mstyle</code> and other presentation elements to set the background
   color of the bounding box, rather than specifying a default for the attribute
   (see <a href="#presm_presatt"></a>).</p>

   <p>In addition to those attributes, the <code class="element">math</code> element accepts:</p>

   <table class="attributes data">

    <thead>

     <tr>
      <th>Name</th>
      <th>values</th>
      <th>default</th>
     </tr>
    </thead>

    <tbody>

     <tr>
      <td rowspan="2" class="attname"><a class="coreyes" href="https://w3c.github.io/mathml-core/spec.html#dfn-display">display</a></td>
      <td>"block" | "inline"</td>
      <td>inline</td>
     </tr>

     <tr>
      <td colspan="2" class="attdesc">
       specifies whether the enclosed MathML expression should be rendered
       as a separate vertical block (in display style)
       or inline, aligned with adjacent text.
       When <code class="attribute">display</code>=<code class="attributevalue">block</code>, <code class="attribute">displaystyle</code> is initialized
       to <code class="attributevalue">true</code>,
       whereas when <code class="attribute">display</code>=<code class="attributevalue">inline</code>, <code class="attribute">displaystyle</code>
       is initialized to <code class="attributevalue">false</code>;
       in both cases <code class="attribute">scriptlevel</code> is initialized to 0
       (see <a href="#presm_scriptlevel"></a>).
       Moreover, when the math element is embedded in a larger document,
       a block math element should be treated as a block element as appropriate
       for the document type (typically as a new vertical block),
       whereas an inline math element should be treated as inline
       (typically exactly as if it were a sequence of words in normal text).
       In particular, this applies to spacing and linebreaking: for instance,
       there should not be spaces or line breaks inserted between inline math
       and any immediately following punctuation.
       When the display attribute is missing, a rendering agent is free to initialize
       as appropriate to the context.
      </td>
     </tr>

     <tr>
      <td rowspan="2" class="attname"><span class="coreno">maxwidth</span></td>
      <td><a class="intref" href="#type_length"><em>length</em></a></td>
      <td><em>available width</em></td>
     </tr>

     <tr>
      <td colspan="2" class="attdesc">
       specifies the maximum width to be used for linebreaking.
       The default is the maximum width available in the surrounding environment.
       If that value cannot be determined, the renderer should assume an infinite rendering
       width.
      </td>
     </tr>

     <tr>
      <td rowspan="2" class="attname"><span class="coreno">overflow</span></td>
      <td>"linebreak" | "scroll" | "elide" | "truncate" | "scale"</td>
      <td>linebreak</td>
     </tr>

     <tr>
      <td colspan="2" class="attdesc">
       specifies the preferred handing in cases where an expression is too long to
       fit in the allowed width. See the discussion below.
      </td>
     </tr>

     <tr>
      <td rowspan="2" class="attname"><span class="coreno">altimg</span></td>
      <td><a class="intref" href="#type_uri"><em>URI</em></a></td>
      <td><em>none</em></td>
     </tr>

     <tr>
      <td colspan="2" class="attdesc">
       provides a URI referring to an image to display as a fall-back
       for user agents that do not support embedded MathML.
      </td>
     </tr>

     <tr>
      <td rowspan="2" class="attname"><span class="coreno">altimg-width</span></td>
      <td><a class="intref" href="#type_length"><em>length</em></a></td>
      <td><em>width of </em><code class="attribute">altimg</code></td>
     </tr>

     <tr>
      <td colspan="2" class="attdesc">
       specifies the width to display <code class="attribute">altimg</code>, scaling the image if necessary;
       see <code class="attribute">altimg-height</code>.
      </td>
     </tr>

     <tr>
      <td rowspan="2" class="attname"><span class="coreno">altimg-height</span></td>
      <td><a class="intref" href="#type_length"><em>length</em></a></td>
      <td><em>height of </em><code class="attribute">altimg</code></td>
     </tr>

     <tr>
      <td colspan="2" class="attdesc">
       specifies the height to display <code class="attribute">altimg</code>, scaling the image if necessary;
       if only one of the attributes <code class="attribute">altimg-width</code> and <code class="attribute">altimg-height</code>
       are given, the scaling should preserve the image's aspect ratio;
       if neither attribute is given, the image should be shown at its natural size.
      </td>
     </tr>

     <tr>
      <td rowspan="2" class="attname"><span class="coreno">altimg-valign</span></td>
      <td><a class="intref" href="#type_length"><em>length</em></a>
      | "top" | "middle" | "bottom" </td>
      <td>0ex</td>
     </tr>

     <tr>
      <td colspan="2" class="attdesc">
       specifies the vertical alignment of the image with respect to adjacent inline material.
       A positive value of <code class="attribute">altimg-valign</code> shifts the bottom of the image above the
       current baseline, while a negative value lowers it.
       The keyword "top" aligns the top of the image with the top of adjacent inline material;
       "center" aligns the middle of the image to the middle of adjacent material;
       "bottom" aligns the bottom of the image to the bottom of adjacent material
       (not necessarily the baseline). This attribute only has effect
       when <code class="attribute">display</code>=<code class="attributevalue">inline</code>.
       By default, the bottom of the image aligns to the baseline.
      </td>
     </tr>

     <tr>
      <td rowspan="2" class="attname"><a class="coreyes" href="#parsing_rnc_core">alttext</a></td>
      <td><em>[=string=]</em></td>
      <td><em>none</em></td>
     </tr>

     <tr>
      <td colspan="2" class="attdesc">
       provides a textual alternative as a fall-back for user agents
       that do not support embedded MathML or images.
      </td>
     </tr>

     <tr>
      <td rowspan="2" class="attname"><span class="coreno">cdgroup</span></td>
      <td><a class="intref" href="#type_uri"><em>URI</em></a></td>
      <td><em>none</em></td>
     </tr>

     <tr>
      <td colspan="2" class="attdesc">
       specifies a CD group file that acts as a catalogue of CD bases for locating
       OpenMath content dictionaries of <code class="element">csymbol</code>, <code class="element">annotation</code>, and
       <code class="element">annotation-xml</code> elements in this <code class="element">math</code> element; see <a href="#contm_csymbol_sec"></a>. When no <code class="attribute">cdgroup</code> attribute is explicitly specified, the
       document format embedding this <code class="element">math</code> element may provide a method for determining
       CD bases. Otherwise the system must determine a CD base; in the absence of specific
       information <code>http://www.openmath.org/cd</code> is assumed as the CD base for all
       <code class="element">csymbol</code>, <code class="element">annotation</code>, and <code class="element">annotation-xml</code> elements.  This is the
       CD base for the collection of standard CDs maintained by the OpenMath Society.
      </td>
     </tr>
    </tbody>
   </table>

   <p>In cases where size negotiation is not possible or fails
   (for example in the case of an expression that is too long to fit in the allowed width),
   the <code class="attribute">overflow</code> attribute is provided to suggest a processing method to the renderer.
   Allowed values are:</p>

   <table id="fund_table-overflow" class="data">
    <thead>
     <tr>
      <th> Value   </th>
      <th> Meaning</th>
     </tr>
    </thead>

    <tbody>

     <tr>
      <td>"linebreak"</td>
      <td>The expression will be broken across several lines.
      See <a href="#presm_linebreaking"></a> for further discussion.
       <span class="coreno"></span>
      </td>
     </tr>

     <tr>

      <td>"scroll"</td>
      <td>The window provides a viewport
      into the larger complete display of the mathematical
      expression. Horizontal or vertical scroll bars are added to the window
      as necessary to allow the viewport to be moved to a different
	position.
       <span class="coreno"></span>
      </td>
     </tr>

     <tr>
      <td>"elide"</td>
      <td>The display is abbreviated by removing enough of it so that
      the remainder fits into the window. For example, a large polynomial
      might have the first and last terms displayed with <q>+ ... +</q>
      between
      them. Advanced renderers may provide a facility to zoom in on elided
      areas.
       <span class="coreno"></span>
      </td>
     </tr>

     <tr>
      <td>"truncate"</td>
      <td>The display is abbreviated by simply truncating it at the right and
      bottom borders. It is recommended that some indication of truncation is
	made to the viewer.
       <span class="coreno"></span>
      </td>
     </tr>

     <tr>
      <td>"scale"</td>
      <td>The fonts used to display the mathematical expression are
      chosen so that the full expression fits in the window. Note that this
      only happens if the expression is too large. In the case of a window
      larger than necessary, the expression is shown at its normal size
	within the larger window.
       <span class="coreno"></span>
      </td>
     </tr>
    </tbody>
   </table>

  </section>

 </section>



</section>