MathML Presentation Markup for the Impatient

Hussein Shafie

XMLmind Software

This article is published under the Creative Commons "Attribution-Share Alike" license.

May 23, 2017


Table of Contents

1. Basic elements
2. More basic elements
2.1. The math top-level element
2.2. Plain text
2.3. Explicit space between elements
3. Fractions
4. Radicals
5. Subscripts and superscripts
6. Underscripts and overscripts
7. The ubiquitous mo element
8. Matrices
9. Equations
10. Other, less useful, elements

MathML comprises two sets of elements: Presentation Markup, the XML equivalent of TeX math, and Content Markup, which may be used to encode the mathematical structure of an expression, regardless of the way this expression is rendered visually. This short tutorial is exclusively about Presentation Markup. After reading it, you should be able to add equations to your DocBook, DITA or XHTML documents.

1. Basic elements

MathML most basic elements are mrow, mi, mo and mn. Example: is encoded in MathML as:

<mrow>
  <mrow>
    <mi>x</mi>
    <mo>+</mo>
    <mi>y</mi>
  </mrow>
  <mo>=</mo>
  <mn>2</mn>
</mrow>
mrow

Use this element to group any number of subexpressions horizontally.

mi

Use this element to specify an identifier, that is, the name of a variable, a constant, a function, etc.

If this name is just one character long, the identifier is automatically rendered using an italic font, otherwise the name is rendered using a normal, upright, font.

mo

Use this element to specify an operator (e.g. '+'), a fence (e.g. '{') or a separator (e.g. ',').

The appropriate amount of space is added on the left and on the right of an mo depending on the textual contents of this element. Example: if in the above expression you replace <mo>+</mo> by <mo>,</mo>, this will suppress the space at the left of the mo element.

mn

Use this element to specify a numeric literal.

For example, PI should be specified as <mi>PI</mi> and not as <mn>PI</mn> while 3.14 should be specified as <mn>3.14</mn> and not as <mi>3.14</mi>.

Important

It is really important to use mi, mo and mn appropriately because otherwise the MathML rendering engine will not be able to apply its built-in typographic rules.

2. More basic elements

2.1. The math top-level element

The above MathML expression cannot be inserted as is in a DocBook, DITA or XHTML document because the mrow element should be enclosed in a math element. The math element is the root of all MathML expressions.

<math xmlns="http://www.w3.org/1998/Math/MathML"1
      display="inline">2
  <mrow>
    <mrow>
      <mi>x</mi>
      <mo>+</mo>
      <mi>y</mi>
    </mrow>
    <mo>=</mo>xml
    <mn>2</mn>
  </mrow>
</math>

1

The namespace of all MathML elements is "http://www.w3.org/1998/Math/MathML". Specifying such namespace is mandatory but it will be omitted in this tutorial for brevity.

2

Note the display="inline" attribute which specifies that the math element is to be displayed inline (``like a word in a paragraph''). The other value is display="block" which specifies that the math element is to be displayed as a block (``like a paragraph''). This attribute has an influence on the typographic rules applied by the MathML rendering engine.

2.2. Plain text

We have already recommended to be very precise in the use of mi, mo and mn when tagging some text. But what if you just want to type plain text? Here enters the mtext element, which with mi, mo, mn and ms are the only MathML elements which may contain text. All the other MathML elements (math, mrow, mfrac, msqrt, etc) may only contain child elements.

Example:

is encoded in MathML as:

<mrow>
  <mtext>if</mtext>
  <mspace depth="0.5ex" height="0.5ex" width="1ex"/>
  <mrow>
    <mi>x</mi>
    <mo>=</mo>
    <mi>y</mi>
  </mrow>
  <mspace depth="0.5ex" height="0.5ex" width="1ex"/>
  <mtext>then</mtext>
  <mspace depth="0.5ex" height="0.5ex" width="1ex"/>
  <mrow>
    <mrow>
      <mi>a</mi>
      <mi>x</mi>
    </mrow>
    <mo>=</mo>
    <mrow>
      <mi>a</mi>
      <mi>y</mi>
    </mrow>
  </mrow>
</mrow>

2.3. Explicit space between elements

If in the above example, you want to add some space after word "if", do not attempt to insert one or more whitespace characters in the corresponding mtext element (e.g. <mtext>if    </mtext>). Doing so is useless because, leading and trailing whitespace characters are automatically removed from mi, mo, mn, and mtext by the MathML processor. Instead, you need to insert an mspace element in your MathML expression. Note that due to the built-in typographic rules, doing so is just occasionally needed.

width

This optional attribute specifies the overall width of the mspace element.

height

This optional attribute specifies the overall height above the baseline.

depth

This optional attribute specifies the overall height below the baseline.

The value of these attributes is a number followed by one of the following units: em, ex, px, in, cm, mm, pt, pc.

3. Fractions

Fractions are specified using the mfrac element. Example:

<mfrac>
  <mrow>
    <mi>x</mi>
    <mo>-</mo>
    <mn>1</mn>
  </mrow>
  <mn>100</mn>
</mfrac>

First child element is the numerator of the fraction. Second child element is its denominator.

Attribute bevelled="true" may be used to change the style of the fraction. Example: .

4. Radicals

MathML has two elements allowing to specify radicals:

msqrt

Use this element to specify a square root. Example:

<msqrt>
  <mi>x</mi>
  <mo>+</mo>
  <mi>y</mi>
</msqrt>

Note that, like a number of other MathML elements (mstyle, merror, menclose, mpadded, mphantom, mtd and math), msqrt may have one or more child elements. Below the radical sign, msqrt behaves as if it had an implicit mrow element grouping all its child elements.

mroot

Use this element to specify a radical with an arbitrary index. Example:

<mroot>
  <mi>x</mi>
  <mn>3</mn>
</mroot>

Unlike msqrt, mroot may only have two child elements. First child element is the base of the root. Second child element is its index. If you need more that one element below the radical sign, then use an explicit mrow element.

5. Subscripts and superscripts

Subscripts and superscripts elements are:

msub

Use this element to attach a subscript to a base. Example:

<msub>
  <mi>x</mi>
  <mi>i</mi>
</msub>
msup

Use this element to attach a superscript to a base. Example:

<msup>
  <mi>x</mi>
  <mi>j</mi>
</msup>
msubsup

Use this element to attach both a subscript and a superscript to a base. Example:

<msubsup>
  <mi>x</mi>
  <mi>i</mi>
  <mi>j</mi>
</msubsup>

Note that for all the above elements, the base is the first child element.

6. Underscripts and overscripts

Underscripts and overscripts are similar to subscripts and superscripts, except that script elements are centered above and/or below the base element.

munder

Use this element to attach a underscript to a base. Example:

<munder>
  <mi>x</mi>
  <mo>&#9472;</mo>
</munder>
mover

Use this element to attach a overscript to a base. Example:

<mover>
  <mi>v</mi>
  <mo>&#8594;</mo>
</mover>
munderover

Use this element to attach both a underscript and a overscript to a base. Example:

<munderover>
  <mi>x</mi>
  <mi>a</mi>
  <mi>b</mi>
</munderover>

7. The ubiquitous mo element

Even after all these explanations, it is probably still not obvious to figure out how to encode in MathML many common constructs such as integrals, limits, etc. The answer is simple: use an mo element containing the right character. This character typically belongs to the "Mathematical Operators" U+2200-U+22FF Unicode range or to the "Arrows" U+2190-U+21FF Unicode range.

Example 1:

<mrow>
  <munderover>
    <mo>&#8747;</mo>
    <mn>-1</mn>
    <mn>+1</mn>
  </munderover>
  <mfrac>
    <mrow>
      <mi>d</mi>
      <mi>x</mi>
    </mrow>
    <mi>x</mi>
  </mfrac>
</mrow>

Example 2:

<mrow>
  <mi>x</mi>
  <munder>
    <mo>&#8594;</mo>
    <mtext>maps to</mtext>
  </munder>
  <mi>y</mi>
</mrow>

Note how the mo element stretches vertically or horizontally when needed to. The amount of stretching is normally automatically determined by the MathML renderer, but it is possible to influence it by specifying the minsize and/or maxsize attributes. Example: <mo minsize="10">&#8594;</mo> means: make the arrow at least 10 times its normal size.

8. Matrices

Matrices are specified using the mtable element which is similar to the simple — no tbody — XHTML table. An mtable table element contains mtr row elements and an mtr element contains mtd cell elements.

Example:

<mrow>
  <mo>[</mo>
  <mtable>
    <mtr>
      <mtd>
        <mn>1</mn>
      </mtd>
      <mtd>
        <mn>0</mn>
      </mtd>
      <mtd>
        <mn>0</mn>
      </mtd>
    </mtr>
    <mtr>
      <mtd>
        <mn>0</mn>
      </mtd>
      <mtd>
        <mn>1</mn>
      </mtd>
      <mtd>
        <mn>0</mn>
      </mtd>
    </mtr>
    <mtr>
      <mtd>
        <mn>0</mn>
      </mtd>
      <mtd>
        <mn>0</mn>
      </mtd>
      <mtd>
        <mn>1</mn>
      </mtd>
    </mtr>
  </mtable>
  <mo>]</mo>
</mrow>

Note that by default, an mtable element has no borders at all. This is why you'll generally need to add an mo containing a fence character (e.g. '[', ']', '(', ')', '|') before and after the mtable when you specify a matrix or the determinant of a matrix.

9. Equations

The MathML mtable element is fairly generic. Use it whenever you need to layout elements in a rectangular grid. This feature is of course useful to specify matrices. It is also useful to specify a set of equations.

Example (how to properly align this set of equations is explained below):

<mrow>
  <mo>{</mo>
  <mtable>
    <mtr>
      <mtd>
        <mrow>
          <mrow>
            <mrow>
              <mn>2</mn>
              <mo>&#8290;</mo>
              <mi>x</mi>
            </mrow>
            <mo>+</mo>
            <mi>y</mi>
          </mrow>
          <mo>=</mo>
          <mn>8</mn>
        </mrow>
      </mtd>
    </mtr>
    <mtr>
      <mtd>
        <mrow>
          <mrow>
            <mi>x</mi>
            <mo>+</mo>
            <mi>y</mi>
          </mrow>
          <mo>=</mo>
          <mn>6</mn>
        </mrow>
      </mtd>
    </mtr>
  </mtable>
</mrow>

Replacing an mtr row element by an mlabeledtr labeled row element allows to use the first mtd cell element of this row as the caption of the equation. Example:

<mtable side="left">
  <mlabeledtr>
    <mtd>
      <mtext>Gauss' law</mtext>
    </mtd>
    <mtd>
      <mrow>
        <mrow>
          <mo>&#8711;</mo>
          <mo>&#8729;</mo>
          <mi mathvariant="normal">E</mi>
        </mrow>
        <mo>=</mo>
        <mfrac>
          <mi>&#961;</mi>
          <msub>
            <mi>&#949;</mi>
            <mn>0</mn>
          </msub>
        </mfrac>
      </mrow>
    </mtd>
  </mlabeledtr>
  <mlabeledtr>
    <mtd>
      <mtext>Gauss's law for magnetism</mtext>
    </mtd>
    <mtd>
      <mrow>
        <mrow>
          <mo>&#8711;</mo>
          <mo>&#8729;</mo>
          <mi mathvariant="normal">B</mi>
        </mrow>
        <mo>=</mo>
        <mn>0</mn>
      </mrow>
    </mtd>
  </mlabeledtr>
</mtable>

Note that without the side="left" attribute, captions are displayed at the right of equations and this, despite the fact that the caption is always specified by the contents of the first mtd child of a mlabeledtr element.

10. Other, less useful, elements

We'll not describe in this tutorial the following, rarely needed, elements: mglyph, mmultiscripts, malignmark, merror, maction. This being said, you may also skip this section if you are really impatient.

ms

Use this element to specify a quoted string literal. Example:

<ms>Hello word!</ms>
mfenced

The mfenced element is a shorthand notation for common forms of mrow. Example:

<mfenced>
  <mi>x</mi>
  <mi>y</mi>
  <mi>z</mi>
</mfenced>

is equivalent to:

<mrow>
  <mo>(</mo>
  <mi>x</mi>
  <mo>,</mo>
  <mi>y</mi>
  <mo>,</mo>
  <mi>z</mi>
  <mo>)</mo>
</mrow>

The open, separators and close attributes of an mfenced element specify the opening fence added before its first child element, the separators added between child elements and the closing fence added after its last child element. By default, the values of these attributes are "(", "," and ")".

menclose

The menclose element allows to draw lines, typically a box, around its child elements. Example:

<menclose notation="box">
  <mi>n</mi>
  <mo>!</mo>
</menclose>

The notation attribute of an menclose element specify which kind of lines are drawn around the child elements. The allowed values for this attribute are: longdiv (default value), actuarial, radical, box, roundedbox, circle, left, right, top, bottom, updiagonalstrike, downdiagonalstrike, verticalstrike, horizontalstrike.

mpadded

The mpadded element allows to add padding, that is extra space, around its child elements. It's an alternative to using mspace. Example:

<mrow>
  <mpadded width="+1ex">
    <mtext>if</mtext>
  </mpadded>
  <mrow>
    <mi>x</mi>
    <mo>=</mo>
    <mi>y</mi>
  </mrow>
  <mpadded lspace="1ex" width="+2ex">
    <mtext>then</mtext>
  </mpadded>
  <mrow>
    <mrow>
      <mi>a</mi>
      <mi>x</mi>
    </mrow>
    <mo>=</mo>
    <mrow>
      <mi>a</mi>
      <mi>y</mi>
    </mrow>
  </mrow>
</mrow>

The attributes allowing to specify the padding are:

width

This optional attribute specifies the overall width of the mpadded element.

The value of this attribute, as well as the values of the height and depth attributes (but not the lspace attribute) described below, may start with a "+" sign which means: add specified amount to the intrinsic size.

lspace

This optional attribute specifies the amount of space added before the first child of the mpadded element.

There is no rspace attribute. The amount of space added after the last child of the mpadded element is: value of the above width attribute - intrinsic width of all the child elements - value of this lspace attribute.

height

This optional attribute specifies the overall height above the baseline.

depth

This optional attribute specifies the overall height below the baseline.

mphantom

The mphantom element transforms its descendant elements into ‘‘phantoms'': they are there, they occupy some space, but you cannot see them. The mphantom element is often the only way to properly align some elements. Example:

<mrow>
  <mfrac>
    <mn>1</mn>
    <msup>
      <mi>x</mi>
      <mphantom>
        <msup>
          <mi>y</mi>
          <mi>z</mi>
        </msup>
      </mphantom>
    </msup>
  </mfrac>
  <mo>+</mo>
  <mfrac>
    <mn>1</mn>
    <msup>
      <mi>x</mi>
      <msup>
        <mi>y</mi>
        <mi>z</mi>
      </msup>
    </msup>
  </mfrac>
</mrow>
mstyle

The mstyle element allows to specify attributes which are intended to be inherited by all its descendant elements. As such, the mstyle element supports all the attributes of all the other MathML elements.

The most commonly used attributes are those used to style the mi, mo, mn and mtext text container elements:

Attribute NameAttribute ValueDefault Value
mathvariantnormal | bold | italic | bold-italic | double-struck | bold-fraktur | script | bold-script | fraktur | sans-serif | bold-sans-serif | sans-serif-italic | sans-serif-bold-italic | monospacenormal (except on mi)
mathsizesmall | normal | big | number v-unitinherited
mathcolor#rgb | #rrggbb | html-color-nameinherited
mathbackground#rgb | #rrggbb | html-color-nameinherited

Example:

<mstyle mathbackground="yellow" mathcolor="navy" mathsize="16pt"
        mathvariant="bold">
  <mrow>
    <mi>x</mi>
    <mo>+</mo>
    <mi>y</mi>
  </mrow>
  <mo>=</mo>
  <mn mathcolor="red">2</mn>
</mstyle>
maligngroup

Use this element to properly align a set of equations. Each inserted maligngroup specifies a ``sub-column'' within the column of an mtable. The groupalign attribute of the mtable element specifies the horizontal alignment within each ``sub-column''. Example:

<mrow>
  <mo>{</mo>
  <mtable groupalign="{right center right center right}">
    <mtr>
      <mtd>
        <mrow>
          <mrow>
            <mrow>
              <maligngroup/>
              <mn>2</mn>
              <mo>&#8290;</mo>
              <mi>x</mi>
            </mrow>
            <maligngroup/>
            <mo>+</mo>
            <maligngroup/>
            <mi>y</mi>
          </mrow>
          <maligngroup/>
          <mo>=</mo>
          <maligngroup/>
          <mn>8</mn>
        </mrow>
      </mtd>
    </mtr>
    <mtr>
      <mtd>
        <mrow>
          <mrow>
            <maligngroup/>
            <mi>x</mi>
            <maligngroup/>
            <mo>+</mo>
            <maligngroup/>
            <mi>y</mi>
          </mrow>
          <maligngroup/>
          <mo>=</mo>
          <maligngroup/>
          <mn>6</mn>
        </mrow>
      </mtd>
    </mtr>
  </mtable>
</mrow>

The value of the groupalign attribute has the following syntax: one "{...}" group per column. A "{...}" group contains one alignment specification per sub-column (that is, per maligngroup). Alignment specifications are: left, center or right.