Welcome to UnicodeMathML

UnicodeMath is a linear representation of math that often resembles math notation and is easy to enter. For example, a/b is UnicodeMath for $\frac{a}{b}.$ It works well in Microsoft desktop apps such as Word, PowerPoint, Outlook, and OneNote but it hasn't been widely available elsewhere. This open-source applet implements UnicodeMath on the web.

1. Entering equations

You can enter equations in five ways:

1. Enter UnicodeMath into the input (upper-left) window. The corresponding 2D built-up math displays in the output (upper-right) window and the MathML for it displays below the output window.
2. Enter Nemeth braille, [La]TeX, or MathML into the input window. If the input window starts with a Unicode braille character (U+2800..U+28FF), Nemeth ASCII braille input is enabled. If the input starts with $, $$, \(, or \[, LaTeX input is enabled. If it starts with <math, MathML input is enabled.
3. Enter UnicodeMath directly into the output window. This option builds up what you enter automatically, similarly to entry in the Microsoft Office apps. This option is a work in progress.
4. Click on the Dictate button or type Alt+d, wait for the bell, and dictate the equation in English. You need to have Internet access, and you need to enunciate clearly. This option is also a work in progress but if you get it to work it’s the fastest entry method except for:
5. Paste MathML into the input or output window.

The control-word dictionary includes some control-word aliases, such as \union for \cup (∪), since you might not guess \cup is the LaTeX control word for the union operator ∪.

Unicode has almost all math symbols in use today. The symbol galleries located at the bottom of the web page contain the most common math symbols. You can enter a symbol in a gallery by clicking on it or by typing its control word as described in the Entering symbols section above.

Hovering over a symbol displays a tooltip with information about the symbol, specifically the Unicode code point, name, and block, as well as a LaTeX control word for entering the symbol, the symbol's math class, and the Nemeth braille sequence (if defined). The symbol's Unicode category is defined in Table 4-4 of the Unicode Standard and the symbol's math class is defined in the comments of MathClass.txt, a file for Unicode Technical Report #25: Unicode Support for Mathematics. For example, hovering a script X (𝒳) displays

Here the category "Lu" stands for upper-case letter and the math class "A" stands for alphabetic.

13. Output window editing

You can enter equations and edit the built-up display in the output window as shown in this video

This "in-place" editing mimics the math editing experience in desktop Microsoft Word, Outlook, PowerPoint, and OneNote, and in the Windows Calculator. The hot keys listed above work here too, as do the symbol galleries and the math autocomplete menus. The copy hot key, Ctrl+c, copies the MathML for the selected content into the plain-text copy slot, rather than copying the underlying plain text. This enables you to paste built-up math equations into Word and other apps that interpret "plain-text" MathML as MathML rather than as plain text. Note: math autobuildup works with native MathML rendering; if MathJax is active, only Ctrl+c works.

The implementation uses JavaScript to manipulate the MathML in the browser DOM.

14. Intents

UnicodeMathML generates Presentation MathML 4. A key addition in MathML 4 is the intent attribute, which allows authors to disambiguate math notation and control math speech.

For example, does |𝑥| mean the absolute value of 𝑥 or the cardinality of 𝑥? Absolute value is assumed by default since absolute value is more common than cardinality. The default MathML for |x| is

<mrow intent="absolute-value(𝑥)">
  <mo>|</mo><mi>𝑥</mi><mo>|</mo></mrow>.

To specify cardinality, enter \card(x) (or ⓒ(x)). These inputs produce the MathML

<mrow intent="cardinality(𝑥)">
  <mo>|</mo><mi>𝑥</mi><mo>|</mo></mrow>.

If you enter an absolute value or cardinality containing more than one symbol as in |a+b|, the MathML intent contains an argument reference $a. For |a+b|, the MathML is

<mrow intent="absolute-value($a)">
  <mo>|</mo>
    <mrow arg="a">
      <mi>𝑎</mi><mo>+</mo><mi>𝑏</mi></mrow>
  <mo>|</mo></mrow>

A matrix enclosed in vertical bars is treated as a determinant. For example, the UnicodeMath |■(a&b@c&d)| builds up to

$$\left|\begin{array}{cc}𝑎& 𝑏\\ 𝑐& 𝑑\end{array}\right|$$

which has the MathML

<mrow intent="determinant($a)">
  <mo>|</mo>
    <mtable arg="a">
      <mtr>
        <mtd><mi>𝑎</mi></mtd><mtd><mi>𝑏</mi></mtd></mtr>
      <mtr><mtd><mi>𝑐</mi></mtd><mtd><mi>𝑑</mi></mtd></mtr></mtable>
  <mo>|</mo></mrow>.

The program infers intent attributes for absolute value and determinant, so only cardinality needs to be input without vertical bars. Note that the ambiguous expression |𝑎|𝑏+𝑐|𝑑| is assumed to be (|𝑎|)𝑏+𝑐(|𝑑|). If you want |𝑎(|𝑏+𝑐|)𝑑|, enter |(𝑎|𝑏+𝑐|𝑑)| and the parentheses will be removed.

As we see here, some intent attribute values are implied by the input notations of LaTeX and UnicodeMath. Others are implied by context. Still others must be declared explicitly by the content author, by a math-knowledgeable copy editor, or maybe eventually by AI.

15. Author intents

Since most content authors don’t know MathML, we need a way to allow them to enter intents easily. To this end, UnicodeMathML has an output-window context-menu option that lets you tag entities with intents. For example, right-clicking on the 𝐸 in 𝐸 = 𝑚𝑐², you get the input box

and you can type in “energy” or whatever you want followed by the Enter key. If you type in “energy”, the resulting MathML is

<mrow>
  <mi intent="energy">𝐸</mi>
  <mo>=</mo>
  <mrow>
    <mi>𝑚</mi>
    <msup><mi>𝑐</mi>
    <mn>2</mn></msup></mrow></mrow>

Typing Atl+d speaks this as "energy equals m c squared".

16. TeX macros

You can use [La]TeX macros with [La]TeX input. Simple examples are:

The last equation in the Examples gallery is LaTeX that defines a macro and then uses it:

\[\def\g#1#2{#1f(#2)}\g\relax{x}=\int_{-\infty}^\infty \g\hat\xi,e^{2 \pi i \xi x} ,d\xi\]

This displays as

$$𝑓\left(𝑥\right)={\int }_{-\infty }^{\infty }\widehat{𝑓}\left(𝜉\right){𝑒}^{2𝜋𝑖𝜉𝑥}𝑑𝜉$$

The LaTeX \newcommand syntax is also supported.

17. UnicodeMath selection attributes

Technical stuff: When you edit the output window, the resulting MathML includes attributes that represent the state of the user selection. These attributes have been added partly because they are needed to make editing accessible. The attribute "selanchor" defines the selection "anchor" end (the nonmoving end) and "selfocus" defines the selection active end, e.g., the end that moves with Shift+→. The attribute values define the offsets for the selection setBaseAndExtent method. If the selection is an insertion point (a degenerate selection), only selanchor is included since the anchor and focus ends coincide.

Corresponding constructs have been added to UnicodeMath to represent the selection state. They are needed for the multilevel undo facility, which saves back states by caching the back-state UnicodeMath strings. The enclosure Ⓐ(offset) defines the position of the selection anchor and the enclosure Ⓕ(offset) defines the position of the selection focus. If no offset appears, 0 is assumed. To increase readability, these enclosures are not included in the UnicodeMath displayed in the input window. Nondegenerate selections have the focus enclosure as well, as in the UnicodeMath "Ⓐ()Ⓕ(1)⬚" for the selected "⬚".

A negative offset is used if the selection construct refers to a text node. The absolute value of a negative offset gives the offset into a string. For example, <mi selanchor="-1">sin</mi> sets the anchor to the "i" in "sin". Positive attribute values give the index of a child element. So, <mi selanchor="1">sin</mi> places the anchor immediately following "sin".

To facilitate entering Unicode symbols, control words can be used as discussed in Sec. 3. The following is a table of control words for Unicode math symbols not including the math alphanumerics discussed in Sec. 4. For a more complete list, see unimath-symbols. Circled and parenthesized symbols index the Examples in the Playground. E.g., \Faraday gives ⑭, which inserts the fourteenth Example: 𝛁⨯𝐄=−𝜕𝐁/𝜕𝑡. Circled letters are special UnicodeMath operators that build up to bracketed matrices, fractions, absolute values, cardinality, cases, binomial coefficients, etc.