MathML Core

Abstract

This specification defines a core subset of Mathematical Markup Language, or MathML, that is suitable for browser implementation. MathML is a markup language for describing mathematical notation and capturing both its structure and content. The goal of MathML is to enable mathematics to be served, received, and processed on the World Wide Web, just as HTML has enabled this functionality for text.

The default display property is described in A. User Agent Stylesheet:

For the <math> root, it is equal to inline math or block math according to the value of the display attribute.
For Tabular MathML elements mtable, mtr, mtd it is respectively equal to inline-table, table-row and table-cell.
For all but the first children of the maction and semantics elements, it is equal to none.
For all the other MathML elements it is equal to block math.

In order to specify math layout in different writing modes, this specification uses concepts from [CSS-WRITING-MODES-4]:

Note

Unless specified otherwise, the figures in this specification use a writing mode of horizontal-lr and ltr. See Figure 4, Figure 5 and Figure 6 for examples of other writing modes that are sometimes used for math layout.

Boxes used for MathML elements rely on several parameters in order to perform layout in a way that is compatible with CSS but also to take into account very accurate positions and spacing within math formulas:

Inline metrics. min-content inline size, max-content inline size and inline size from CSS. See Figure 1.

Figure 1 Generic Box Model for MathML elements
Block metrics. The block size, first baseline set and last baseline set. The following baselines are defined for MathML boxes:
1. The alphabetic baseline which typically aligns with the bottom of uppercase Latin glyphs. The algebraic distance from the alphabetic baseline to the line-over edge of the box is called the line-ascent. The algebraic distance from the line-under edge to the alphabetic baseline of the box is called the line-descent.
2. The mathematical baseline, also called math axis, which typically aligns with the fraction bar, middle of fences and binary operators. It is shifted away from the alphabetic baseline by AxisHeight towards the line-over.
3. The ink-over baseline, indicating the line-over theorical limit of the math content drawn, excluding any extra space. If not specified, it is aligned with the line-over edge. The algebraic distance from the alphabetic baseline to the ink-over baseline is called the ink line-ascent.
4. The ink-under baseline, indicating the line-under theorical limit of the math content drawn, excluding any extra space. If not specified, it is aligned with the line-under edge. The algebraic distance from the ink-under baseline to the alphabetic baseline is called the ink line-descent.
Note
For math layout, it is very important to rely on the ink extent when positioning text. This is not the case for more complex notations (e.g. square root). Although ink-ascent and ink-descent are defined for all MathML elements they are really only used for the token elements. In other cases, they just match normal ascent and descent.
Unless specified otherwise, the last baseline set is equal to the first baseline set for MathML boxes.
An optional italic correction which provides a measure of how much the text of a box is slanted along the inline axis. See Figure 2.

Figure 2 Examples of italic correction for italic f and large integral

If it is requested during calculation of min-content inline size and max-content inline size or during layout then 0 is used as a fallback value.
An optional top accent attachment which provides a reference offset on the inline axis of a box that should be used when positioning that box as an accent. See Figure 3.

Figure 3 Example of top accent attachment for a circumflex accent

If it is requested during calculation of min-content inline size (respectively max-content inline size) then half the min-content inline size (respectively max-content inline size) is used as a fallback value. If it is requested during layout then half the inline size of the box is used as a fallback value.

Given a MathML box, the following offsets are defined:

The inline offset of a child box is the offset between the inline-start edge of the parent box and the inline-start edge of the child box.
The block offset of a child box is the offset between the block-start edge of the parent box and the block-start edge of the child box.
The line-left offset of a child box is the offset between the line-left edge of the parent box and the line-left edge of the child box.

Figure 4 Box model for writing mode `horizontal-tb` and `rtl` that may be used in e.g. Arabic math.

Figure 5 Box model for writing mode `vertical-lr` and `ltr` that may be used in e.g. Mongolian math.

Figure 6 Box model for writing mode `vertical-rl` and `ltr` that may be used in e.g. Japanese math.

Note

The position of child boxes and graphical items inside a MathML box are expressed using the inline offset and block offset. For convenience, the layout algorithms may describe offsets using flow-relative directions, line-relative directions or the alphabetic baseline. It is always possible to pass from one description to the other because position of child boxes is always performed after the metrics of the box and of its child boxes are calculated.

Here are examples of offsets obtained from line-relative metrics:

The inline offset of a child box is the line-left offset if the CSS property direction is ltr and is the inline size of the box − (line-left offset + inline size of the child box) otherwise.
The block offset of the alphabetic baseline of a box is the line-ascent if the CSS property writing-mode is horizontal-lr, vertical-rl or sideways-rl and is the line-descent otherwise.

Issue 78: Ink ascent/descent opentype/tex needs-tests

Improve definition of ink ascent/descent?

Each MathML element has an associated math content box, which is calculated as described in this chapter's layout algorithms using the following structure:

Calculation of min-content inline size and max-content inline size of the math content.
Box layout:
1. Layout of in-flow child boxes.
2. Calculation of inline size, ink line-ascent, ink line-descent, line-ascent and line-ascent of the math content.
3. Calculation of offsets of child boxes within the math content box as well as sizes and offsets of extra graphical items (bars, radical symbol, etc).
4. Layout and positioning of absolutely-positioned and fixed-positioned boxes, as described in [CSS-POSITION-3].

The following extra steps must be performed:

After calculating the line-ascent and line-descent of a math content box, its block size is set to their sum.
By default, the box metrics, offsets, baselines, italic correction and top accent attachment of the content box are set to the one calculated for the math content box. However if a different size is specified for the content box (via width, height or related properties), that size is used instead and the inline-start and block-start edges of the math content box are aligned with the ones of the content box, unless otherwise specified in a specific layout algorithm.
The box metrics and offsets of the padding box are obtained from the content box by taking into account the corresponding padding properties as described in CSS.

The baselines of the padding box are the same as the one of the content box.

If the content box has a top accent attachment then the padding box has the same property, increased by the inline-start padding. If the content box has an italic correction then the padding box has the same property, increased by the inline-end padding.
The box metrics and offsets of the border box are obtained from the padding box by taking into account the corresponding border-width property as described in CSS.

In general, the baselines of the border box are the same as the one of the padding box. However, if the line-over border is positive then the ink-over baseline is set to the line-over edge of the border box and if the line-under border is positive then the ink-under baseline is set to the line-under edge of the border box.

If the padding box has a top accent attachment then the border box has the same property, increased by the border-width of its inline-start egde. If the padding box has an italic correction then the border box has the same property, increased by the border-width of its inline-end egde.
The box metrics and offsets of the margin box are obtained from the border box by taking into account the corresponding margin properties as described in CSS.

The baselines of the margin box are the same as the one of the border box.

If the padding box has a top accent attachment then the margin box has the same property, increased by the inline-start margin. If the padding box has an italic correction then the margin box has the same property, increased by the inline-end margin.

Note

Per the description above, margin-collapsing does not apply to MathML elements.

During box layout, optional inline stretch size constraint and block stretch size constraint parameters may be used on embellished operators. The former indicates a target size that a core operator stretched along the inline axis should cover. The latter indicates an ink line-ascent and ink line-descent that a core operator stretched along the block axis should cover. Unless specified otherwise, these parameters are ignored during box layout and child boxes are laid out without any stretch size constraint.

Issue 76: Define what inline percentages resolve against. css/html5 need specification update needs-tests

Define what inline percentages resolve against

Issue 77: Define what block percentages resolve against. css/html5 need specification update needs-tests

Define what block percentages resolve against

An anonymous box is a box without any associated element in the DOM tree and which is generated for layout purpose only. The properties of anonymous boxes are inherited from the enclosing non-anonymous box while non-inherited properties have their initial value. An anonymous <mrow> box is an anonymous box with display equal to block math and which is laid out as described in section 3.3.1.2 Layout of <mrow>.

If a MathML element generates an anonymous <mrow> box then it wraps its children in an anonymous <mrow> box. I.e., its subtree in the visual formatting model is made of an anonymous <mrow> box which itself contains the boxes associated to the children of this MathML element.

In the following example, the math and mrow elements are laid out as described in section 3.3.1.2 Layout of <mrow>. In particular, the <math> element adds proper spacing around its <mo>≠</mo> child and the <mrow> element stretches its <mo>|</mo> children vertically.

The mtd element has display: table-cell and the msqrt element displays a radical symbol around its children. However, they also place their children in a way that is similar to what is described in section 3.3.1.2 Layout of <mrow>: the <msqrt> element adds proper spacing around its <mo>+</mo> child while the <mtd> element stretches its <mo> children vertically. In order to make this possible, each of these two elements generates an anonymous <mrow> box.

<math>   <mrow>     <mo>|</mo>     <mtable>       <mtr>         <mtd>           <mi>x</mi>         </mtd>         <mtd>           <mo>(</mo>           <mfrac linethickness="0">             <mn>5</mn>             <mn>3</mn>           </mfrac>           <mo>)</mo>         </mtd>       </mtr>       <mtr>         <mtd>           <msqrt>             <mn>7</mn>             <mo>+</mo>             <mn>2</mn>           </msqrt>         </mtd>         <mtd>           <mi>y</mi>         </mtd>       </mtr>     </mtable>     <mo>|</mo>   </mrow>   <mo>≠</mo>   <mn>0</mn> </math>

MathML elements can overlap due to various spacing rules. They can as well contain extra graphical items (bars, radical symbol, etc). A MathML element with computed style display: block math or display: inline math generates a new stacking context. The painting order of in-flow children of such a MathML element is exactly the same as block elements. The extra graphical items are painted after text and background (right after step 7.2.4 for display: inline math and right after step 7.2 for display: block math).

Token elements in presentation markup are broadly intended to represent the smallest units of mathematical notation which carry meaning. Tokens are roughly analogous to words in text. However, because of the precise, symbolic nature of mathematical notation, the various categories and properties of token elements figure prominently in MathML markup. By contrast, in textual data, individual words rarely need to be marked up or styled specially.

Note

In practice, most MathML token elements just contain simple text for variables, numbers, operators etc and don't need sophisticated layout. However, it can contain text with line breaks or arbitrary HTML5 phrasing elements.

The mtext element is used to represent arbitrary text that should be rendered as itself. In general, the <mtext> element is intended to denote commentary text.

The <mtext> element accepts the attributes described in 2.1.3 Global Attributes.

In the following example, mtext is used to put conditional words in a definition:

<math>   <mi>y</mi>   <mo>=</mo>   <mrow>     <msup>       <mi>x</mi>       <mn>2</mn>     </msup>     <mtext>&nbsp;if&nbsp;</mtext>     <mrow>       <mi>x</mi>       <mo>≥</mo>       <mn>1</mn>     </mrow>     <mtext>&nbsp;and&nbsp;</mtext>     <mn>2</mn>     <mtext>&nbsp;otherwise.</mtext>   </mrow> </math>

If the element does not have its computed display property equal to block math or inline math then it is laid out according to the CSS specification where the corresponding value is described. Otherwise, the layout below is performed.

If the <mtext> element contains only text content without forced line break or soft wrap opportunity then, the anonymous child node generated for that text is laid out as defined in the relevant CSS specification and:

The min-content inline size, max-content inline size and inline size of the math content box are equal to the one of the anonymous child.
The ink line-ascent and ink line-descent of the math content box are set so that its ink-over baseline, ink-under baseline and alphabetic baseline match the one of the ink bounding box of the text.
The line-ascent (respectively line-descent) of the math content box is set to the ink line-ascent (respectively ink line-descent).
If the text content is made of a single glyph and this glyph has an entry in the MathItalicsCorrectionInfo table then the specified value is used as the italic correction.
If the text content is made of a single glyph and this glyph has an entry in the MathTopAccentAttachment table then the specified value is used as the top accent attachment of the <mtext> element.

Otherwise, the mtext element is laid out as a block box and corresponding min-content inline size, max-content inline size, inline size, block size, first baseline set and last baseline set are used for the math content box.

The mi element represents a symbolic name or arbitrary text that should be rendered as an identifier. Identifiers can include variables, function names, and symbolic constants.

The <mi> element accepts the attributes described in 2.1.3 Global Attributes as well as the following attribute:

mathvariant

The layout algorithm is the same as the mtext element. The user agent stylesheet must contain the following property in order to implement automatic italic via the text-transform value introduced in 4.2 The math-auto transform:

mi {   text-transform: math-auto; }

The mathvariant attribute, if present, must be an ASCII case-insensitive match of normal. In that case, the user agent is expected to treat the attribute as a presentational hint setting the element's text-transform property to none. Otherwise it has no effects.

Note

In [MathML3], the mathvariant attribute was used to define logical classes of token elements, each class providing a collection of typographically-related symbolic tokens with specific meaning within a given mathematical expression.

In MathML Core, this attribute is only used to cancel automatic italic of the mi element. For other use cases, the proper Mathematical Alphanumeric Symbols [UNICODE] should be used instead. See also section C. Mathematical Alphanumeric Symbols.

In the following example, mi is used to render variables and function names. Note that per 4.2 The math-auto transform the default style text-transform: math-auto has no effect on the first <mi> ("cos" is made of three characters), makes the second <mi> render as math italic ("c" is made of a single character U+0063 Latin Small Letter C which is mapped to U+1D450 Mathematical Italic Small C per the italic table), has no effect on the third <mi> (overridden by mathvariant="normal", setting text-transform to none) or on the fourth <mi> (no mapping defined for U+221E Infinity in the italic table).

<math>   <mi>cos</mi>   <mo>,</mo>   <mi>c</mi>   <mo>,</mo>   <mi mathvariant="normal">c</mi>   <mo>,</mo>   <mi>∞</mi> </math>

The mn element represents a "numeric literal" or other data that should be rendered as a numeric literal. Generally speaking, a numeric literal is a sequence of digits, perhaps including a decimal point, representing an unsigned integer or real number.

The <mn> element accepts the attributes described in 2.1.3 Global Attributes. Its layout algorithm is the same as the mtext element.

In the following example, mn is used to write a decimal number.

<math>   <mn>3.141592653589793</mn> </math>

The mo element represents an operator or anything that should be rendered as an operator. In general, the notational conventions for mathematical operators are quite complicated, and therefore MathML provides a relatively sophisticated mechanism for specifying the rendering behavior of an <mo> element.

As a consequence, in MathML the list of things that should "render as an operator" includes a number of notations that are not mathematical operators in the ordinary sense. Besides ordinary operators with infix, prefix, or postfix forms, these include fence characters such as braces, parentheses, and "absolute value" bars; separators such as comma and semicolon; and mathematical accents such as a bar or tilde over a symbol. This chapter uses the term "operator" to refer to operators in this broad sense.

The <mo> element accepts the attributes described in 2.1.3 Global Attributes as well as the following attributes:

This specification does not define any observable behavior that is specific to the fence and separator attributes.

Note

Authors may use the fence and separator to describe specific semantics of operators. The default values may be determined from the Operators_fence and Operators_separator tables, or equivalently the human-readable version of the operator dictionary.

In the following example, the mo element is used for the binary operator +. Default spacing is symmetric around that operator. A tighter spacing is used if you rely on the form attribute to force it to be treated as a prefix operator. Spacing can also be specified explicitly using the lspace and rspace attributes.

<math>   <mn>1</mn>   <mo>+</mo>   <mn>2</mn>   <mo form="prefix">+</mo>   <mn>3</mn>   <mo lspace="2em">+</mo>   <mn>4</mn>   <mo rspace="3em">+</mo>   <mn>5</mn> </math>

Another use case is for big operators such as summation. When displaystyle is true, such an operator is drawn larger but one can change that with the largeop attribute. When displaystyle is false, underscripts are actually rendered as subscripts but one can change that with the movablelimits attribute.

<math>   <mrow displaystyle="true">   <munder>     <mo>∑</mo>     <mn>5</mn>   </munder>   <munder>     <mo largeop="false">∑</mo>     <mn>6</mn>   </munder>   </mrow>   <mrow>     <munder>       <mo>∑</mo>       <mn>5</mn>     </munder>     <munder>       <mo movablelimits="false">∑</mo>       <mn>7</mn>     </munder>   </mrow> </math>

Operators are also used for stretchy symbols such as fences, accents, arrows etc. In the following example, the vertical arrow stretches to the height of the mspace element. One can override default stretch behavior with the stretchy attribute e.g. to force an unstretched arrow. The symmetric attribute allows to indicate whether the operator should stretch symmetrically above and below the math axis (fraction bar). Finally the minsize and maxsize attributes add additional constraints over the stretch size.

<math>   <mfrac>     <mspace height="50px" depth="50px" width="10px" style="background: blue"/>     <mspace height="25px" depth="25px" width="10px" style="background: green"/>   </mfrac>   <mo>↑</mo>   <mo stretchy="false">↑</mo>   <mo symmetric="true">↑</mo>   <mo minsize="250px">↑</mo>   <mo maxsize="50px">↑</mo> </math>

Note that the default properties of operators are dictionary-based, as explained in 3.2.4.2 Dictionary-based attributes. For example a binary operator typically has default symmetric spacing around it while a fence is generally stretchy by default.

A MathML Core element is an embellished operator if it is:

An mo element;
a scripted element or an mfrac, whose first in-flow child exists and is an embellished operator;
a grouping element or mpadded, whose in-flow children consist (in any order) of one embellished operator and zero or more space-like elements.

The core operator of an embellished operator is the <mo> element defined recursively as follows:

The core operator of an mo element; is the element itself.
The core operator of an embellished scripted element or mfrac element is the core operator of its first in-flow child.
The core operator of an embellished grouping element or mpadded is the core operator of its unique embellished operator in-flow child.

The stretch axis of an embellished operator is inline if its core operator contains only text content made of a single character c, and that character has inline intrinsic stretch axis. Otherwise, the stretch axis of the embellished operator is block.

The same definitions apply for boxes in the visual formatting model where an anonymous <mrow> box is treated as a grouping element.

The form property of an embellished operator is either infix, prefix or postfix. The corresponding form attribute on the mo element, if present, must be an ASCII case-insensitive match to one of these values.

The algorithm for determining the form of an embellished operator is as follows:

If the form attribute is present and valid on the core operator, then its ASCII lowercased value is used.
If the embellished operator is the first in-flow child of a grouping element, mpadded or msqrt with more than one in-flow child (ignoring all space-like children) then it has form prefix.
Or, if the embellished operator is the last in-flow child of a grouping element, mpadded or msqrt with more than one in-flow child (ignoring all space-like children) then it has form postfix.
Or, if the embellished operator is an in-flow child of a scripted element, other than the first in-flow child, then it has form postfix.
Otherwise, the embellished operator has form infix.

The stretchy, symmetric, largeop, movablelimits properties of an embellished operator are either false or true. In the latter case, it is said that the embellished operator has the property. The corresponding stretchy, symmetric, largeop, movablelimits attributes on the mo element, if present, must be a boolean.

The lspace, rspace, minsize properties of an embellished operator are <length-percentage>. The maxsize property of an embellished operator is either a <length-percentage> or ∞. The lspace, rspace, minsize and maxsize attributes on the mo element, if present, must be a <length-percentage>.

The algorithm for determining the properties of an embellished operator is as follows:

If the corresponding stretchy, symmetric, largeop, movablelimits, lspace, rspace, maxsize or minsize attribute is present and valid on the core operator, then the ASCII lowercased value of this property is used.
Otherwise, run the algorithm for determining the form of an embellished operator.
If the core operator contains only text content Content, then set Category to the result of the algorithm to determine the category of an operator (Content, Form) where Form is the form calculated at the previous step.
If Category is Default and the form of embellished operator was not explicitly specified as an attribute on its core operator:
1. Set Category to the result of the algorithm to determine the category of an operator (Content, Form) where Form is infix.
2. If Category is Default, then run the algorithm again with Form set to postfix.
3. If Category is Default, then run the algorithm again with Form set to prefix.
Run the algorithm to set the properties of an operator from its category Category.

When used during layout, the values of stretchy, symmetric, largeop, movablelimits, lspace, rspace, minsize are obtained by the algorithm for determining the properties of an embellished operator with the following extra resolutions:

Percentage values for lspace, rspace are interpreted relative to the value read from the dictionary or to the fallback value above.
Interpretation of percentage values for minsize and maxsize are described in 3.2.4.3 Layout of operators.
Font-relative lengths for lspace, rspace, minsize and maxsize rely on the font style of the core operator, not the one of the embellished operator.

If the <mo> element does not have its computed display property equal to block math or inline math then it is laid out according to the CSS specification where the corresponding value is described. Otherwise, the layout below is performed.

The text of the operator must only be painted if the visibility of the <mo> element is visible. In that case, it must be painted with the color of the <mo> element.

Let dir be the element's computed direction.

Operators are laid out as follows:

If the content of the <mo> element is not made of a single character c then fall back to the layout algorithm of 3.2.1.1 Layout of <mtext>. If it is not possible to get a glyph corresponding to c given directionality dir, then fall back to the layout algorithm of 3.2.1.1 Layout of <mtext>. Otherwise, let g be the result of running get a glyph corresponding to c given directionality dir.
If the operator has the stretchy property:
- If the stretch axis of the operator is inline:
  1. If it is not possible to shape a stretchy glyph g in the inline direction with the first available font then fall back to the layout algorithm of 3.2.1.1 Layout of <mtext>.
  2. The min-content inline size and max-content inline size of the math content are set to the one obtained by the layout algorithm of 3.2.1.1 Layout of <mtext>.
  3. If there is not any inline stretch size constraint T_inline then fall back to the layout algorithm of 3.2.1.1 Layout of <mtext>.
  4. The inline size and (ink) block metrics of the math content are given by algorithm to shape a stretchy glyph g to inline dimension T_inline.
  5. The painting of the operator is performed by the algorithm to shape a stretchy glyph g stretched to inline dimension T_inline and at position determined by the previous box metrics.
- Otherwise, the stretch axis of the operator is block. The following steps are performed:
  1. If it is not possible to shape a stretchy glyph g in the block direction with the first available font then fall back to the layout algorithm of 3.2.1.1 Layout of <mtext>.
  2. The min-content inline size and max-content inline size of the math content are set to the preferred inline size of a glyph stretched along the block axis.
  3. If there is not any block stretch size constraint (U_ascent, U_descent) then fall back to the layout algorithm of 3.2.1.1 Layout of <mtext>.
  4. If the operator has the symmetric property then set the target sizes T_ascent and T_descent to S_ascent and S_descent respectively:
    - S_ascent = max( U_ascent − AxisHeight, U_descent + AxisHeight ) + AxisHeight
    - S_descent = max( U_ascent − AxisHeight, U_descent + AxisHeight ) − AxisHeight
    Otherwise set them to U_ascent and U_descent respectively.
    Note
    The property T_ascent − AxisHeight = T_descent + AxisHeight means that an operator stretching exactly T_ascent above the baseline and T_descent below the baseline would actually stretch symmetrically above and below the math axis. S_ascent and S_descent are the minimal values, that are respectively not less than U_ascent and U_descent, which satisfy this property.
  5. Let minsize and maxsize be the minsize and maxsize properties on the operator. Percentage values are interpreted relative to the height of g. Let T = T_ascent + T_descent be the target size. If minsize < 0 then set minsize to 0. If maxsize < minsize then set maxsize to minsize. With 0 ≤ minsize ≤ maxsize:
    - If T ≤ 0 then set T_ascent to minsize / 2 + AxisHeight and then set T_descent to minsize − T_ascent.
    - Otherwise, if 0 < T < minsize then set T_ascent to max(0, (T_ascent − AxisHeight) × minsize / T + AxisHeight) and T_descent to minsize − T_ascent.
    - Otherwise, if maxsize < T then set T_ascent to max(0, (T_ascent − AxisHeight) × maxsize / T + AxisHeight) and T_descent to maxsize − T_ascent.
    Note
    The default maxsize is value ∞ is interpreted above as being larger than any other size, i.e. minsize ≤ maxsize is always true while maxsize < minsize and maxsize < T are always false.
    
    Note
    This step ensures that the condition minsize ≤ T ≤ maxsize holds. Additionnally, if the target values correspond to symmetric stretching with respect to the math axis then property T_ascent − AxisHeight = T_descent + AxisHeight is preserved.
  6. The inline size, ink line-ascent, ink line-descent, line-ascent and line-descent of the math content are obtained by the algorithm to shape a stretchy glyph g to block dimension T_ascent + T_descent. The inline size of the math content is the width of the stretchy glyph. The stretchy glyph is shifted towards the line-under by a value Δ so that its center aligns with the center of the target: the ink ascent of the math content is the ascent of the stretchy glyph − Δ and the ink descent of the math content is the descent of the stretchy glyph + Δ. These centers have coordinates "½(ascent − descent)" so Δ = [(ascent of stretchy glyph − descent of stretchy glyph) − (T_ascent − T_descent)] / 2.
  7. The painting of the operator is performed by the algorithm to shape a stretchy glyph g stretched to block dimension T_ascent + T_descent and at position determined by the previous box metrics shifted by Δ towards the line-over.
  Figure 7 Base size, size variants and glyph assembly for the left brace
If the operator has the largeop property and if math-style on the <mo> element is normal, then:
1. If it is not possible to shape a stretchy glyph g in the block direction with the first available font then fall back to the layout algorithm of 3.2.1.1 Layout of <mtext>.
  Note
  Here we treat a non-stretchy largeop glyph as stretchy with target dimension DisplayOperatorMinHeight.
2. The min-content inline size and max-content inline size of the math content are set to the preferred inline size of a glyph stretched along the block axis.
3. The inline size, ink line-ascent, ink line-descent, line-ascent and line-descent of the math content are obtained by the algorithm to shape a stretchy glyph g to block dimension DisplayOperatorMinHeight. The inline size of the math content is the width of the stretchy glyph. The stretchy glyph is shifted towards the line-under by a value Δ so that its center aligns with the center of the target when symmetric: the ink ascent of the math content is the ascent of the stretchy glyph − Δ and the ink descent of the math content is the descent of the stretchy glyph + Δ.
  - If the operator has the symmetric property, then Δ = [(ascent of stretchy glyph − descent of stretchy glyph) − 2 * AxisHeight] / 2.
  - Otherwise, Δ = 0.
  Note
  The point of Δ here is simply to vertically align the operator when symmetric.
4. The painting of the operator is performed by the algorithm to shape a stretchy glyph g stretched to block dimension DisplayOperatorMinHeight and at position determined by the previous box metrics shifted by Δ towards the line-over.
Figure 8 Base and displaystyle sizes of the summation symbol
Otherwise fall back to the layout algorithm of 3.2.1.1 Layout of <mtext>.

If the algorithm to shape a stretchy glyph has been used for one of the step above, then the italic correction of the math content is set to the value returned by that algorithm.

The mspace empty element represents a blank space of any desired size, as set by its attributes.

The <mspace> element accepts the attributes described in 2.1.3 Global Attributes as well as the following attributes:

The width, height, depth, if present, must have a value that is a valid <length-percentage>.

If the width attribute is present, valid and not a percentage then that attribute is used as a presentational hint setting the element's width property to the corresponding value.
If the height attribute is absent, invalid or a percentage then the requested line-ascent is 0. Otherwise the requested line-ascent is the resolved value of the height attribute, clamping negative values to 0.
If both the height and depth attributes are present, valid and not a percentage then they are used as a presentational hint setting the element's height property to the concatenation of the strings "calc(", the height attribute value, " + ", the depth attribute value, and ")". If only one of these attributes is present, valid and not a percentage then it is treated as a presentational hint setting the element's height property to the corresponding value.

In the following example, mspace is used to force spacing within the formula (a 1px blue border is added to easily visualize the space):

<math>   <mn>1</mn>   <mspace width="1em"           style="border-top: 1px solid blue"/>    <mfrac>     <mrow>       <mn>2</mn>       <mspace depth="1em"               style="border-left: 1px solid blue"/>     </mrow>     <mrow>       <mn>3</mn>       <mspace height="2em"               style="border-left: 1px solid blue"/>     </mrow>   </mfrac> </math>

If the <mspace> element does not have its computed display property equal to block math or inline math then it is laid out according to the CSS specification where the corresponding value is described. Otherwise, the <mspace> element is laid out as shown on Figure 9. The min-content inline size, max-content inline size and inline size of the math content are equal to the resolved value of the width property. The block size of the math content is equal to the resolved value of the height property. The line-ascent of the math content is equal to the requested line-ascent determined above.

Figure 9 Box model for the `<mspace>` element

Note

The terminology height/depth comes from [MATHML3], itself inspired from [TEXBOOK].

A number of MathML presentation elements are "space-like" in the sense that they typically render as whitespace, and do not affect the mathematical meaning of the expressions in which they appear. As a consequence, these elements often function in somewhat exceptional ways in other MathML expressions.

A MathML Core element is a space-like element if it is:

an mtext or mspace;
or a grouping element or mpadded all of whose in-flow children are space-like.

The same definitions apply for boxes in the visual formatting model where an anonymous <mrow> box is treated as a grouping element.

Note

Note that an mphantom is not automatically defined to be space-like, unless its content is space-like. This is because operator spacing is affected by whether adjacent elements are space-like. Since the <mphantom> element is primarily intended as an aid in aligning expressions, operators adjacent to an <mphantom> should behave as if they were adjacent to the contents of the <mphantom>, rather than to an equivalently sized area of whitespace.

ms element is used to represent "string literals" in expressions meant to be interpreted by computer algebra systems or other systems containing "programming languages".

The <ms> element accepts the attributes described in 2.1.3 Global Attributes. Its layout algorithm is the same as the mtext element.

In the following example, ms is used to write a literal string of characters:

<math>   <mi>s</mi>   <mo>=</mo>   <ms>"hello world"</ms> </math>

Note

In MathML3, it was possible to use the lquote and rquote attributes to respectively specify the strings to use as opening and closing quotes. These are no longer supported and the quotes must instead be specified as part of the text of the <ms> element. One can add CSS rules to legacy documents in order to preserve visual rendering. For example, in left-to-right direction:

ms:before, ms:after {   content: "\0022"; } ms[lquote]:before {   content: attr(lquote); } ms[rquote]:after {   content: attr(rquote); }

Besides tokens there are several families of MathML presentation elements. One family of elements deals with various "scripting" notations, such as subscript and superscript. Another family is concerned with matrices and tables. The remainder of the elements, discussed in this section, describe other basic notations such as fractions and radicals, or deal with general functions such as setting style properties and error handling.

The mrow element is used to group together any number of sub-expressions, usually consisting of one or more <mo> elements acting as "operators" on one or more other expressions that are their "operands".

In the following example, mrow is used to group a sum "1 + 2/3" as a fraction numerator (first child of mfrac) and to construct a fenced expression (first child of msup) that is raised to the power of 5. Note that mrow alone does not add visual fences around its grouped content, one has to explicitly specify them using the mo element.

Within the mrow elements, one can see that vertical alignment of children (according to the alphabetic baseline or the mathematical baseline) is properly performed, fences are vertically stretched and spacing around the binary + operator automatically calculated.

<math>   <msup>     <mrow>       <mo>(</mo>       <mfrac>         <mrow>           <mn>1</mn>           <mo>+</mo>           <mfrac>             <mn>2</mn>             <mn>3</mn>           </mfrac>         </mrow>         <mn>4</mn>       </mfrac>       <mo>)</mo>     </mrow>     <mn>5</mn>   </msup> </math>

The <mrow> element accepts the attributes described in 2.1.3 Global Attributes. An <mrow> element with in-flow children child₁, child₂, …, child_N is laid out as shown on Figure 10. The child boxes are put in a row one after the other with all their alphabetic baselines aligned.

Figure 10 Box model for the `<mrow>` element

Note

Because the box model ensures alignment of alphabetic baselines, fraction bars or symmetric stretchy operators will also be aligned along the math axis in the typical case when AxisHeight is the same for all in-flow children.

Figure 11 Symmetric and non-symmetric stretching of operators along the block axis

The algorithm for stretching operators along the block axis consists in the following steps:

If there is a block stretch size constraint or an inline stretch size constraint then the element being laid out is an embellished operator. Lay out the one in-flow child that is an embellished operator with the same stretch size constraint and all the other in-flow children without any stretch size constraint and stop.
Otherwise, split the list of in-flow children into a first list L_ToStretch containing embellished operators with a stretchy property and block stretch axis; and a second list L_NotToStretch.
Perform layout without any stretch size constraint on all the items of L_NotToStretch. If L_ToStretch is empty then stop. If L_NotToStretch is empty, perform layout with block stretch size constraint (0, 0) for all the items of L_ToStretch.
Calculate the unconstrained target sizes U_ascent and U_descent as respectively the maximum ink ascent and maximum ink descent of the margin boxes of in-flow children that have been laid out in the previous step.
Lay out or relayout all the elements of L_ToStretch with block stretch size constraint (U_ascent, U_descent).

If the box is not an anonymous <mrow> box and the associated element does not have its computed display property equal to block math or inline math then it is laid out according to the CSS specification where the corresponding value is described. Otherwise, the layout below is performed.

A child box is slanted if it is not an embellished operator and has nonzero italic correction.

Note

Large operators may have nonzero italic correction but that one is used when attaching scripts. More generally, all embellished operators are treated as non-slanted since the spacing around them is calculated as specified by lspace and rspace.

The min-content inline size (respectively max-content inline size) are calculated using the following algorithm:

Set add-space to true if the box corresponds to a math element or is not an embellished operator; and to false otherwise.
Set inline-offset to 0.
Set previous-italic-correction to 0.
For each in-flow child:
1. If the child is not slanted, then increment inline-offset by previous-italic-correction.
2. If the child is an embellished operator and add-space is true then increment inline-offset by its lspace property.
3. Increment inline-offset by the min-content inline size (respectively max-content inline size) of the child's margin box.
4. If the child is slanted then set previous-italic-correction to its italic correction. Otherwise set it to 0.
5. If the child is an embellished operator and add-space is true then increment inline-offset by its rspace property.
Increment inline-offset by previous-italic-correction.
Return inline-offset.

The in-flow children are laid out using the algorithm for stretching operators along the block axis.

The inline size of the math content is calculated like the min-content inline size and max-content inline size of the math content, using the inline size of the in-flow children's margin boxes instead.

The ink line-ascent (respectively line-ascent) of the math content is the maximum of the ink line-ascents (respectively line-ascents) of all the in-flow children's margin boxes. Similarly, the ink line-descent (respectively line-descent) of the math content is the maximum of the ink line-descents (respectively ink line-ascents) of all the in-flow children's margin boxes.

The in-flow children are positioned using the following algorithm:

Set add-space to true if the box corresponds to a math element or is not an embellished operator; and to false otherwise.
Set inline-offset to 0.
Set previous-italic-correction to 0.
For each in-flow child:
1. If the child is not slanted, then increment inline-offset by previous-italic-correction.
2. If the child is an embellished operator and add-space is true then increment inline-offset by its lspace property.
3. Set the inline offset of the child to inline-offset and its block offset such that the alphabetic baseline of the child is aligned with the alphabetic baseline.
4. Increment inline-offset by the inline size of the child's margin box.
5. If the child is slanted then set previous-italic-correction to its italic correction. Otherwise set it to 0.
6. If the child is an embellished operator and add-space is true then increment inline-offset by its rspace property.

The italic correction of the math content is set to the italic correction of the last in-flow child, which is the final value of previous-italic-correction.

The mfrac element is used for fractions. It can also be used to mark up fraction-like objects such as binomial coefficients and Legendre symbols.

If the <mfrac> element does not have its computed display property equal to block math or inline math then it is laid out according to the CSS specification where the corresponding value is described. Otherwise, the layout below is performed.

The <mfrac> element accepts the attributes described in 2.1.3 Global Attributes as well as the following attribute:

linethickness

The linethickness attribute indicates the fraction line thickness to use for the fraction bar. If present, it must have a value that is a valid <length-percentage>. If the attribute is absent or has an invalid value, FractionRuleThickness is used as the default value. A percentage is interpreted relative to that default value. A negative value is interpreted as 0.

The following example contains four fractions with different linethickness values. The bars are always aligned with the middle of plus and minus signs. The numerator and denominator are horizontally centered. The fractions that are not in displaystyle use smaller gaps and font-size.

<math>   <mn>0</mn>   <mo>+</mo>   <mfrac displaystyle="true">     <mn>1</mn>     <mn>2</mn>   </mfrac>   <mo>−</mo>   <mfrac>     <mn>1</mn>     <mn>2</mn>   </mfrac>   <mo>+</mo>   <mfrac linethickness="200%">     <mn>1</mn>     <mn>234</mn>   </mfrac>   <mo>−</mo>   <mrow>     <mo>(</mo>     <mfrac linethickness="0">       <mn>123</mn>       <mn>4</mn>     </mfrac>     <mo>)</mo>   </mrow> </math>

$mfrac example$

The <mfrac> element sets displaystyle to false, or if it was already false increments scriptlevel by 1, within its children. It sets math-shift to compact within its second child. To avoid visual confusion between the fraction bar and another adjacent items (e.g. minus sign or another fraction's bar), a default 1-pixel space is added around the element. The user agent stylesheet must contain the following rules:

mfrac {   padding-inline: 1px; } mfrac > * {   math-depth: auto-add;   math-style: compact; } mfrac > :nth-child(2) {   math-shift: compact; }

If the <mfrac> element has less or more than two in-flow children, its layout algorithm is the same as the mrow element. Otherwise, the first in-flow child is called numerator, the second in-flow child is called denominator and the layout algorithm is explained below.

Note

In practice, an <mfrac> element has two children that are in-flow. Hence the CSS rules basically perform scriptlevel, displaystyle and math-shift changes for the numerator and denominator.

If the fraction line thickness is nonzero, the <mfrac> element is laid out as shown on Figure 12. The fraction bar must only be painted if the visibility of the <mfrac> element is visible. In that case, the fraction bar must be painted with the color of the <mfrac> element.

Figure 12 Box model for the `<mfrac>` element

The min-content inline size (respectively max-content inline size) of content is the maximum between the min-content inline size (respectively max-content inline size) of the numerator's margin box and the min-content inline size (respectively max-content inline size) of the denominator's margin box.

If there is an inline stretch size constraint or a block stretch size constraint then the numerator is also laid out with the same stretch size constraint, otherwise it is laid out without any stretch size constraint. The denominator is always laid out without any stretch size constraint.

The inline size of the math content is the maximum between the inline size of the numerator's margin box and the inline size of the denominator's margin box.

NumeratorShift is the maximum between:

FractionNumeratorShiftUp (respectively FractionNumeratorDisplayStyleShiftUp) if the math-style is compact (respectively normal).
The AxisHeight + half the fraction line thickness + FractionNumeratorGapMin (respectively FractionNumDisplayStyleGapMin) if the math-style is compact (respectively normal) + the ink line-descent of the numerator's margin box.

DenominatorShift is the maximum between:

FractionDenominatorShiftDown (respectively FractionDenominatorDisplayStyleShiftDown) if the math-style is compact (respectively normal).
Half the fraction line thickness + FractionDenominatorGapMin (respectively FractionDenomDisplayStyleGapMin) if the math-style is compact (respectively normal) + the ink line-ascent of the denominator's margin box − the AxisHeight.

The line-ascent of the math content is the maximum between:

Numerator Shift + the line-ascent of the numerator's margin box.
−Denominator Shift + the line-ascent of the denominator's margin box
AxisHeight plus half the fraction line thickness.

The line-descent of the math content is the maximum between:

−Numerator Shift + the line-descent of the numerator's margin box.
Denominator Shift + the line-descent of the denominator's margin box.
−AxisHeight plus half the fraction line thickness.
0

The inline offset of the numerator (respectively denominator) is half the inline size of the math content − half the inline size of the numerator's margin box (respectively denominator's margin box).

The alphabetic baseline of the numerator (respectively denominator) is shifted away from the alphabetic baseline by a distance of NumeratorShift (respectively DenominatorShift) towards the line-over (respectively line-under).

The math content box is placed within the content box so that their block-start edges are aligned and the middles of these edges are at the same position.

The inline size of the fraction bar is the inline size of the content box and its inline-start edge is the aligned with the one the content box. The center of the fraction bar is shifted away from the alphabetic baseline of the math content box by a distance of AxisHeight towards the line-over. Its block size is the fraction line thickness.

If the fraction line thickness is zero, the <mfrac> element is instead laid out as shown on Figure 13.

Figure 13 Box model for the `<mfrac>` element without bar

The min-content inline size, max-content inline size and inline size of the math content are calculated the same as in 3.3.2.1 Fraction with nonzero line thickness.

If there is an inline stretch size constraint or a block stretch size constraint then the numerator is also laid out with the same stretch size constraint and otherwise it is laid out without any stretch size constraint. The denominator is always laid out without any stretch size constraint.

If the math-style is compact then TopShift and BottomShift are respectively set to StackTopShiftUp and StackBottomShiftDown. Otherwise math-style is normal and they are respectively set to StackTopDisplayStyleShiftUp and StackBottomDisplayStyleShiftDown.

The Gap is defined to be (BottomShift − the ink line-ascent of the denominator's margin box) + (TopShift − the ink line-descent of the numerator's margin box). If math-style is compact then GapMin is StackGapMin, otherwise math-style is normal and it is StackDisplayStyleGapMin. If Δ = GapMin − Gap is positive then TopShift and BottomShift are respectively increased by Δ/2 and Δ − Δ/2.

The line-ascent of the math content is the maximum between:

TopShift + the line-ascent of the numerator's margin box.
−BottomShift + the line-ascent of the denominator's margin box.

The line-descent of the math content is the maximum between:

−TopShift + the line-descent of the numerator's margin box.
BottomShift + the line-descent of the denominator's margin box.
0

The inline offsets of the numerator and denominator are calculated the same as in 3.3.2.1 Fraction with nonzero line thickness.

The alphabetic baseline of the numerator (respectively denominator) is shifted away from the alphabetic baseline by a distance of TopShift (respectively − BottomShift) towards the line-over (respectively line-under).

The math content box is placed within the content box so that their block-start edges are aligned and the middles of these edges are at the same position.

The radical elements construct an expression with a root symbol √ with a line over the content. The msqrt element is used for square roots, while the mroot element is used to draw radicals with indices, e.g. a cube root.

The <msqrt> and <mroot> elements accept the attributes described in 2.1.3 Global Attributes.

The following example contains a square root written with msqrt and a cube root written with mroot. Note that msqrt has several children and the square root applies to all of them. mroot has exactly two children: it is a root of index the second child (the number 3), applied to the first child (the square root). Also note these elements only change the font-size within the mroot index, but it is scaled down more than within the numerator and denumerator of the fraction.

<math>   <mroot>     <msqrt>       <mfrac>         <mn>1</mn>         <mn>2</mn>       </mfrac>       <mo>+</mo>       <mn>4</mn>     </msqrt>     <mn>3</mn>   </mroot>   <mo>+</mo>   <mn>0</mn> </math>

The <msqrt> and <mroot> elements sets math-shift to compact. The <mroot> element increments scriptlevel by 2, and sets displaystyle to "false" in all but its first child. The user agent stylesheet must contain the following rule in order to implement that behavior:

mroot > :not(:first-child) {   math-depth: add(2);   math-style: compact; } mroot, msqrt {   math-shift: compact; }

If the <msqrt> or <mroot> element do not have their computed display property equal to block math or inline math then they are laid out according to the CSS specification where the corresponding value is described. Otherwise, the layout below is performed.

If the <mroot> has less or more than two in-flow children, its layout algorithm is the same as the mrow element. Otherwise, the first in-flow child is called mroot base and the second in-flow child is called mroot index and its layout algorithm is explained below.

Note

In practice, an <mroot> element has two children that are in-flow. Hence the CSS rules basically perform scriptlevel and displaystyle changes for the index.

The <msqrt> element generates an anonymous <mrow> box called the msqrt base.

The radical symbol must only be painted if the visibility of the <msqrt> or <mroot> element is visible. In that case, the radical symbol must be painted with the color of that element.

Let dir be the computed direction of the <msqrt> or <mroot> element. The radical glyph is the glyph obtained as a result of running get a glyph corresponding to the U+221A SQUARE ROOT character given dir.

The radical gap is given by RadicalVerticalGap if the math-style is compact and RadicalDisplayStyleVerticalGap if the math-style is normal.

The radical target size for the stretchy radical glyph is the sum of RadicalRuleThickness, radical gap and the ink height of the base.

The box metrics of the radical glyph and painting of the surd are given by the algorithm to shape a stretchy glyph to the target size for the radical glyph in the block dimension.

The <msqrt> element is laid out as shown on Figure 14.

Figure 14 Box model for the `<msqrt>` element

The min-content inline size (respectively max-content inline size) of the math content is the sum of the preferred inline size of a glyph stretched along the block axis for the radical glyph and of the min-content inline size (respectively max-content inline size) of the msqrt base's margin box.

The inline size of the math content is the sum of the advance width of the box metrics of the radical glyph and of the inline size of the msqrt base's margin's box.

The line-ascent of the math content is the maximum between:

The line-ascent of the msqrt base's margin box.
The sum of the ink line-ascent of the msqrt base, the radical gap, the RadicalRuleThickness and RadicalExtraAscender.

The line-descent of the math content is the maximum between:

The line-descent of the msqrt base's margin box.
The sum of the line-ascent and line-descent for the box metrics of the radical glyph and of the RadicalExtraAscender, minus the line-ascent of the math content.

The inline size of the overbar is the inline size of the msqrt base's margin's box. The inline offsets of the msqrt base and overbar are also the same and equal to the width of the box metrics of the radical glyph.

The alphabetic baseline of the msqrt base is aligned with the alphabetic baseline. The block size of the overbar is RadicalRuleThickness. Its vertical center is shifted away from the alphabetic baseline by a distance towards the line-over equal to the line-ascent of the math content, minus the RadicalExtraAscender, minus half the RadicalRuleThickness.

Finally, the painting of the surd is performed:

At inline offset 0.
At block offset shifted away from the line-over edge of the overbar towards the line-under by a distance given by the ascent of the box metrics of the radical glyph.

The <mroot> element is laid out as shown on Figure 15. The mroot index is first ignored and the mroot base and radical glyph are laid out as shown on figure Figure 14 using the same algorithm as in 3.3.3.2 Square root in order to produce a margin box B (represented in green).

Figure 15 Box model for the `<mroot>` element

The min-content inline size (respectively max-content inline size) of the math content is the sum of max(0, RadicalKernBeforeDegree), the mroot index's min-content inline size (respectively max-content inline size) of the mroot index's margin box, max(−min-content inline size, RadicalKernAfterDegree) (respectively max(−max-content inline size of the mroot index's margin box, RadicalKernAfterDegree)) and of the min-content inline size (respectively max-content inline size) of B.

Using the same clamping, AdjustedRadicalKernBeforeDegree and AdjustedRadicalKernAfterDegree are respectively defined as max(0, RadicalKernBeforeDegree) and is max(−inline size of the index's margin box, RadicalKernAfterDegree).

The inline size of the math content is the sum of AdjustedRadicalKernBeforeDegree, the inline size of the index's margin box, AdjustedRadicalKernAfterDegree and of the inline size of B.

The line-ascent of the math content is the maximum between:

−the line-descent of B + RadicalDegreeBottomRaisePercent × the block size of B + the line-ascent of the index's margin box
The line-ascent of B

The line-descent of the math content is the maximum between:

the line-descent of B − RadicalDegreeBottomRaisePercent × the block size of B + the line-ascent of the index's margin box
The line-descent of B

The inline offset of the index is AdjustedRadicalKernBeforeDegree. The inline-offset of the mroot base is the same + the inline size of the index's margin box.

The alphabetic baseline of B is aligned with the alphabetic baseline. The alphabetic baseline of the index is shifted away from the line-under edge by a distance of RadicalDegreeBottomRaisePercent × the block size of B + the line-descent of the index's margin box.

Note

In general, the kerning before the root index is positive while the kerning after it is negative, which means that the root element will have some inline-start space and that the root index will overlap the surd.

Historically, the mstyle element was introduced to make style changes that affect the rendering of its contents.

The <mstyle> element accepts the attributes described in 2.1.3 Global Attributes. Its layout algorithm is the same as the mrow element.

Note

<mstyle> is implemented for compatibility with full MathML. Authors whose only target is MathML Core are encouraged to use CSS for styling.

In the following example, mstyle is used to set the scriptlevel and displaystyle. Observe this is respectively affecting the font-size and placement of subscripts of their descendants. In MathML Core, one could just have used mrow elements instead.

<math>   <munder>     <mo movablelimits="true">*</mo>     <mi>A</mi>   </munder>   <mstyle scriptlevel="1">     <mstyle displaystyle="true">       <munder>         <mo movablelimits="true">*</mo>         <mi>B</mi>       </munder>       <munder>         <mo movablelimits="true">*</mo>         <mi>C</mi>       </munder>     </mstyle>     <munder>       <mo movablelimits="true">*</mo>       <mi>D</mi>     </munder>   </mstyle> </math>

The merror element displays its contents as an ”error message”. The intent of this element is to provide a standard way for programs that generate MathML from other input to report syntax errors in their input.

In the following example, merror is used to indicate a parsing error for some LaTeX-like input:

<math>   <mfrac>     <merror>       <mtext>Syntax error: \frac{1}</mtext>     </merror>     <mn>3</mn>   </mfrac> </math>

The <merror> element accepts the attributes described in 2.1.3 Global Attributes. Its layout algorithm is the same as the mrow element. The user agent stylesheet must contain the following rule in order to visually highlight the error message:

merror {   border: 1px solid red;   background-color: lightYellow; }

The mpadded element renders the same as its in-flow child content, but with the size and relative positioning point of its content modified according to <mpadded>’s attributes.

The <mpadded> element accepts the attributes described in 2.1.3 Global Attributes as well as the following attributes:

The width, height, depth, lspace and voffset if present, must have a value that is a valid <length-percentage>.

In the following example, mpadded is used to tweak spacing around a fraction (a blue background is used to visualize it). Without attributes, it behaves like an mrow but the attributes allow to specify the size of the box (width, height, depth) and position of the fraction within that box (lspace and voffset).

<math>   <mrow>     <mn>1</mn>     <mpadded style="background: lightblue;">       <mfrac>         <mn>23456</mn>         <mn>78</mn>       </mfrac>     </mpadded>     <mn>9</mn>   </mrow>   <mo>+</mo>   <mrow>     <mn>1</mn>     <mpadded lspace="2em" voffset="-1em" height="1em" depth="3em" width="7em"              style="background: lightblue;">       <mfrac>         <mn>23456</mn>         <mn>78</mn>       </mfrac>     </mpadded>     <mn>9</mn>   </mrow> </math>

The mpadded element generates an anonymous <mrow> box called the mpadded inner box with parameters called inner inline size, inner line-ascent and inner line-descent.

The requested <mpadded> parameters are determined as follows:

The requested width is the resolved value of the width property. If the width attribute is present, valid and not a percentage then that attribute is used as a presentational hint setting the element's width property to the corresponding value.
If the height attribute is absent, invalid or a percentage then the requested height is the inner line-ascent. Otherwise the requested height is the resolved value of the height attribute, clamping negative values to 0.
If the depth attribute is absent, invalid or a percentage then the requested depth is the inner line-ascent. Otherwise the requested depth is the resolved value of the depth attribute, clamping negative values to 0.
If the lspace attribute is absent, invalid or a percentage then the requested lspace is 0. Otherwise the requested lspace is the resolved value of the lspace attribute, clamping negative values to 0.
If the voffset attribute is absent, invalid or a percentage then the requested voffset is 0. Otherwise the requested voffset is the resolved value of the voffset attribute.
Note
Negative voffset values are not clamped to 0.

If the <mpadded> element does not have its computed display property equal to block math or inline math then it is laid out according to the CSS specification where the corresponding value is described. Otherwise, it is laid out as shown on Figure 16.

Figure 16 Box model for the `<mpadded>` element

The min-content inline size (respectively max-content inline size) of the math content is the requested width calculated in 3.3.6.1 Inner box and requested parameters but using the min-content inline size (respectively max-content inline size) of the mpadded inner box instead of the "inner inline size".

The inline size of the math content is the requested width calculated in 3.3.6.1 Inner box and requested parameters.

The line-ascent of the math content is the requested height. The line-descent of the math content is the requested depth.

The mpadded inner box is placed so that its alphabetic baseline is shifted away from the alphabetic baseline by the requested voffset towards the line-over.

Historically, the mphantom element was introduced to render its content invisibly, but with the same metrics size and other dimensions, including alphabetic baseline position that its contents would have if they were rendered normally.

In the following example, mphantom is used to ensure alignment of corresponding parts of the numerator and denominator of a fraction:

<math>   <mfrac>     <mrow>       <mi>x</mi>       <mo>+</mo>       <mi>y</mi>       <mo>+</mo>       <mi>z</mi>     </mrow>     <mrow>       <mi>x</mi>       <mphantom>         <mo form="infix">+</mo>         <mi>y</mi>       </mphantom>       <mo>+</mo>       <mi>z</mi>     </mrow>   </mfrac> </math>

The <mphantom> element accepts the attributes described in 2.1.3 Global Attributes. Its layout algorithm is the same as the mrow element. The user agent stylesheet must contain the following rule in order to hide the content:

mphantom {   visibility: hidden; }

Note

<mphantom> is implemented for compatibility with full MathML. Authors whose only target is MathML Core are encouraged to use CSS for styling.

The elements described in this section position one or more scripts around a base. Attaching various kinds of scripts and embellishments to symbols is a very common notational device in mathematics. For purely visual layout, a single general-purpose element could suffice for positioning scripts and embellishments in any of the traditional script locations around a given base. However, in order to capture the abstract structure of common notation better, MathML provides several more specialized scripting elements.

In addition to sub-/superscript elements, MathML has overscript and underscript elements that place scripts above and below the base. These elements can be used to place limits on large operators, or for placing accents and lines above or below the base.

The msub, msup and msubsup elements are used to attach subscript and superscript to a MathML expression. They accept the attributes described in 2.1.3 Global Attributes.

The following example shows basic use of subscripts and superscripts. The font-size is automatically scaled down within the scripts.

<math>   <msub>     <mn>1</mn>     <mn>2</mn>   </msub>   <mo>+</mo>   <msup>     <mn>3</mn>     <mn>4</mn>   </msup>   <mo>+</mo>   <msubsup>     <mn>5</mn>     <mn>6</mn>     <mn>7</mn>   </msubsup> </math>

If the <msub>, <msup> or <msubsup> elements do not have their computed display property equal to block math or inline math then they are laid out according to the CSS specification where the corresponding value is described. Otherwise, the layout below is performed.

If the <msub> element has less or more than two in-flow children, its layout algorithm is the same as the mrow element. Otherwise, the first in-flow child is called the msub base, the second in-flow child is called the msub subscript and the layout algorithm is explained in 3.4.1.2 Base with subscript.

If the <msup> element has less or more than two in-flow children, its layout algorithm is the same as the mrow element. Otherwise, the first in-flow child is called the msup base, the second in-flow child is called the msup superscript and the layout algorithm is explained in 3.4.1.3 Base with superscript.

If the <msubsup> element has less or more than three in-flow children, its layout algorithm is the same as the mrow element. Otherwise, the first in-flow child is called the msubsup base, the second in-flow child is called the msubsup subscript, its third in-flow child is called the msubsup superscript and the layout algorithm is explained in 3.4.1.4 Base with subscript and superscript.

The <msub> element is laid out as shown on Figure 17. LargeOpItalicCorrection is the italic correction of the msub base if it is an embellished operator with the largeop property and 0 otherwise.

Figure 17 Box model for the `<msub>` element

The min-content inline size (respectively max-content inline size) of the math content is the min-content inline size (respectively max-content inline size) of the msub base's margin box − LargeOpItalicCorrection + min-content inline size (respectively max-content inline size) of the msub subscript's margin box + SpaceAfterScript.

If there is an inline stretch size constraint or a block stretch size constraint then the msub base is also laid out with the same stretch size constraint and otherwise it is laid out without any stretch size constraint. The scripts are always laid out without any stretch size constraint.

The inline size of the math content is the inline size of the msub base's margin box − LargeOpItalicCorrection + the inline size of the msub subscript's margin box + SpaceAfterScript.

SubShift is the maximum between:

SubscriptShiftDown
the ink line-ascent of the subscript's margin box − SubscriptTopMax
SubscriptBaselineDropMin + the ink line-descent of the msub base's margin box

The line-ascent of the math content is the maximum between:

The line-ascent of the msub base's margin box.
The line-ascent of the subscript's margin box − SubShift.

The line-descent of the math content is the maximum between:

The line-descent of the msub base's margin box.
The line-descent of the subscript's margin box + SubShift.

The inline offset of the msub base is 0 and the inline offset of the msub subscript is the inline size of the msub base's margin box − LargeOpItalicCorrection.

The msub base is placed so that its alphabetic baseline matches the alphabetic baseline. The msub subscript is placed so that its alphabetic baseline is shifted away from the alphabetic baseline by SubShift towards the line-under.

The <msup> element is laid out as shown on Figure 18. ItalicCorrection is the italic correction of the msup base if it is not an embellished operator with the largeop property and 0 otherwise.

Figure 18 Box model for the `<msup>` element

The min-content inline size (respectively max-content inline size) of the math content is the min-content inline size (respectively max-content inline size) of the msup base's margin box + ItalicCorrection + the min-content inline size (respectively max-content inline size) of the msup superscript's margin box + SpaceAfterScript.

If there is an inline stretch size constraint or a block stretch size constraint then the msup base is also laid out with the same stretch size constraint and otherwise it is laid out without any stretch size constraint. The scripts are always laid out without any stretch size constraint.

The inline size of the math content is the inline size of the msup base's margin box + ItalicCorrection + the inline size of the msup superscript's margin box + SpaceAfterScript.

SuperShift is the maximum between:

The value SuperscriptShiftUpCramped if the element has a computed math-shift property equal to compact, or SuperscriptShiftUp otherwise.
SuperscriptBottomMin + the ink line-descent of the superscript's margin box
The ink line-ascent of the msup base's margin box − SuperscriptBaselineDropMax

The line-ascent of the math content is the maximum between:

The line-ascent of the msup base's margin box.
The line-ascent of the superscript's margin box + SuperShift.

The line-descent of the math content is the maximum between:

The line-descent of the msup base's margin box.
The line-descent of the superscript's margin box − SuperShift.

The inline offset of the msup base is 0 and the inline offset of msup superscript is the inline size of the msup base's margin box + ItalicCorrection.

The msup base is placed so that its alphabetic baseline matches the alphabetic baseline. The msup superscript is placed so that its alphabetic baseline is shifted away from the alphabetic baseline by SuperShift towards the line-over.

The <msubsup> element is laid out as shown on Figure 18. LargeOpItalicCorrection and SubShift are set as in 3.4.1.2 Base with subscript. ItalicCorrection and SuperShift are set as in 3.4.1.3 Base with superscript.

Figure 19 Box model for the `<msubsup>` element

The min-content inline size (respectively max-content inline size and inline size) of the math content is the maximum between the min-content inline size (respectively max-content inline size and inline size) of the math content calculated in 3.4.1.2 Base with subscript and 3.4.1.3 Base with superscript.

If there is an inline stretch size constraint or a block stretch size constraint then the msubsup base is also laid out with the same stretch size constraint and otherwise it is laid out without any stretch size constraint. The scripts are always laid out without any stretch size constraint.

SubSuperGap is the gap between the two scripts along the block axis and is defined by (SubShift − the ink line-ascent of the msubsup subscript's margin box) + (SuperShift − the ink line-descent of the msubsup superscript's margin box). If SubSuperGap is not at least SubSuperscriptGapMin then the following steps are performed to ensure that the condition holds:

Let Δ be SuperscriptBottomMaxWithSubscript − (SuperShift − the ink line-descent of the msubsup superscript's margin box). If Δ > 0 then set Δ to the minimum between Δ set SubSuperscriptGapMin − SubSuperGap and increase SuperShift (and so SubSuperGap too) by Δ.
Let Δ be SubSuperscriptGapMin − SubSuperGap. If Δ > 0 then increase SubscriptShift (and so SubSuperGap too) by Δ.

The ink line-ascent (respectively line-ascent, ink line-descent, line-descent) of the math content is set to the maximum of the ink line-ascent (respectively line-ascent, ink line-descent, line-descent) of the math content calculated in 3.4.1.2 Base with subscript and 3.4.1.3 Base with superscript but using the adjusted values SubShift and SuperShift above.

The inline offset and block offset of the msubsup base and scripts are performed the same as described in 3.4.1.2 Base with subscript and 3.4.1.3 Base with superscript.

Note

Even when the msubsup subscript (respectively msubsup superscript) is an empty box, <msubsup> does not generally render the same as 3.4.1.3 Base with superscript (respectively 3.4.1.2 Base with subscript) because of the additional constraint on SubSuperGap. Moreover, positioning the empty msubsup subscript (respectively msubsup superscript) may also change the total size.

In order to keep the algorithm simple, no attempt is made to handle empty scripts in a special way.

The munder, mover and munderover elements are used to attach accents or limits placed under or over a MathML expression.

The <munderover> element accepts the attribute described in 2.1.3 Global Attributes as well as the following attributes:

accent
accentunder

Similarly, the <mover> element (respectively <munder> element) accepts the attribute described in 2.1.3 Global Attributes as well as the accent attribute (respectively the accentunder attribute).

accent, accentunder attributes, if present, must have values that are booleans. If these attributes are absent or invalid, they are treated as equal to false. User agents must implement them as described in 3.4.4 Displaystyle, scriptlevel and math-shift in scripts.

The following example shows basic use of under- and overscripts. The font-size is automatically scaled down within the scripts, unless they are meant to be accents.

<math>   <munder>     <mn>1</mn>     <mn>2</mn>   </munder>   <mo>+</mo>   <mover>     <mn>3</mn>     <mn>4</mn>   </mover>   <mo>+</mo>   <munderover>     <mn>5</mn>     <mn>6</mn>     <mn>7</mn>   </munderover>   <mo>+</mo>   <munderover accent="true">     <mn>8</mn>     <mn>9</mn>     <mn>10</mn>   </munderover>   <mo>+</mo>   <munderover accentunder="true">     <mn>11</mn>     <mn>12</mn>     <mn>13</mn>   </munderover> </math>

If the <munder>, <mover> or <munderover> elements do not have their computed display property equal to block math or inline math then they are laid out according to the CSS specification where the corresponding value is described. Otherwise, the layout below is performed.

If the <munder> element has less or more than two in-flow children, its layout algorithm is the same as the mrow element. Otherwise, the first in-flow child is called the munder base and the second in-flow child is called the munder underscript.

If the <mover> element has less or more than two in-flow children, its layout algorithm is the same as the mrow element. Otherwise, the first in-flow child is called the mover base and the second in-flow child is called the mover overscript.

If the <munderover> element has less or more than three in-flow children, its layout algorithm is the same as the mrow element. Otherwise, the first in-flow child is called the munderover base, the second in-flow child is called the munderover underscript and its third in-flow child is called the munderover overscript.

If the <munder>, <mover> or <munderover> elements have a computed math-style property equal to compact and their base is an embellished operator with the movablelimits property, then their layout algorithms are respectively the same as the ones described for <msub>, <msup> and <msubsup> in 3.4.1.2 Base with subscript, 3.4.1.3 Base with superscript and 3.4.1.4 Base with subscript and superscript.

Otherwise, the <munder>, <mover> and <munderover> layout algorithms are respectively described in 3.4.2.3 Base with underscript, 3.4.2.4 Base with overscript and 3.4.2.5 Base with underscript and overscript.

The algorithm for stretching operators along the inline axis is as follows.

If there is an inline stretch size constraint or block stretch size constraint then the element being laid out is an embellished operator. Lay out the base with the same stretch size constraint.
Split the list of in-flow children that have not been laid out yet into a first list L_ToStretch containing embellished operators with a stretchy property and inline stretch axis; and a second list L_NotToStretch.
Perform layout without any stretch size constraint on all the items of L_NotToStretch. If L_ToStretch is empty then stop. If L_NotToStretch is empty, perform layout with inline stretch size constraint 0 for all the items of L_ToStretch.
Calculate the target size T to the maximum inline size of the margin boxes of child boxes that have been laid out in the previous step.
Lay out or relayout all the elements of L_ToStretch with inline stretch size constraint T.

The <munder> element is laid out as shown on Figure 20. LargeOpItalicCorrection is the italic correction of the munder base if it is an embellished operator with the largeop property and 0 otherwise.

Figure 20 Box model for the `<munder>` element

The min-content inline size (respectively max-content inline size) of the math content are calculated like the inline size of the math content below but replacing the inline sizes of the munder base's margin box and munder underscript's margin box with the min-content inline size (respectively max-content inline size) of the munder base's margin box and munder underscript's margin box.

The in-flow children are laid out using the algorithm for stretching operators along the inline axis.

The inline size of the math content is calculated by determining the absolute difference between:

The maximum of:
- Half the inline size of the munder base's margin box.
- Half the inline size of the munder underscript's margin box − half LargeOpItalicCorrection.
The minimum of:
- −half the inline size of the munder base's margin box.
- −half the inline size of the munder underscript's margin box − half LargeOpItalicCorrection.

If m is the minimum calculated in the second item above then the inline offset of the munder base is −m − half the inline size of the base's margin box. The inline offset of the munder underscript is −m − half the inline size of the munder underscript's margin box − half LargeOpItalicCorrection.

Parameters UnderShift and UnderExtraDescender are determined by considering three cases in the following order:

The munder base is an embellished operator with the largeop property. UnderShift is the maximum of
- LowerLimitBaselineDropMin
- LowerLimitGapMin + the ascent of the munder underscript.
UnderExtraDescender is 0.
The munder base is an embellished operator with the stretchy property and stretch axis inline. UnderShift is the maximum of:
- StretchStackBottomShiftDown
- StretchStackGapAboveMin + the ascent of the munder underscript.
UnderExtraDescender is 0.
Otherwise, UnderShift is equal to UnderbarVerticalGap if the accentunder attribute is not an ASCII case-insensitive match to true and to zero otherwise. UnderExtraAscender is UnderbarExtraDescender.

The line-ascent of the math content is the maximum between:

The line-ascent of the munder base's margin box.
The line-ascent of the munder underscript's margin box − UnderShift.

The line-descent of the math content is the maximum between:

The line-descent of the munder base's margin box.
The line-descent of the munder underscript's margin box + UnderShift + UnderExtraAscender.

The alphabetic baseline of the munder base is aligned with the alphabetic baseline. The alphabetic baseline of the munder underscript is shifted away from the alphabetic baseline and towards the line-under by a distance equal to the ink line-descent of the munder base's margin box + UnderShift.

The math content box is placed within the content box so that their block-start edges are aligned and the middles of these edges are at the same position.

The <mover> element is laid out as shown on Figure 21. LargeOpItalicCorrection is the italic correction of the mover base if it is an embellished operator with the largeop property and 0 otherwise.

Figure 21 Box model for the `<mover>` element

The min-content inline size (respectively max-content inline size) of the math content are calculated like the inline size of the math content below but replacing the inline sizes of the mover base's margin box and mover overscript's margin box with the min-content inline size (respectively max-content inline size) of the mover base's margin box and mover overscript's margin box.

The in-flow children are laid out using the algorithm for stretching operators along the inline axis.

The TopAccentAttachment is the top accent attachment of the mover overscript or half the inline size of the mover overscript's margin box if it is undefined.

The inline size of the math content is calculated by applying the algorithm for stretching operators along the inline axis for layout and determining the absolute difference between:

The maximum of:
- Half the inline size of the mover base's margin box.
- The inline size of the mover overscript's margin box − TopAccentAttachment + half LargeOpItalicCorrection.
The minimum of:
- −half the inline size of the mover base's margin box.
- −TopAccentAttachment + half LargeOpItalicCorrection.

If m is the minimum calculated in the second item above then the inline offset of the mover base is −m − half the inline size of the base's margin. The inline offset of the mover overscript is −m − half the inline size of the mover overscript's margin box + half LargeOpItalicCorrection.

Parameters OverShift and OverExtraDescender are determined by considering three cases in the following order:

The mover base is an embellished operator with the largeop property. OverShift is the maximum of
- UpperLimitBaselineRiseMin
- UpperLimitGapMin + the descent of the mover overscript.
OverExtraAscender is 0.
The mover base is an embellished operator with the stretchy property and stretch axis inline. OverShift is the maximum of:
- StretchStackTopShiftUp
- StretchStackGapBelowMin + the descent of the mover overscript.
OverExtraDescender is 0.
Otherwise, OverShift is equal to
1. OverbarVerticalGap if the accent attribute is not an ASCII case-insensitive match to true.
2. Or AccentBaseHeight minus the line-ascent of the mover base's margin box if this difference is nonnegative.
3. Or 0 otherwise.
OverExtraAscender is OverbarExtraAscender.

Note

For accent overscripts and bases with line-ascents that are at most AccentBaseHeight, the rule from [OPEN-FONT-FORMAT] [TEXBOOK] is actually to align the alphabetic baselines of the overscripts and of the bases. This assumes that accent glyphs are designed in such a way that their ink bottoms are more or less AccentBaseHeight above their alphabetic baselines. Hence, the previous rule will guarantee that all the overscript bottoms are aligned while still avoiding collision with the bases. However, MathML can have arbitrary accent overscripts, so a more general and simpler rule is provided above: Ensure that the bottom of overscript is at least AccentBaseHeight above the alphabetic baseline of the base.

The line-ascent of the math content is the maximum between:

The line-ascent of the mover base's margin box.
The line-ascent of the mover overscript's margin box + OverShift + OverExtraAscender.

The line-descent of the math content is the maximum between:

The line-descent of the mover base's margin box.
The line-descent of the mover overscript's margin box − OverShift.

The alphabetic baseline of the mover base is aligned with the alphabetic baseline. The alphabetic baseline of the mover overscript is shifted away from the alphabetic baseline and towards the line-over by a distance equal to the ink line-ascent of the base + OverShift.

The math content box is placed within the content box so that their block-start edges are aligned and the middles of these edges are at the same position.

The general layout of <munderover> is shown on Figure 22. The LargeOpItalicCorrection, UnderShift, UnderExtraDescender, OverShift, OverExtraDescender parameters are calculated the same as in 3.4.2.3 Base with underscript and 3.4.2.4 Base with overscript.

Figure 22 Box model for the `<munderover>` element

The min-content inline size, max-content inline size and inline size of the math content are calculated as an absolute difference between a maximum inline offset and minimum inline offset. These extrema are calculated by taking the extremum value of the corresponding extrema calculated in 3.4.2.3 Base with underscript and 3.4.2.4 Base with overscript. The inline offsets of the munderover base, munderover underscript and munderover overscript are calculated as in these sections but using the new minimum m (minimum of the corresponding minima).

Like in these sections, the in-flow children are laid out using the algorithm for stretching operators along the inline axis.

The line-ascent and line-descent of the math content are also calculated by taking the extremum value of the extrema calculated in 3.4.2.3 Base with underscript and 3.4.2.4 Base with overscript.

Finally, the alphabetic baselines of the munderover base, munderover underscript and munderover overscript are calculated as in sections 3.4.2.3 Base with underscript and 3.4.2.4 Base with overscript.

The math content box is placed within the content box so that their block-start edges are aligned and the middles of these edges are at the same position.

Note

When the underscript (respectively overscript) is an empty box, the base and overscript (respectively underscript) are laid out similarly to 3.4.2.4 Base with overscript (respectively 3.4.2.3 Base with underscript) but the position of the empty underscript (respectively overscript) may add extra space. In order to keep the algorithm simple, no attempt is made to handle empty scripts in a special way.

Presubscripts and tensor notations are represented by the mmultiscripts element. The mprescripts element is used as a separator between the postscripts and prescripts. These two elements accept the attributes described in 2.1.3 Global Attributes.

The following example shows basic use of prescripts and postscripts, involving a mprescripts. Empty mrow elements are used at positions where no scripts are rendered. The font-size is automatically scaled down within the scripts.

<math>   <mmultiscripts>     <mn>1</mn>     <mn>2</mn>     <mn>3</mn>     <mrow></mrow>     <mn>5</mn>     <mprescripts/>     <mn>6</mn>     <mrow></mrow>     <mn>8</mn>     <mn>9</mn>   </mmultiscripts> </math>

If the <mmultiscripts> or <mprescripts> elements do not have their computed display property equal to block math or inline math then they are laid out according to the CSS specification where the corresponding value is described. Otherwise, the layout below is performed.

The <mprescripts> element is laid out as an mrow element.

A valid <mmultiscripts> element contains the following in-flow children:

A first in-flow child, called the mmultiscripts base, that is not an mprescripts element.
Followed by an even number of in-flow children called mmultiscripts postscripts, none of them being a mprescripts element. These scripts form a (possibly empty) list subscript, superscript, subscript, superscript, subscript, superscript, etc. Each consecutive couple of children subscript, superscript is called a subscript/superscript pair.
Optionally followed by an mprescripts element and an even number of in-flow children called mmultiscripts prescripts, none of them being a mprescripts element. These scripts form a (possibly empty) list of subscript/superscript pair.

If an <mmultiscripts> element is not valid then it is laid out the same as the mrow element. Otherwise the layout algorithm is performed as in 3.4.3.1 Base with prescripts and postscripts.

The <mmultiscripts> element is laid out as shown on Figure 23. For each subscript/superscript pair of mmultiscripts postscripts, the ItalicCorrection LargeOpItalicCorrection are defined as in 3.4.1.2 Base with subscript and 3.4.1.3 Base with superscript.

Figure 23 Box model for the `<mmultiscripts>` element

The min-content inline size (respectively max-content inline size) of the math content is calculated the same as the inline size of the math content below, but replacing "inline size" with "min-content inline size" (respectively "max-content inline size") for the mmultiscripts base's margin box and scripts' margin boxes.

If there is an inline stretch size constraint or a block stretch size constraint the mmultiscripts base is also laid out with the same stretch size constraint. Otherwise it is laid out without any stretch size constraint. The other elements are always laid out without any stretch size constraint.

The inline size of the math content is calculated with the following algorithm:

Set inline-offset to 0.
For each subscript/superscript pair of mmultiscripts prescripts, increment inline-offset by SpaceAfterScript + the maximum of
- The inline size of the subscript's margin box.
- The inline size of the superscript's margin box.
Increment inline-offset by the inline size of the mmultiscripts base's margin box and set inline-size to inline-offset.
For each subscript/superscript pair of mmultiscripts postscripts, modify inline-size to be at least:
- x + the inline size of the subscript's margin box + LargeOpItalicCorrection.
- x + the inline size of the superscript's margin box − ItalicCorrection.
Increment inline-offset to the maximum of:
- the inline size of the subscript's margin box.
- the inline size of the superscript's margin box.
Increment inline-offset by SpaceAfterScript.
Return inline-size.

SubShift (respectively SuperShift) is calculated by taking the maximum of all subshifts (respectively supershifts) of each subscript/superscript pair as described in 3.4.1.4 Base with subscript and superscript.

The line-ascent of the math content is calculated by taking the maximum of all the line-ascent of each subscript/superscript pair as described in 3.4.1.4 Base with subscript and superscript but using the SubShift and SuperShift values calculated above.

The line-descent of the math content is calculated by taking the maximum of all the line-descent of each subscript/superscript pair as described in 3.4.1.4 Base with subscript and superscript but using the SubShift and SuperShift values calculated above.

Finally, the placement of the in-flow children is performed using the following algorithm:

Set inline-offset to 0.
For each subscript/superscript pair of mmultiscripts prescripts:
1. Increment inline-offset by SpaceAfterScript.
2. Set pair-inline-size to the maximum of
  - the inline size of the subscript's margin box.
  - the inline size of the superscript's margin box.
3. Place the subscript at inline-start position inline-offset + pair-inline-size − the inline size of the subscript's margin box.
4. Place the superscript at inline-start position inline-offset + pair-inline-size − the inline size of the superscript's margin box.
5. Place the subscript (respectively superscript) so its alphabetic baseline is shifted away from the alphabetic baseline by SubShift (respectively SuperShift) towards the line-under (respectively line-over).
6. Increment inline-offset by pair-inline-size.
Place the mmultiscripts base and <mprescripts> boxes at inline offsets inline-offset and with their alphabetic baselines aligned with the alphabetic baseline.
For each subscript/superscript pair of mmultiscripts postscripts:
1. Set pair-inline-size to the maximum of
  - the inline size of the subscript's margin box.
  - the inline size of the superscript's margin box.
2. Place the subscript at inline-start position inline-offset − LargeOpItalicCorrection.
3. Place the superscript at inline-start position inline-offset + ItalicCorrection.
4. Place the subscript (superscript) so its alphabetic baseline is shifted away from the alphabetic baseline by SubShift (respectively SuperShift) towards the line-under (respectively line-over).
5. Increment inline-offset by pair-inline-size.
6. Increment inline-offset by SpaceAfterScript.

Note

An <mmultiscripts> with only one subscript/superscript pair of mmultiscripts postscripts is laid out the same as a <msubsup> with the same in-flow children. However, as noticed for <msubsup>, if additionally the subscript (respectively superscript) is an empty box then it is not necessarily laid out the same as an <msub> (respectively <msup>) element. In order to keep the algorithm simple, no attempt is made to handle empty scripts in a special way.

For all scripted elements, the rule of thumb is to set displaystyle to false and to increment scriptlevel in all child elements but the first one. However, an mover (respectively munderover) element with an accent attribute that is an ASCII case-insensitive match to true does not increment scriptlevel within its second child (respectively third child). Similarly, mover and munderover elements with an accentunder attribute that is an ASCII case-insensitive match to true do not increment scriptlevel within their second child.

<mmultiscripts> sets math-shift to compact on its children at even position if they are before an mprescripts, and on those at odd position if they are after an mprescripts. The <msub> and <msubsup> elements set math-shift to compact on their second child. mover and munderover elements with an accent attribute that is an ASCII case-insensitive match to true also set math-shift to compact within their first child.

The A. User Agent Stylesheet must contain the following style in order to implement this behavior:

msub > :not(:first-child), msup > :not(:first-child), msubsup > :not(:first-child), mmultiscripts > :not(:first-child), munder > :not(:first-child), mover > :not(:first-child), munderover > :not(:first-child) {   math-depth: add(1);   math-style: compact; } munder[accentunder="true" i] > :nth-child(2), mover[accent="true" i] > :nth-child(2), munderover[accentunder="true" i] > :nth-child(2), munderover[accent="true" i] > :nth-child(3) {   font-size: inherit; } msub > :nth-child(2), msubsup > :nth-child(2), mmultiscripts > :nth-child(even), mmultiscripts > mprescripts ~ :nth-child(odd), mover[accent="true" i] > :first-child, munderover[accent="true" i] > :first-child {   math-shift: compact; } mmultiscripts > mprescripts ~ :nth-child(even) {   math-shift: inherit; }

Note

In practice, all the children of the MathML elements described in this section are in-flow and the <mprescripts> is empty. Hence the CSS rules essentially perform automatic displaystyle and scriptlevel changes for the scripts; and math-shift changes for subscripts and sometimes the base.

Matrices, arrays and other table-like mathematical notation are marked up using mtable mtr mtd elements. These elements are similar to the table, tr and td elements of [HTML].

The following example shows how tabular layout allows to write a matrix. Note that it is vertically centered with the fraction bar and the middle of the equal sign.

<math>   <mfrac>     <mi>A</mi>     <mn>2</mn>   </mfrac>   <mo>=</mo>   <mrow>     <mo>(</mo>     <mtable>       <mtr>         <mtd><mn>1</mn></mtd>         <mtd><mn>2</mn></mtd>         <mtd><mn>3</mn></mtd>       </mtr>       <mtr>         <mtd><mn>4</mn></mtd>         <mtd><mn>5</mn></mtd>         <mtd><mn>6</mn></mtd>       </mtr>       <mtr>         <mtd><mn>7</mn></mtd>         <mtd><mn>8</mn></mtd>         <mtd><mn>9</mn></mtd>       </mtr>     </mtable>     <mo>)</mo>   </mrow> </math>

The mtable is laid out as an inline-table and sets displaystyle to false. The user agent stylesheet must contain the following rules in order to implement these properties:

mtable {   display: inline-table;   math-style: compact; }

The mtable element is as a CSS table and the min-content inline size, max-content inline size, inline size, block size, first baseline set and last baseline set sets are determined accordingly. The center of the table is aligned with the math axis.

The <mtable> accepts the attributes described in 2.1.3 Global Attributes.

The mtr is laid out as table-row. The user agent stylesheet must contain the following rules in order to implement that behavior:

mtr {   display: table-row; }

The <mtr> accepts the attributes described in 2.1.3 Global Attributes.

The mtd is laid out as a table-cell with content centered in the cell and a default padding. The user agent stylesheet must contain the following rules:

mtd {   display: table-cell;   /* Centering inside table cells should rely on box alignment properties.      See https://github.com/w3c/mathml-core/issues/156 */   text-align: center;   padding: 0.5ex 0.4em; }

The <mtd> accepts the attributes described in 2.1.3 Global Attributes as well as the following attributes:

The columnspan (respectively rowspan) attribute has the same syntax and semantics as the colspan (respectively rowspan) attribute on the <td> element from [HTML]. In particular, the parsing of these attributes is handled as described in the algorithm for processing rows, always reading "colspan" as "columnspan".

Note

The name of the column spanning attribute in [MathML3] and earlier versions is columnspan and is preserved for backward compatibility reasons.

The <mtd> element generates an anonymous <mrow> box.

Historically, the maction element provides a mechanism for binding actions to expressions.

The <maction> element accepts the attributes described in 2.1.3 Global Attributes as well as the following attributes:

actiontype
selection

This specification does not define any observable behavior that is specific to the actiontype and selection attributes.

The following example shows the "toggle" action type from [MathML3] where the renderer alternately displays the selected subexpression, starting from "one third" and cycling through them when there is a click on the selected subexpression ("one quarter", "one half", "one third", etc). This is not part of MathML Core but can be implemented using JavaScript and CSS polyfills. The default behavior is just to render the first child.

<math>   <maction actiontype="toggle" selection="2">     <mfrac>       <mn>1</mn>       <mn>2</mn>     </mfrac>     <mfrac>       <mn>1</mn>       <mn>3</mn>     </mfrac>     <mfrac>       <mn>1</mn>       <mn>4</mn>     </mfrac>   </maction> </math>

The layout algorithm of the <maction> element is the same as the <mrow> element. The user agent stylesheet must contain the following rules in order to hide all but its first child element, which is the default behavior for the legacy actiontype values:

maction > :not(:first-child) {   display: none; }

Note

<maction> is implemented for compatibility with full MathML. Authors whose only target is MathML Core are encouraged to use other HTML, CSS and JavaScript mechanisms to implement custom actions. They may rely on maction attributes defined in [MathML3].

The semantics element is the container element that associates annotations with a MathML expression. Typically, the <semantics> element has as its first child element a MathML expression to be annotated while subsequent child elements represent text annotations within an annotation element, or more complex markup annotations within an annotation-xml element.

The following example shows how the fraction "one half" can be annotated with a textual annotation (LaTeX) or an XML annotation (content MathML), which are not intended to be rendered by the user agent. This fraction is also annotated with equivalent SVG and HTML markup.

<math>   <semantics>     <mfrac>       <mn>1</mn>       <mn>2</mn>     </mfrac>     <annotation encoding="application/x-tex">\frac{1}{2}</annotation>     <annotation-xml encoding="application/mathml-content+xml">       <apply>         <divide/>          <cn>1</cn>          <cn>2</cn>       </apply>     </annotation-xml>     <annotation-xml>       <svg width="25" height="75" xmlns="http://www.w3.org/2000/svg">         <path stroke-width="5.8743"               d="m5.9157 27.415h6.601v-22.783l-7.1813 1.4402v-3.6805l7.1408                  -1.4402h4.0406v26.464h6.601v3.4005h-17.203z"/>         <path stroke="#000000" stroke-width="2.3409"               d="m0.83496 39.228h23.327"/>         <path stroke-width="5.8743"               d="m8.696 70.638h14.102v3.4005h-18.963v-3.4005q2.3004-2.3804                  6.2608-6.3813 3.9806-4.0206 5.0007-5.1808 1.9403-2.1803                  2.7004-3.6805 0.78011-1.5202 0.78011-2.9804 0-2.3804                  -1.6802-3.8806-1.6603-1.5002-4.3406-1.5002-1.9003 0-4.0206                  0.6601-2.1003 0.6601-4.5007 2.0003v-4.0806q2.4404-0.98013                  4.5607-1.4802 2.1203-0.50007 3.8806-0.50007 4.6407 0 7.401                  2.3203 2.7604 2.3203 2.7604 6.2009 0 1.8403-0.7001 3.5006                  -0.68013 1.6402-2.5004 3.8806-0.50007 0.58009-3.1805 3.3605                  -2.6804 2.7604-7.5614 7.7412z"/>       </svg>     </annotation-xml>     <annotation-xml encoding="application/xhtml+xml">       <div style="display: inline-flex;                   flex-direction: column; align-items: center;">         <div>1</div>         <div>―</div>         <div>2</div>       </div>     </annotation-xml>   </semantics> </math>

The <semantics> element accepts the attributes described in 2.1.3 Global Attributes. Its layout algorithm is the same as the mrow element. The user agent stylesheet must contain the following rule in order to only render the annotated MathML expression:

semantics > :not(:first-child) {   display: none; }

The <annotation-xml> and <annotation> element accepts the attributes described in 2.1.3 Global Attributes as well as the following attribute:

encoding

This specification does not define any observable behavior that is specific to the encoding attribute.

The layout algorithm of the <annotation-xml> and <annotation> element is the same as the mtext element.

Note

Authors can use the encoding attribute to distinguish annotations for HTML integration point, clipboard copy, alternative rendering, etc. In particular, CSS can be used to render alternative annotations, e.g.

/* Hide the annotated child. */ semantics > :first-child { display: none; }  /* Show all text annotations. */ semantics > annotation { display: inline; } /* Show all HTML annotations. */ semantics > annotation-xml[encoding="text/html" i], semantics > annotation-xml[encoding="application/xhtml+xml" i] {   display: inline-block; }

Name:	display
New values:	<display-outside> \|\| [ <display-inside> \| math ]

Name:	math-style
Value:	normal \| compact
Initial:	normal
Applies to:	All elements
Inherited:	yes
Percentages:	n/a
Computed value:	specified keyword
Canonical order:	n/a
Animation type:	not animatable
Media:	visual

Name:	math-shift
Value:	normal \| compact
Initial:	normal
Applies to:	All elements
Inherited:	yes
Percentages:	n/a
Computed value:	specified keyword
Canonical order:	n/a
Animation type:	not animatable
Media:	visual

Name:	math-depth
Value:	auto-add \| add(<integer>) \| <integer>
Initial:	0
Applies to:	All elements
Inherited:	yes
Percentages:	n/a
Computed value:	an integer, see below
Canonical order:	n/a
Animation type:	not animatable
Media:	visual

Note

This section describes how to determine values of 3.2.4.2 Dictionary-based attributes and stretch axis of operators. Compact tables below are suitable for computer manipulation, see B.2 Operator Dictionary (human-readable) for an alternative presentation.

The algorithm to set the properties of an operator from its category is as follows:

Set minsize to 100%.
Set maxsize to ∞.
Find the row corresponding to the specified category on Figure 26.
Set lspace and rspace to the value specified in the corresponding column.
For each property stretchy, symmetric, largeop, movablelimits, set that property to true if it is listed in the last column or to false otherwise.

The algorithm to determine the category of an operator (Content, Form) is as folllows:

If Content as an UTF-16 string does not have length or 1 or 2 then exit with category Default.
If Content is a single character in the range U+0320–U+03FF then exit with category Default. Otherwise, if it has two characters:
- If Content is the surrogate pairs corresponding to U+1EEF0 ARABIC MATHEMATICAL OPERATOR MEEM WITH HAH WITH TATWEEL or U+1EEF1 ARABIC MATHEMATICAL OPERATOR HAH WITH DAL and Form is postfix, exit with category I.
- If the second character is U+0338 COMBINING LONG SOLIDUS OVERLAY or U+20D2 COMBINING LONG VERTICAL LINE OVERLAY then replace Content with the first character and move to step 3.
- Otherwise, if Content is listed in Operators_2_ascii_chars then replace Content with the Unicode character "U+0320 plus the index of Content in Operators_2_ascii_chars" and move to step 3.
- Otherwise exit with category Default.
If Form is infix and Content corresponds to one of U+007C VERTICAL LINE or U+223C TILDE OPERATOR then exit with category ForceDefault. If the category of (Content, Form) provided by table Figure 25 has N/A encoding in table Figure 26 (namely if it has category L or M), then exit with that category. Otherwise:
- Set Key to Content if it is in range U+0000–U+03FF; or to Content − 0x1C00 if it is in range U+2000–U+2BFF. Otherwise, exit with category Default.
- Add 0x0000, 0x1000, 0x2000 to Key according to whether Form is infix, prefix, postfix respectively.
- Assert: Key is at most 0x2FFF.
- Search an Entry in table Figure 27 such that Entry % 0x4000 is equal to Key. If one is found then return the category corresponding to encoding Entry / 0x1000 in Figure 26. Otherwise, return category Default.

Special Table	Entries
`Operators_2_ascii_chars`	18 entries (2-characters ASCII strings): `'!!', '!=', '&&', '*', '=', '++', '+=', '--', '-=', '->', '//', '/=', ':=', '<=', '<>', '==', '>=', '\|\|',`
`Operators_fence`	61 entries (16 Unicode ranges): `[U+0028–U+0029], {U+005B}, {U+005D}, [U+007B–U+007D], {U+0331}, {U+2016}, [U+2018–U+2019], [U+201C–U+201D], [U+2308–U+230B], [U+2329–U+232A], [U+2772–U+2773], [U+27E6–U+27EF], {U+2980}, [U+2983–U+2999], [U+29D8–U+29DB], [U+29FC–U+29FD],`
`Operators_separator`	3 entries: `U+002C, U+003B, U+2063,`

Figure 24 Special tables for the operator dictionary.
Total size: 82 entries, 90 bytes
(assuming characters are UTF-16 and 1-byte range lengths).

(Content, Form) keys	Category
313 entries (35 Unicode ranges) in infix form: [U+2190–U+2195], [U+219A–U+21AE], [U+21B0–U+21B5], {U+21B9}, [U+21BC–U+21D5], [U+21DA–U+21F0], [U+21F3–U+21FF], {U+2794}, {U+2799}, [U+279B–U+27A1], [U+27A5–U+27A6], [U+27A8–U+27AF], {U+27B1}, {U+27B3}, {U+27B5}, {U+27B8}, [U+27BA–U+27BE], [U+27F0–U+27F1], [U+27F4–U+27FF], [U+2900–U+2920], [U+2934–U+2937], [U+2942–U+2975], [U+297C–U+297F], [U+2B04–U+2B07], [U+2B0C–U+2B11], [U+2B30–U+2B3E], [U+2B40–U+2B4C], [U+2B60–U+2B65], [U+2B6A–U+2B6D], [U+2B70–U+2B73], [U+2B7A–U+2B7D], [U+2B80–U+2B87], {U+2B95}, [U+2BA0–U+2BAF], {U+2BB8},	A
108 entries (31 Unicode ranges) in infix form: `{U+002B}, {U+002D}, {U+00B1}, {U+00F7}, {U+0322}, {U+2044}, [U+2212–U+2216], [U+2227–U+222A], {U+2236}, {U+2238}, [U+228C–U+228E], [U+2293–U+2296], {U+2298}, [U+229D–U+229F], [U+22BB–U+22BD], [U+22CE–U+22CF], [U+22D2–U+22D3], [U+2795–U+2797], {U+29B8}, {U+29BC}, [U+29C4–U+29C5], [U+29F5–U+29FB], [U+2A1F–U+2A2E], [U+2A38–U+2A3A], {U+2A3E}, [U+2A40–U+2A4F], [U+2A51–U+2A63], {U+2ADB}, {U+2AF6}, {U+2AFB}, {U+2AFD},`	B
64 entries (33 Unicode ranges) in infix form: `{U+0025}, {U+002A}, {U+002E}, [U+003F–U+0040], {U+005E}, {U+00B7}, {U+00D7}, {U+0323}, {U+032E}, {U+2022}, {U+2043}, [U+2217–U+2219], {U+2240}, {U+2297}, [U+2299–U+229B], [U+22A0–U+22A1], {U+22BA}, [U+22C4–U+22C7], [U+22C9–U+22CC], [U+2305–U+2306], {U+27CB}, {U+27CD}, [U+29C6–U+29C8], [U+29D4–U+29D7], {U+29E2}, [U+2A1D–U+2A1E], [U+2A2F–U+2A37], [U+2A3B–U+2A3D], {U+2A3F}, {U+2A50}, [U+2A64–U+2A65], [U+2ADC–U+2ADD], {U+2AFE},`	C
52 entries (22 Unicode ranges) in prefix form: `{U+0021}, {U+002B}, {U+002D}, {U+00AC}, {U+00B1}, {U+0331}, {U+2018}, {U+201C}, [U+2200–U+2201], [U+2203–U+2204], {U+2207}, [U+2212–U+2213], [U+221F–U+2222], [U+2234–U+2235], {U+223C}, [U+22BE–U+22BF], {U+2310}, {U+2319}, [U+2795–U+2796], {U+27C0}, [U+299B–U+29AF], [U+2AEC–U+2AED],`	D
40 entries (21 Unicode ranges) in postfix form: `[U+0021–U+0022], [U+0025–U+0027], {U+0060}, {U+00A8}, {U+00B0}, [U+00B2–U+00B4], [U+00B8–U+00B9], [U+02CA–U+02CB], [U+02D8–U+02DA], {U+02DD}, {U+0311}, {U+0320}, {U+0325}, {U+0327}, {U+0331}, [U+2019–U+201B], [U+201D–U+201F], [U+2032–U+2037], {U+2057}, [U+20DB–U+20DC], {U+23CD},`	E
30 entries in prefix form: `U+0028, U+005B, U+007B, U+007C, U+2016, U+2308, U+230A, U+2329, U+2772, U+27E6, U+27E8, U+27EA, U+27EC, U+27EE, U+2980, U+2983, U+2985, U+2987, U+2989, U+298B, U+298D, U+298F, U+2991, U+2993, U+2995, U+2997, U+2999, U+29D8, U+29DA, U+29FC,`	F
30 entries in postfix form: `U+0029, U+005D, U+007C, U+007D, U+2016, U+2309, U+230B, U+232A, U+2773, U+27E7, U+27E9, U+27EB, U+27ED, U+27EF, U+2980, U+2984, U+2986, U+2988, U+298A, U+298C, U+298E, U+2990, U+2992, U+2994, U+2996, U+2998, U+2999, U+29D9, U+29DB, U+29FD,`	G
27 entries (2 Unicode ranges) in prefix form: `[U+222B–U+2233], [U+2A0B–U+2A1C],`	H
22 entries (13 Unicode ranges) in postfix form: `[U+005E–U+005F], {U+007E}, {U+00AF}, [U+02C6–U+02C7], {U+02C9}, {U+02CD}, {U+02DC}, {U+02F7}, {U+0302}, {U+203E}, [U+2322–U+2323], [U+23B4–U+23B5], [U+23DC–U+23E1],`	I
22 entries (6 Unicode ranges) in prefix form: `[U+220F–U+2211], [U+22C0–U+22C3], [U+2A00–U+2A0A], [U+2A1D–U+2A1E], {U+2AFC}, {U+2AFF},`	J
8 entries (5 Unicode ranges) in infix form: `{U+002F}, {U+005C}, {U+005F}, [U+2061–U+2064], {U+2206},`	K
6 entries (3 Unicode ranges) in prefix form: `[U+2145–U+2146], {U+2202}, [U+221A–U+221C],`	L
3 entries in infix form: `U+002C, U+003A, U+003B,`	M

Figure 25 Mapping from operator (Content, Form) to a category.
Total size: 725 entries, 639 bytes
(assuming characters are UTF-16 and 1-byte range lengths).

Category	Form	Encoding	lspace	rspace	properties
Default	N/A	N/A	`0.2777777777777778em`	`0.2777777777777778em`	N/A
ForceDefault	N/A	N/A	`0.2777777777777778em`	`0.2777777777777778em`	N/A
A	infix	0x0	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
B	infix	0x4	`0.2222222222222222em`	`0.2222222222222222em`	N/A
C	infix	0x8	`0.16666666666666666em`	`0.16666666666666666em`	N/A
D	prefix	0x1	`0`	`0`	N/A
E	postfix	0x2	`0`	`0`	N/A
F	prefix	0x5	`0`	`0`	stretchy symmetric
G	postfix	0x6	`0`	`0`	stretchy symmetric
H	prefix	0x9	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop
I	postfix	0xA	`0`	`0`	stretchy
J	prefix	0xD	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop movablelimits
K	infix	0xC	`0`	`0`	N/A
L	prefix	N/A	`0.16666666666666666em`	`0`	N/A
M	infix	N/A	`0`	`0.16666666666666666em`	N/A

Figure 26 Operators values for each category.
The third column provides a 4-bit encoding of the categories
where the 2 least significant bits encode the form infix (0), prefix (1) and postfix (2).

716 entries (236 ranges of length at most 16):

{0x8025}, {0x802A}, {0x402B}, {0x402D}, {0x802E}, {0xC02F}, [0x803F–0x8040], {0xC05C}, {0x805E}, {0xC05F}, {0x40B1}, {0x80B7}, {0x80D7}, {0x40F7}, {0x4322}, {0x8323}, {0x832E}, {0x8422}, {0x8443}, {0x4444}, [0xC461–0xC464], [0x0590–0x0595], [0x059A–0x05A9], [0x05AA–0x05AE], [0x05B0–0x05B5], {0x05B9}, [0x05BC–0x05CB], [0x05CC–0x05D5], [0x05DA–0x05E9], [0x05EA–0x05F0], [0x05F3–0x05FF], {0xC606}, [0x4612–0x4616], [0x8617–0x8619], [0x4627–0x462A], {0x4636}, {0x4638}, {0x8640}, [0x468C–0x468E], [0x4693–0x4696], {0x8697}, {0x4698}, [0x8699–0x869B], [0x469D–0x469F], [0x86A0–0x86A1], {0x86BA}, [0x46BB–0x46BD], [0x86C4–0x86C7], [0x86C9–0x86CC], [0x46CE–0x46CF], [0x46D2–0x46D3], [0x8705–0x8706], {0x0B94}, [0x4B95–0x4B97], {0x0B99}, [0x0B9B–0x0BA1], [0x0BA5–0x0BA6], [0x0BA8–0x0BAF], {0x0BB1}, {0x0BB3}, {0x0BB5}, {0x0BB8}, [0x0BBA–0x0BBE], {0x8BCB}, {0x8BCD}, [0x0BF0–0x0BF1], [0x0BF4–0x0BFF], [0x0D00–0x0D0F], [0x0D10–0x0D1F], {0x0D20}, [0x0D34–0x0D37], [0x0D42–0x0D51], [0x0D52–0x0D61], [0x0D62–0x0D71], [0x0D72–0x0D75], [0x0D7C–0x0D7F], {0x4DB8}, {0x4DBC}, [0x4DC4–0x4DC5], [0x8DC6–0x8DC8], [0x8DD4–0x8DD7], {0x8DE2}, [0x4DF5–0x4DFB], [0x8E1D–0x8E1E], [0x4E1F–0x4E2E], [0x8E2F–0x8E37], [0x4E38–0x4E3A], [0x8E3B–0x8E3D], {0x4E3E}, {0x8E3F}, [0x4E40–0x4E4F], {0x8E50}, [0x4E51–0x4E60], [0x4E61–0x4E63], [0x8E64–0x8E65], {0x4EDB}, [0x8EDC–0x8EDD], {0x4EF6}, {0x4EFB}, {0x4EFD}, {0x8EFE}, [0x0F04–0x0F07], [0x0F0C–0x0F11], [0x0F30–0x0F3E], [0x0F40–0x0F4C], [0x0F60–0x0F65], [0x0F6A–0x0F6D], [0x0F70–0x0F73], [0x0F7A–0x0F7D], [0x0F80–0x0F87], {0x0F95}, [0x0FA0–0x0FAF], {0x0FB8}, {0x1021}, {0x5028}, {0x102B}, {0x102D}, {0x505B}, [0x507B–0x507C], {0x10AC}, {0x10B1}, {0x1331}, {0x5416}, {0x1418}, {0x141C}, [0x1600–0x1601], [0x1603–0x1604], {0x1607}, [0xD60F–0xD611], [0x1612–0x1613], [0x161F–0x1622], [0x962B–0x9633], [0x1634–0x1635], {0x163C}, [0x16BE–0x16BF], [0xD6C0–0xD6C3], {0x5708}, {0x570A}, {0x1710}, {0x1719}, {0x5729}, {0x5B72}, [0x1B95–0x1B96], {0x1BC0}, {0x5BE6}, {0x5BE8}, {0x5BEA}, {0x5BEC}, {0x5BEE}, {0x5D80}, {0x5D83}, {0x5D85}, {0x5D87}, {0x5D89}, {0x5D8B}, {0x5D8D}, {0x5D8F}, {0x5D91}, {0x5D93}, {0x5D95}, {0x5D97}, {0x5D99}, [0x1D9B–0x1DAA], [0x1DAB–0x1DAF], {0x5DD8}, {0x5DDA}, {0x5DFC}, [0xDE00–0xDE0A], [0x9E0B–0x9E1A], [0x9E1B–0x9E1C], [0xDE1D–0xDE1E], [0x1EEC–0x1EED], {0xDEFC}, {0xDEFF}, [0x2021–0x2022], [0x2025–0x2027], {0x6029}, {0x605D}, [0xA05E–0xA05F], {0x2060}, [0x607C–0x607D], {0xA07E}, {0x20A8}, {0xA0AF}, {0x20B0}, [0x20B2–0x20B4], [0x20B8–0x20B9], [0xA2C6–0xA2C7], {0xA2C9}, [0x22CA–0x22CB], {0xA2CD}, [0x22D8–0x22DA], {0xA2DC}, {0x22DD}, {0xA2F7}, {0xA302}, {0x2311}, {0x2320}, {0x2325}, {0x2327}, {0x2331}, {0x6416}, [0x2419–0x241B], [0x241D–0x241F], [0x2432–0x2437], {0xA43E}, {0x2457}, [0x24DB–0x24DC], {0x6709}, {0x670B}, [0xA722–0xA723], {0x672A}, [0xA7B4–0xA7B5], {0x27CD}, [0xA7DC–0xA7E1], {0x6B73}, {0x6BE7}, {0x6BE9}, {0x6BEB}, {0x6BED}, {0x6BEF}, {0x6D80}, {0x6D84}, {0x6D86}, {0x6D88}, {0x6D8A}, {0x6D8C}, {0x6D8E}, {0x6D90}, {0x6D92}, {0x6D94}, {0x6D96}, [0x6D98–0x6D99], {0x6DD9}, {0x6DDB}, {0x6DFD},

Figure 27 List of entries for the largest categories, sorted by key.
Key is Entry % 0x4000, category encoding is Entry / 0x1000.
Total size: 716 entries, 590 bytes
(assuming 4 bits for range lengths).

Note

Tables of Figure 25 and Figure 27 are encoded as ranges to take profit of the presence of many contiguous Unicode blocks.
To quickly find an entry in these tables, one can still perform a binary search over the range starts, followed by an extra check on the range length.
Since log is concave, it is more efficient to perform one binary search on the whole table of Figure 27 rather than on each large subtable of Figure 25.

The intrinsic stretch axis a Unicode character c is inline if it belongs to the list below. Otherwise, the intrinsic stretch axis of c is block.

U+003D, U+005E, U+005F, U+007E, U+00AF, U+02C6, U+02C7, U+02C9, U+02CD, U+02DC, U+02F7, U+0302, U+0332, U+203E, U+20D0, U+20D1, U+20D6, U+20D7, U+20E1, U+2190, U+2192, U+2194, U+2198, U+2199, U+219A, U+219B, U+219C, U+219D, U+219E, U+21A0, U+21A2, U+21A3, U+21A4, U+21A6, U+21A9, U+21AA, U+21AB, U+21AC, U+21AD, U+21AE, U+21B4, U+21B9, U+21BC, U+21BD, U+21C0, U+21C1, U+21C4, U+21C6, U+21C7, U+21C9, U+21CB, U+21CC, U+21CD, U+21CE, U+21CF, U+21D0, U+21D2, U+21D4, U+21DA, U+21DB, U+21DC, U+21DD, U+21E0, U+21E2, U+21E4, U+21E5, U+21E6, U+21E8, U+21F0, U+21F4, U+21F6, U+21F7, U+21F8, U+21F9, U+21FA, U+21FB, U+21FC, U+21FD, U+21FE, U+21FF, U+2322, U+2323, U+23B4, U+23B5, U+23DC, U+23DD, U+23DE, U+23DF, U+23E0, U+23E1, U+2500, U+2794, U+2799, U+279B, U+279C, U+279D, U+279E, U+279F, U+27A0, U+27A1, U+27A5, U+27A6, U+27A8, U+27A9, U+27AA, U+27AB, U+27AC, U+27AD, U+27AE, U+27AF, U+27B1, U+27B3, U+27B5, U+27B8, U+27BA, U+27BB, U+27BC, U+27BD, U+27BE, U+27F4, U+27F5, U+27F6, U+27F7, U+27F8, U+27F9, U+27FA, U+27FB, U+27FC, U+27FD, U+27FE, U+27FF, U+2900, U+2901, U+2902, U+2903, U+2904, U+2905, U+2906, U+2907, U+290C, U+290D, U+290E, U+290F, U+2910, U+2911, U+2914, U+2915, U+2916, U+2917, U+2918, U+2919, U+291A, U+291B, U+291C, U+291D, U+291E, U+291F, U+2920, U+2942, U+2943, U+2944, U+2945, U+2946, U+2947, U+2948, U+294A, U+294B, U+294E, U+2950, U+2952, U+2953, U+2956, U+2957, U+295A, U+295B, U+295E, U+295F, U+2962, U+2964, U+2966, U+2967, U+2968, U+2969, U+296A, U+296B, U+296C, U+296D, U+2970, U+2971, U+2972, U+2973, U+2974, U+2975, U+297C, U+297D, U+2B04, U+2B05, U+2B0C, U+2B30, U+2B31, U+2B32, U+2B33, U+2B34, U+2B35, U+2B36, U+2B37, U+2B38, U+2B39, U+2B3A, U+2B3B, U+2B3C, U+2B3D, U+2B3E, U+2B40, U+2B41, U+2B42, U+2B43, U+2B44, U+2B45, U+2B46, U+2B47, U+2B48, U+2B49, U+2B4A, U+2B4B, U+2B4C, U+2B60, U+2B62, U+2B64, U+2B6A, U+2B6C, U+2B70, U+2B72, U+2B7A, U+2B7C, U+2B80, U+2B82, U+2B84, U+2B86, U+2B95, U+FE35, U+FE36, U+FE37, U+FE38, U+1EEF0, U+1EEF1,

Figure 28 Sorted list of Unicode code points corresponding to operators with inline stretch axis.
Total size: 246 entries, 492 bytes (assuming 16 bits for all but the non-BMP entries).

Note

The intrinsic stretch axis could be included as a boolean property of the operator dictionary. But since it does not depend on the form and since very few operators can stretch along the inline axis, it is better implemented as a separate sorted array. Each entry can be encoded with 16 bytes if U+1EEF0 ARABIC MATHEMATICAL OPERATOR MEEM WITH HAH WITH TATWEEL and U+1EEF1 ARABIC MATHEMATICAL OPERATOR HAH WITH DAL are tested separately.

This section is non-normative.

The following dictionary provides a human-readable version of B.1 Operator Dictionary. Please refer to 3.2.4.2 Dictionary-based attributes for explanation about how to use this dictionary and how to determine the values Content and Form indexing together the dictionary.

The values for rspace and lspace are indicated in the corresponding columns. The values of stretchy, symmetric, largeop, movablelimits are true if they are listed in the "properties" column.

Content	Stretch Axis	form	lspace	rspace	properties
< U+003C	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
= U+003D	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
> U+003E	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
\| U+007C	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	fence
↖ U+2196	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
↗ U+2197	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
↘ U+2198	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
↙ U+2199	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
↯ U+21AF	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
↶ U+21B6	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
↷ U+21B7	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
↸ U+21B8	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
↺ U+21BA	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
↻ U+21BB	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⇖ U+21D6	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⇗ U+21D7	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⇘ U+21D8	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⇙ U+21D9	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⇱ U+21F1	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⇲ U+21F2	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
∈ U+2208	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
∉ U+2209	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
∊ U+220A	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
∋ U+220B	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
∌ U+220C	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
∍ U+220D	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
∝ U+221D	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
∣ U+2223	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
∤ U+2224	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
∥ U+2225	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
∦ U+2226	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
∷ U+2237	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
∹ U+2239	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
∺ U+223A	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
∻ U+223B	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
∼ U+223C	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
∽ U+223D	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
∾ U+223E	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≁ U+2241	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≂ U+2242	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≃ U+2243	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≄ U+2244	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≅ U+2245	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≆ U+2246	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≇ U+2247	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≈ U+2248	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≉ U+2249	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≊ U+224A	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≋ U+224B	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≌ U+224C	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≍ U+224D	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≎ U+224E	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≏ U+224F	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≐ U+2250	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≑ U+2251	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≒ U+2252	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≓ U+2253	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≔ U+2254	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≕ U+2255	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≖ U+2256	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≗ U+2257	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≘ U+2258	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≙ U+2259	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≚ U+225A	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≛ U+225B	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≜ U+225C	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≝ U+225D	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≞ U+225E	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≟ U+225F	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≠ U+2260	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≡ U+2261	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≢ U+2262	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≣ U+2263	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≤ U+2264	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≥ U+2265	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≦ U+2266	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≧ U+2267	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≨ U+2268	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≩ U+2269	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≪ U+226A	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≫ U+226B	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≬ U+226C	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≭ U+226D	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≮ U+226E	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≯ U+226F	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≰ U+2270	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≱ U+2271	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≲ U+2272	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≳ U+2273	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≴ U+2274	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≵ U+2275	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≶ U+2276	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≷ U+2277	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≸ U+2278	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≹ U+2279	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≺ U+227A	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≻ U+227B	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≼ U+227C	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≽ U+227D	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≾ U+227E	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
≿ U+227F	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊀ U+2280	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊁ U+2281	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊂ U+2282	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊃ U+2283	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊄ U+2284	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊅ U+2285	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊆ U+2286	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊇ U+2287	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊈ U+2288	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊉ U+2289	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊊ U+228A	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊋ U+228B	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊏ U+228F	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊐ U+2290	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊑ U+2291	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊒ U+2292	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊜ U+229C	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊢ U+22A2	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊣ U+22A3	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊦ U+22A6	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊧ U+22A7	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊨ U+22A8	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊩ U+22A9	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊪ U+22AA	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊫ U+22AB	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊬ U+22AC	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊭ U+22AD	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊮ U+22AE	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊯ U+22AF	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊰ U+22B0	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊱ U+22B1	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊲ U+22B2	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊳ U+22B3	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊴ U+22B4	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊵ U+22B5	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊶ U+22B6	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊷ U+22B7	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⊸ U+22B8	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋈ U+22C8	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋍ U+22CD	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋐ U+22D0	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋑ U+22D1	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋔ U+22D4	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋕ U+22D5	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋖ U+22D6	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋗ U+22D7	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋘ U+22D8	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋙ U+22D9	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋚ U+22DA	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋛ U+22DB	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋜ U+22DC	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋝ U+22DD	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋞ U+22DE	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋟ U+22DF	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋠ U+22E0	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋡ U+22E1	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋢ U+22E2	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋣ U+22E3	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋤ U+22E4	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋥ U+22E5	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋦ U+22E6	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋧ U+22E7	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋨ U+22E8	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋩ U+22E9	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋪ U+22EA	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋫ U+22EB	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋬ U+22EC	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋭ U+22ED	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋲ U+22F2	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋳ U+22F3	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋴ U+22F4	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋵ U+22F5	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋶ U+22F6	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋷ U+22F7	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋸ U+22F8	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋹ U+22F9	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋺ U+22FA	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋻ U+22FB	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋼ U+22FC	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋽ U+22FD	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋾ U+22FE	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⋿ U+22FF	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⌁ U+2301	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⍼ U+237C	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⎋ U+238B	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
➘ U+2798	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
➚ U+279A	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
➧ U+27A7	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
➲ U+27B2	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
➴ U+27B4	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
➶ U+27B6	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
➷ U+27B7	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
➹ U+27B9	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⟂ U+27C2	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⟲ U+27F2	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⟳ U+27F3	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⤡ U+2921	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⤢ U+2922	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⤣ U+2923	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⤤ U+2924	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⤥ U+2925	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⤦ U+2926	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⤧ U+2927	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⤨ U+2928	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⤩ U+2929	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⤪ U+292A	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⤫ U+292B	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⤬ U+292C	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⤭ U+292D	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⤮ U+292E	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⤯ U+292F	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⤰ U+2930	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⤱ U+2931	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⤲ U+2932	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⤳ U+2933	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⤸ U+2938	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⤹ U+2939	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⤺ U+293A	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⤻ U+293B	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⤼ U+293C	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⤽ U+293D	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⤾ U+293E	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⤿ U+293F	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⥀ U+2940	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⥁ U+2941	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⥶ U+2976	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⥷ U+2977	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⥸ U+2978	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⥹ U+2979	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⥺ U+297A	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⥻ U+297B	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⦁ U+2981	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⦂ U+2982	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⦶ U+29B6	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⦷ U+29B7	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⦹ U+29B9	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⧀ U+29C0	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⧁ U+29C1	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⧎ U+29CE	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⧏ U+29CF	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⧐ U+29D0	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⧑ U+29D1	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⧒ U+29D2	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⧓ U+29D3	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⧟ U+29DF	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⧡ U+29E1	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⧣ U+29E3	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⧤ U+29E4	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⧥ U+29E5	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⧦ U+29E6	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⧴ U+29F4	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⩦ U+2A66	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⩧ U+2A67	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⩨ U+2A68	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⩩ U+2A69	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⩪ U+2A6A	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⩫ U+2A6B	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⩬ U+2A6C	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⩭ U+2A6D	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⩮ U+2A6E	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⩯ U+2A6F	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⩰ U+2A70	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⩱ U+2A71	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⩲ U+2A72	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⩳ U+2A73	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⩴ U+2A74	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⩵ U+2A75	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⩶ U+2A76	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⩷ U+2A77	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⩸ U+2A78	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⩹ U+2A79	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⩺ U+2A7A	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⩻ U+2A7B	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⩼ U+2A7C	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⩽ U+2A7D	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⩾ U+2A7E	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⩿ U+2A7F	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪀ U+2A80	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪁ U+2A81	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪂ U+2A82	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪃ U+2A83	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪄ U+2A84	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪅ U+2A85	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪆ U+2A86	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪇ U+2A87	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪈ U+2A88	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪉ U+2A89	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪊ U+2A8A	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪋ U+2A8B	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪌ U+2A8C	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪍ U+2A8D	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪎ U+2A8E	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪏ U+2A8F	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪐ U+2A90	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪑ U+2A91	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪒ U+2A92	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪓ U+2A93	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪔ U+2A94	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪕ U+2A95	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪖ U+2A96	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪗ U+2A97	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪘ U+2A98	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪙ U+2A99	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪚ U+2A9A	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪛ U+2A9B	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪜ U+2A9C	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪝ U+2A9D	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪞ U+2A9E	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪟ U+2A9F	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪠ U+2AA0	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪡ U+2AA1	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪢ U+2AA2	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪣ U+2AA3	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪤ U+2AA4	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪥ U+2AA5	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪦ U+2AA6	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪧ U+2AA7	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪨ U+2AA8	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪩ U+2AA9	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪪ U+2AAA	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪫ U+2AAB	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪬ U+2AAC	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪭ U+2AAD	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪮ U+2AAE	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪯ U+2AAF	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪰ U+2AB0	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪱ U+2AB1	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪲ U+2AB2	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪳ U+2AB3	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪴ U+2AB4	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪵ U+2AB5	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪶ U+2AB6	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪷ U+2AB7	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪸ U+2AB8	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪹ U+2AB9	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪺ U+2ABA	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪻ U+2ABB	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪼ U+2ABC	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪽ U+2ABD	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪾ U+2ABE	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⪿ U+2ABF	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫀ U+2AC0	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫁ U+2AC1	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫂ U+2AC2	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫃ U+2AC3	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫄ U+2AC4	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫅ U+2AC5	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫆ U+2AC6	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫇ U+2AC7	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫈ U+2AC8	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫉ U+2AC9	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫊ U+2ACA	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫋ U+2ACB	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫌ U+2ACC	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫍ U+2ACD	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫎ U+2ACE	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫏ U+2ACF	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫐ U+2AD0	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫑ U+2AD1	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫒ U+2AD2	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫓ U+2AD3	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫔ U+2AD4	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫕ U+2AD5	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫖ U+2AD6	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫗ U+2AD7	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫘ U+2AD8	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫙ U+2AD9	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫚ U+2ADA	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫞ U+2ADE	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫟ U+2ADF	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫠ U+2AE0	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫡ U+2AE1	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫢ U+2AE2	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫣ U+2AE3	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫤ U+2AE4	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫥ U+2AE5	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫦ U+2AE6	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫧ U+2AE7	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫨ U+2AE8	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫩ U+2AE9	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫪ U+2AEA	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫫ U+2AEB	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫮ U+2AEE	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫲ U+2AF2	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫳ U+2AF3	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫴ U+2AF4	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫵ U+2AF5	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫷ U+2AF7	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫸ U+2AF8	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫹ U+2AF9	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⫺ U+2AFA	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⬀ U+2B00	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⬁ U+2B01	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⬂ U+2B02	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⬃ U+2B03	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⬈ U+2B08	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⬉ U+2B09	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⬊ U+2B0A	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⬋ U+2B0B	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⬿ U+2B3F	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⭍ U+2B4D	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⭎ U+2B4E	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⭏ U+2B4F	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⭚ U+2B5A	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⭛ U+2B5B	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⭜ U+2B5C	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⭝ U+2B5D	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⭞ U+2B5E	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⭟ U+2B5F	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⭦ U+2B66	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⭧ U+2B67	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⭨ U+2B68	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⭩ U+2B69	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⭮ U+2B6E	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⭯ U+2B6F	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⭶ U+2B76	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⭷ U+2B77	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⭸ U+2B78	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⭹ U+2B79	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⮈ U+2B88	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⮉ U+2B89	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⮊ U+2B8A	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⮋ U+2B8B	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⮌ U+2B8C	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⮍ U+2B8D	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⮎ U+2B8E	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⮏ U+2B8F	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⮔ U+2B94	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⮰ U+2BB0	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⮱ U+2BB1	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⮲ U+2BB2	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⮳ U+2BB3	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⮴ U+2BB4	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⮵ U+2BB5	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⮶ U+2BB6	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⮷ U+2BB7	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
⯑ U+2BD1	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
String != U+0021 U+003D	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
String *= U+002A U+003D	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
String += U+002B U+003D	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
String -= U+002D U+003D	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
String -> U+002D U+003E	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
String // U+002F U+002F	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
String /= U+002F U+003D	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
String := U+003A U+003D	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
String <= U+003C U+003D	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
String == U+003D U+003D	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
String >= U+003E U+003D	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	N/A
String \|\| U+007C U+007C	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	fence
← U+2190	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↑ U+2191	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
→ U+2192	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↓ U+2193	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↔ U+2194	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↕ U+2195	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↚ U+219A	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↛ U+219B	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↜ U+219C	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↝ U+219D	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↞ U+219E	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↟ U+219F	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↠ U+21A0	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↡ U+21A1	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↢ U+21A2	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↣ U+21A3	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↤ U+21A4	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↥ U+21A5	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↦ U+21A6	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↧ U+21A7	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↨ U+21A8	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↩ U+21A9	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↪ U+21AA	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↫ U+21AB	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↬ U+21AC	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↭ U+21AD	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↮ U+21AE	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↰ U+21B0	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↱ U+21B1	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↲ U+21B2	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↳ U+21B3	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↴ U+21B4	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↵ U+21B5	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↹ U+21B9	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↼ U+21BC	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↽ U+21BD	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↾ U+21BE	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
↿ U+21BF	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇀ U+21C0	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇁ U+21C1	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇂ U+21C2	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇃ U+21C3	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇄ U+21C4	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇅ U+21C5	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇆ U+21C6	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇇ U+21C7	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇈ U+21C8	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇉ U+21C9	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇊ U+21CA	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇋ U+21CB	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇌ U+21CC	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇍ U+21CD	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇎ U+21CE	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇏ U+21CF	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇐ U+21D0	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇑ U+21D1	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇒ U+21D2	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇓ U+21D3	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇔ U+21D4	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇕ U+21D5	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇚ U+21DA	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇛ U+21DB	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇜ U+21DC	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇝ U+21DD	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇞ U+21DE	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇟ U+21DF	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇠ U+21E0	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇡ U+21E1	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇢ U+21E2	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇣ U+21E3	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇤ U+21E4	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇥ U+21E5	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇦ U+21E6	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇧ U+21E7	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇨ U+21E8	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇩ U+21E9	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇪ U+21EA	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇫ U+21EB	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇬ U+21EC	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇭ U+21ED	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇮ U+21EE	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇯ U+21EF	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇰ U+21F0	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇳ U+21F3	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇴ U+21F4	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇵ U+21F5	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇶ U+21F6	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇷ U+21F7	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇸ U+21F8	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇹ U+21F9	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇺ U+21FA	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇻ U+21FB	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇼ U+21FC	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇽ U+21FD	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇾ U+21FE	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⇿ U+21FF	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
➔ U+2794	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
➙ U+2799	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
➛ U+279B	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
➜ U+279C	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
➝ U+279D	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
➞ U+279E	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
➟ U+279F	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
➠ U+27A0	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
➡ U+27A1	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
➥ U+27A5	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
➦ U+27A6	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
➨ U+27A8	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
➩ U+27A9	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
➪ U+27AA	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
➫ U+27AB	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
➬ U+27AC	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
➭ U+27AD	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
➮ U+27AE	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
➯ U+27AF	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
➱ U+27B1	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
➳ U+27B3	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
➵ U+27B5	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
➸ U+27B8	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
➺ U+27BA	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
➻ U+27BB	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
➼ U+27BC	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
➽ U+27BD	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
➾ U+27BE	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⟰ U+27F0	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⟱ U+27F1	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⟴ U+27F4	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⟵ U+27F5	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⟶ U+27F6	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⟷ U+27F7	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⟸ U+27F8	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⟹ U+27F9	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⟺ U+27FA	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⟻ U+27FB	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⟼ U+27FC	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⟽ U+27FD	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⟾ U+27FE	inline	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
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⮥ U+2BA5	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⮦ U+2BA6	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⮧ U+2BA7	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⮨ U+2BA8	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⮩ U+2BA9	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⮪ U+2BAA	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⮫ U+2BAB	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⮬ U+2BAC	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⮭ U+2BAD	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⮮ U+2BAE	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⮯ U+2BAF	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
⮸ U+2BB8	block	`infix`	`0.2777777777777778em`	`0.2777777777777778em`	stretchy
+ U+002B	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
- U+002D	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
± U+00B1	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
÷ U+00F7	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⁄ U+2044	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
− U+2212	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
∓ U+2213	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
∔ U+2214	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
∕ U+2215	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
∖ U+2216	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
∧ U+2227	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
∨ U+2228	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
∩ U+2229	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
∪ U+222A	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
∶ U+2236	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
∸ U+2238	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⊌ U+228C	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⊍ U+228D	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⊎ U+228E	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⊓ U+2293	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⊔ U+2294	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⊕ U+2295	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⊖ U+2296	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⊘ U+2298	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⊝ U+229D	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⊞ U+229E	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⊟ U+229F	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⊻ U+22BB	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⊼ U+22BC	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⊽ U+22BD	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⋎ U+22CE	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⋏ U+22CF	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⋒ U+22D2	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⋓ U+22D3	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
➕ U+2795	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
➖ U+2796	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
➗ U+2797	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⦸ U+29B8	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⦼ U+29BC	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⧄ U+29C4	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⧅ U+29C5	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⧵ U+29F5	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⧶ U+29F6	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⧷ U+29F7	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⧸ U+29F8	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⧹ U+29F9	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⧺ U+29FA	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⧻ U+29FB	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⨟ U+2A1F	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⨠ U+2A20	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⨡ U+2A21	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⨢ U+2A22	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⨣ U+2A23	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⨤ U+2A24	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⨥ U+2A25	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⨦ U+2A26	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⨧ U+2A27	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⨨ U+2A28	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⨩ U+2A29	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⨪ U+2A2A	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⨫ U+2A2B	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⨬ U+2A2C	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⨭ U+2A2D	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⨮ U+2A2E	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⨸ U+2A38	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⨹ U+2A39	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⨺ U+2A3A	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⨾ U+2A3E	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩀ U+2A40	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩁ U+2A41	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩂ U+2A42	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩃ U+2A43	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩄ U+2A44	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩅ U+2A45	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩆ U+2A46	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩇ U+2A47	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩈ U+2A48	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩉ U+2A49	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩊ U+2A4A	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩋ U+2A4B	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩌ U+2A4C	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩍ U+2A4D	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩎ U+2A4E	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩏ U+2A4F	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩑ U+2A51	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩒ U+2A52	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩓ U+2A53	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩔ U+2A54	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩕ U+2A55	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩖ U+2A56	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩗ U+2A57	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩘ U+2A58	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩙ U+2A59	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩚ U+2A5A	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩛ U+2A5B	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩜ U+2A5C	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩝ U+2A5D	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩞ U+2A5E	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩟ U+2A5F	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩠ U+2A60	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩡ U+2A61	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩢ U+2A62	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⩣ U+2A63	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⫛ U+2ADB	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⫶ U+2AF6	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⫻ U+2AFB	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
⫽ U+2AFD	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
String && U+0026 U+0026	block	`infix`	`0.2222222222222222em`	`0.2222222222222222em`	N/A
% U+0025	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
* U+002A	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
. U+002E	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
? U+003F	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
@ U+0040	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
^ U+005E	inline	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
· U+00B7	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
× U+00D7	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
• U+2022	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⁃ U+2043	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
∗ U+2217	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
∘ U+2218	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
∙ U+2219	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
≀ U+2240	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⊗ U+2297	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⊙ U+2299	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⊚ U+229A	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⊛ U+229B	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⊠ U+22A0	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⊡ U+22A1	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⊺ U+22BA	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⋄ U+22C4	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⋅ U+22C5	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⋆ U+22C6	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⋇ U+22C7	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⋉ U+22C9	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⋊ U+22CA	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⋋ U+22CB	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⋌ U+22CC	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⌅ U+2305	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⌆ U+2306	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⟋ U+27CB	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⟍ U+27CD	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⧆ U+29C6	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⧇ U+29C7	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⧈ U+29C8	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⧔ U+29D4	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⧕ U+29D5	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⧖ U+29D6	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⧗ U+29D7	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⧢ U+29E2	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⨝ U+2A1D	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⨞ U+2A1E	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⨯ U+2A2F	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⨰ U+2A30	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⨱ U+2A31	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⨲ U+2A32	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⨳ U+2A33	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⨴ U+2A34	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⨵ U+2A35	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⨶ U+2A36	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⨷ U+2A37	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⨻ U+2A3B	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⨼ U+2A3C	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⨽ U+2A3D	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⨿ U+2A3F	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⩐ U+2A50	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⩤ U+2A64	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⩥ U+2A65	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⫝̸ U+2ADC	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⫝ U+2ADD	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
⫾ U+2AFE	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
String ** U+002A U+002A	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
String <> U+003C U+003E	block	`infix`	`0.16666666666666666em`	`0.16666666666666666em`	N/A
! U+0021	block	`prefix`	`0`	`0`	N/A
+ U+002B	block	`prefix`	`0`	`0`	N/A
- U+002D	block	`prefix`	`0`	`0`	N/A
¬ U+00AC	block	`prefix`	`0`	`0`	N/A
± U+00B1	block	`prefix`	`0`	`0`	N/A
‘ U+2018	block	`prefix`	`0`	`0`	fence
“ U+201C	block	`prefix`	`0`	`0`	fence
∀ U+2200	block	`prefix`	`0`	`0`	N/A
∁ U+2201	block	`prefix`	`0`	`0`	N/A
∃ U+2203	block	`prefix`	`0`	`0`	N/A
∄ U+2204	block	`prefix`	`0`	`0`	N/A
∇ U+2207	block	`prefix`	`0`	`0`	N/A
− U+2212	block	`prefix`	`0`	`0`	N/A
∓ U+2213	block	`prefix`	`0`	`0`	N/A
∟ U+221F	block	`prefix`	`0`	`0`	N/A
∠ U+2220	block	`prefix`	`0`	`0`	N/A
∡ U+2221	block	`prefix`	`0`	`0`	N/A
∢ U+2222	block	`prefix`	`0`	`0`	N/A
∴ U+2234	block	`prefix`	`0`	`0`	N/A
∵ U+2235	block	`prefix`	`0`	`0`	N/A
∼ U+223C	block	`prefix`	`0`	`0`	N/A
⊾ U+22BE	block	`prefix`	`0`	`0`	N/A
⊿ U+22BF	block	`prefix`	`0`	`0`	N/A
⌐ U+2310	block	`prefix`	`0`	`0`	N/A
⌙ U+2319	block	`prefix`	`0`	`0`	N/A
➕ U+2795	block	`prefix`	`0`	`0`	N/A
➖ U+2796	block	`prefix`	`0`	`0`	N/A
⟀ U+27C0	block	`prefix`	`0`	`0`	N/A
⦛ U+299B	block	`prefix`	`0`	`0`	N/A
⦜ U+299C	block	`prefix`	`0`	`0`	N/A
⦝ U+299D	block	`prefix`	`0`	`0`	N/A
⦞ U+299E	block	`prefix`	`0`	`0`	N/A
⦟ U+299F	block	`prefix`	`0`	`0`	N/A
⦠ U+29A0	block	`prefix`	`0`	`0`	N/A
⦡ U+29A1	block	`prefix`	`0`	`0`	N/A
⦢ U+29A2	block	`prefix`	`0`	`0`	N/A
⦣ U+29A3	block	`prefix`	`0`	`0`	N/A
⦤ U+29A4	block	`prefix`	`0`	`0`	N/A
⦥ U+29A5	block	`prefix`	`0`	`0`	N/A
⦦ U+29A6	block	`prefix`	`0`	`0`	N/A
⦧ U+29A7	block	`prefix`	`0`	`0`	N/A
⦨ U+29A8	block	`prefix`	`0`	`0`	N/A
⦩ U+29A9	block	`prefix`	`0`	`0`	N/A
⦪ U+29AA	block	`prefix`	`0`	`0`	N/A
⦫ U+29AB	block	`prefix`	`0`	`0`	N/A
⦬ U+29AC	block	`prefix`	`0`	`0`	N/A
⦭ U+29AD	block	`prefix`	`0`	`0`	N/A
⦮ U+29AE	block	`prefix`	`0`	`0`	N/A
⦯ U+29AF	block	`prefix`	`0`	`0`	N/A
⫬ U+2AEC	block	`prefix`	`0`	`0`	N/A
⫭ U+2AED	block	`prefix`	`0`	`0`	N/A
String \|\| U+007C U+007C	block	`prefix`	`0`	`0`	fence
! U+0021	block	`postfix`	`0`	`0`	N/A
" U+0022	block	`postfix`	`0`	`0`	N/A
% U+0025	block	`postfix`	`0`	`0`	N/A
& U+0026	block	`postfix`	`0`	`0`	N/A
' U+0027	block	`postfix`	`0`	`0`	N/A
` U+0060	block	`postfix`	`0`	`0`	N/A
¨ U+00A8	block	`postfix`	`0`	`0`	N/A
° U+00B0	block	`postfix`	`0`	`0`	N/A
² U+00B2	block	`postfix`	`0`	`0`	N/A
³ U+00B3	block	`postfix`	`0`	`0`	N/A
´ U+00B4	block	`postfix`	`0`	`0`	N/A
¸ U+00B8	block	`postfix`	`0`	`0`	N/A
¹ U+00B9	block	`postfix`	`0`	`0`	N/A
ˊ U+02CA	block	`postfix`	`0`	`0`	N/A
ˋ U+02CB	block	`postfix`	`0`	`0`	N/A
˘ U+02D8	block	`postfix`	`0`	`0`	N/A
˙ U+02D9	block	`postfix`	`0`	`0`	N/A
˚ U+02DA	block	`postfix`	`0`	`0`	N/A
˝ U+02DD	block	`postfix`	`0`	`0`	N/A
̑ U+0311	block	`postfix`	`0`	`0`	N/A
’ U+2019	block	`postfix`	`0`	`0`	fence
‚ U+201A	block	`postfix`	`0`	`0`	N/A
‛ U+201B	block	`postfix`	`0`	`0`	N/A
” U+201D	block	`postfix`	`0`	`0`	fence
„ U+201E	block	`postfix`	`0`	`0`	N/A
‟ U+201F	block	`postfix`	`0`	`0`	N/A
′ U+2032	block	`postfix`	`0`	`0`	N/A
″ U+2033	block	`postfix`	`0`	`0`	N/A
‴ U+2034	block	`postfix`	`0`	`0`	N/A
‵ U+2035	block	`postfix`	`0`	`0`	N/A
‶ U+2036	block	`postfix`	`0`	`0`	N/A
‷ U+2037	block	`postfix`	`0`	`0`	N/A
⁗ U+2057	block	`postfix`	`0`	`0`	N/A
⃛ U+20DB	block	`postfix`	`0`	`0`	N/A
⃜ U+20DC	block	`postfix`	`0`	`0`	N/A
⏍ U+23CD	block	`postfix`	`0`	`0`	N/A
String !! U+0021 U+0021	block	`postfix`	`0`	`0`	N/A
String ++ U+002B U+002B	block	`postfix`	`0`	`0`	N/A
String -- U+002D U+002D	block	`postfix`	`0`	`0`	N/A
String \|\| U+007C U+007C	block	`postfix`	`0`	`0`	fence
( U+0028	block	`prefix`	`0`	`0`	stretchy symmetric fence
[ U+005B	block	`prefix`	`0`	`0`	stretchy symmetric fence
{ U+007B	block	`prefix`	`0`	`0`	stretchy symmetric fence
\| U+007C	block	`prefix`	`0`	`0`	stretchy symmetric fence
‖ U+2016	block	`prefix`	`0`	`0`	stretchy symmetric fence
⌈ U+2308	block	`prefix`	`0`	`0`	stretchy symmetric fence
⌊ U+230A	block	`prefix`	`0`	`0`	stretchy symmetric fence
⟨ U+2329	block	`prefix`	`0`	`0`	stretchy symmetric fence
❲ U+2772	block	`prefix`	`0`	`0`	stretchy symmetric fence
⟦ U+27E6	block	`prefix`	`0`	`0`	stretchy symmetric fence
⟨ U+27E8	block	`prefix`	`0`	`0`	stretchy symmetric fence
⟪ U+27EA	block	`prefix`	`0`	`0`	stretchy symmetric fence
⟬ U+27EC	block	`prefix`	`0`	`0`	stretchy symmetric fence
⟮ U+27EE	block	`prefix`	`0`	`0`	stretchy symmetric fence
⦀ U+2980	block	`prefix`	`0`	`0`	stretchy symmetric fence
⦃ U+2983	block	`prefix`	`0`	`0`	stretchy symmetric fence
⦅ U+2985	block	`prefix`	`0`	`0`	stretchy symmetric fence
⦇ U+2987	block	`prefix`	`0`	`0`	stretchy symmetric fence
⦉ U+2989	block	`prefix`	`0`	`0`	stretchy symmetric fence
⦋ U+298B	block	`prefix`	`0`	`0`	stretchy symmetric fence
⦍ U+298D	block	`prefix`	`0`	`0`	stretchy symmetric fence
⦏ U+298F	block	`prefix`	`0`	`0`	stretchy symmetric fence
⦑ U+2991	block	`prefix`	`0`	`0`	stretchy symmetric fence
⦓ U+2993	block	`prefix`	`0`	`0`	stretchy symmetric fence
⦕ U+2995	block	`prefix`	`0`	`0`	stretchy symmetric fence
⦗ U+2997	block	`prefix`	`0`	`0`	stretchy symmetric fence
⦙ U+2999	block	`prefix`	`0`	`0`	stretchy symmetric fence
⧘ U+29D8	block	`prefix`	`0`	`0`	stretchy symmetric fence
⧚ U+29DA	block	`prefix`	`0`	`0`	stretchy symmetric fence
⧼ U+29FC	block	`prefix`	`0`	`0`	stretchy symmetric fence
) U+0029	block	`postfix`	`0`	`0`	stretchy symmetric fence
] U+005D	block	`postfix`	`0`	`0`	stretchy symmetric fence
\| U+007C	block	`postfix`	`0`	`0`	stretchy symmetric fence
} U+007D	block	`postfix`	`0`	`0`	stretchy symmetric fence
‖ U+2016	block	`postfix`	`0`	`0`	stretchy symmetric fence
⌉ U+2309	block	`postfix`	`0`	`0`	stretchy symmetric fence
⌋ U+230B	block	`postfix`	`0`	`0`	stretchy symmetric fence
⟩ U+232A	block	`postfix`	`0`	`0`	stretchy symmetric fence
❳ U+2773	block	`postfix`	`0`	`0`	stretchy symmetric fence
⟧ U+27E7	block	`postfix`	`0`	`0`	stretchy symmetric fence
⟩ U+27E9	block	`postfix`	`0`	`0`	stretchy symmetric fence
⟫ U+27EB	block	`postfix`	`0`	`0`	stretchy symmetric fence
⟭ U+27ED	block	`postfix`	`0`	`0`	stretchy symmetric fence
⟯ U+27EF	block	`postfix`	`0`	`0`	stretchy symmetric fence
⦀ U+2980	block	`postfix`	`0`	`0`	stretchy symmetric fence
⦄ U+2984	block	`postfix`	`0`	`0`	stretchy symmetric fence
⦆ U+2986	block	`postfix`	`0`	`0`	stretchy symmetric fence
⦈ U+2988	block	`postfix`	`0`	`0`	stretchy symmetric fence
⦊ U+298A	block	`postfix`	`0`	`0`	stretchy symmetric fence
⦌ U+298C	block	`postfix`	`0`	`0`	stretchy symmetric fence
⦎ U+298E	block	`postfix`	`0`	`0`	stretchy symmetric fence
⦐ U+2990	block	`postfix`	`0`	`0`	stretchy symmetric fence
⦒ U+2992	block	`postfix`	`0`	`0`	stretchy symmetric fence
⦔ U+2994	block	`postfix`	`0`	`0`	stretchy symmetric fence
⦖ U+2996	block	`postfix`	`0`	`0`	stretchy symmetric fence
⦘ U+2998	block	`postfix`	`0`	`0`	stretchy symmetric fence
⦙ U+2999	block	`postfix`	`0`	`0`	stretchy symmetric fence
⧙ U+29D9	block	`postfix`	`0`	`0`	stretchy symmetric fence
⧛ U+29DB	block	`postfix`	`0`	`0`	stretchy symmetric fence
⧽ U+29FD	block	`postfix`	`0`	`0`	stretchy symmetric fence
∫ U+222B	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop
∬ U+222C	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop
∭ U+222D	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop
∮ U+222E	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop
∯ U+222F	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop
∰ U+2230	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop
∱ U+2231	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop
∲ U+2232	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop
∳ U+2233	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop
⨋ U+2A0B	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop
⨌ U+2A0C	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop
⨍ U+2A0D	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop
⨎ U+2A0E	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop
⨏ U+2A0F	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop
⨐ U+2A10	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop
⨑ U+2A11	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop
⨒ U+2A12	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop
⨓ U+2A13	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop
⨔ U+2A14	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop
⨕ U+2A15	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop
⨖ U+2A16	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop
⨗ U+2A17	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop
⨘ U+2A18	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop
⨙ U+2A19	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop
⨚ U+2A1A	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop
⨛ U+2A1B	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop
⨜ U+2A1C	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop
^ U+005E	inline	`postfix`	`0`	`0`	stretchy
_ U+005F	inline	`postfix`	`0`	`0`	stretchy
~ U+007E	inline	`postfix`	`0`	`0`	stretchy
¯ U+00AF	inline	`postfix`	`0`	`0`	stretchy
ˆ U+02C6	inline	`postfix`	`0`	`0`	stretchy
ˇ U+02C7	inline	`postfix`	`0`	`0`	stretchy
ˉ U+02C9	inline	`postfix`	`0`	`0`	stretchy
ˍ U+02CD	inline	`postfix`	`0`	`0`	stretchy
˜ U+02DC	inline	`postfix`	`0`	`0`	stretchy
˷ U+02F7	inline	`postfix`	`0`	`0`	stretchy
̂ U+0302	inline	`postfix`	`0`	`0`	stretchy
‾ U+203E	inline	`postfix`	`0`	`0`	stretchy
⌢ U+2322	inline	`postfix`	`0`	`0`	stretchy
⌣ U+2323	inline	`postfix`	`0`	`0`	stretchy
⎴ U+23B4	inline	`postfix`	`0`	`0`	stretchy
⎵ U+23B5	inline	`postfix`	`0`	`0`	stretchy
⏜ U+23DC	inline	`postfix`	`0`	`0`	stretchy
⏝ U+23DD	inline	`postfix`	`0`	`0`	stretchy
⏞ U+23DE	inline	`postfix`	`0`	`0`	stretchy
⏟ U+23DF	inline	`postfix`	`0`	`0`	stretchy
⏠ U+23E0	inline	`postfix`	`0`	`0`	stretchy
⏡ U+23E1	inline	`postfix`	`0`	`0`	stretchy
𞻰 U+1EEF0	inline	`postfix`	`0`	`0`	stretchy
𞻱 U+1EEF1	inline	`postfix`	`0`	`0`	stretchy
∏ U+220F	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop movablelimits
∐ U+2210	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop movablelimits
∑ U+2211	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop movablelimits
⋀ U+22C0	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop movablelimits
⋁ U+22C1	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop movablelimits
⋂ U+22C2	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop movablelimits
⋃ U+22C3	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop movablelimits
⨀ U+2A00	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop movablelimits
⨁ U+2A01	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop movablelimits
⨂ U+2A02	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop movablelimits
⨃ U+2A03	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop movablelimits
⨄ U+2A04	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop movablelimits
⨅ U+2A05	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop movablelimits
⨆ U+2A06	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop movablelimits
⨇ U+2A07	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop movablelimits
⨈ U+2A08	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop movablelimits
⨉ U+2A09	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop movablelimits
⨊ U+2A0A	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop movablelimits
⨝ U+2A1D	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop movablelimits
⨞ U+2A1E	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop movablelimits
⫼ U+2AFC	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop movablelimits
⫿ U+2AFF	block	`prefix`	`0.16666666666666666em`	`0.16666666666666666em`	symmetric largeop movablelimits
/ U+002F	block	`infix`	`0`	`0`	N/A
\ U+005C	block	`infix`	`0`	`0`	N/A
_ U+005F	inline	`infix`	`0`	`0`	N/A
⁡ U+2061	block	`infix`	`0`	`0`	N/A
⁢ U+2062	block	`infix`	`0`	`0`	N/A
⁣ U+2063	block	`infix`	`0`	`0`	separator
⁤ U+2064	block	`infix`	`0`	`0`	N/A
∆ U+2206	block	`infix`	`0`	`0`	N/A
ⅅ U+2145	block	`prefix`	`0.16666666666666666em`	`0`	N/A
ⅆ U+2146	block	`prefix`	`0.16666666666666666em`	`0`	N/A
∂ U+2202	block	`prefix`	`0.16666666666666666em`	`0`	N/A
√ U+221A	block	`prefix`	`0.16666666666666666em`	`0`	N/A
∛ U+221B	block	`prefix`	`0.16666666666666666em`	`0`	N/A
∜ U+221C	block	`prefix`	`0.16666666666666666em`	`0`	N/A
, U+002C	block	`infix`	`0`	`0.16666666666666666em`	separator
: U+003A	block	`infix`	`0`	`0.16666666666666666em`	N/A
; U+003B	block	`infix`	`0`	`0.16666666666666666em`	separator

Figure 29 Mapping from operator (Content, Form) to properties.
Total size: 1177 entries, ≥ 3679 bytes
(assuming 'Content' uses at least one UTF-16 character, 'Stretch Axis' 1 bit, 'Form' 2 bits, the different combinations of 'rspace' and 'space' at least 3 bits, and the different combinations of properties 3 bits).

This section is non-normative.

The following table gives mappings between spacing and non spacing characters when used in MathML accent constructs.

Non Combining		Style	Combining
U+002B	plus sign	below	U+031F	combining plus sign below
U+002D	hyphen-minus	above	U+0305	combining overline
U+002D	hyphen-minus	below	U+0320	combining minus sign below
U+002D	hyphen-minus	below	U+0332	combining low line
U+002E	full stop	above	U+0307	combining dot above
U+002E	full stop	below	U+0323	combining dot below
U+005E	circumflex accent	above	U+0302	combining circumflex accent
U+005E	circumflex accent	below	U+032D	combining circumflex accent below
U+005F	low line	below	U+0332	combining low line
U+0060	grave accent	above	U+0300	combining grave accent
U+0060	grave accent	below	U+0316	combining grave accent below
U+007E	tilde	above	U+0303	combining tilde
U+007E	tilde	below	U+0330	combining tilde below
U+00A8	diaeresis	above	U+0308	combining diaeresis
U+00A8	diaeresis	below	U+0324	combining diaeresis below
U+00AF	macron	above	U+0304	combining macron
U+00AF	macron	above	U+0305	combining overline
U+00B4	acute accent	above	U+0301	combining acute accent
U+00B4	acute accent	below	U+0317	combining acute accent below
U+00B8	cedilla	below	U+0327	combining cedilla
U+02C6	modifier letter circumflex accent	above	U+0302	combining circumflex accent
U+02C7	caron	above	U+030C	combining caron
U+02C7	caron	below	U+032C	combining caron below
U+02D8	breve	above	U+0306	combining breve
U+02D8	breve	below	U+032E	combining breve below
U+02D9	dot above	above	U+0307	combining dot above
U+02D9	dot above	below	U+0323	combining dot below
U+02DB	ogonek	below	U+0328	combining ogonek
U+02DC	small tilde	above	U+0303	combining tilde
U+02DC	small tilde	below	U+0330	combining tilde below
U+02DD	double acute accent	above	U+030B	combining double acute accent
U+203E	overline	above	U+0305	combining overline
U+2190	leftwards arrow	above	U+20D6
U+2192	rightwards arrow	above	U+20D7	combining right arrow above
U+2192	rightwards arrow	above	U+20EF	combining right arrow below
U+2212	minus sign	above	U+0305	combining overline
U+2212	minus sign	below	U+0332	combining low line
U+27F6	long rightwards arrow	above	U+20D7	combining right arrow above
U+27F6	long rightwards arrow	above	U+20EF	combining right arrow below

Combining		Style	Non Combining
U+0300	combining grave accent	above	U+0060	grave accent
U+0301	combining acute accent	above	U+00B4	acute accent
U+0302	combining circumflex accent	above	U+005E	circumflex accent
U+0302	combining circumflex accent	above	U+02C6	modifier letter circumflex accent
U+0303	combining tilde	above	U+007E	tilde
U+0303	combining tilde	above	U+02DC	small tilde
U+0304	combining macron	above	U+00AF	macron
U+0305	combining overline	above	U+002D	hyphen-minus
U+0305	combining overline	above	U+00AF	macron
U+0305	combining overline	above	U+203E	overline
U+0305	combining overline	above	U+2212	minus sign
U+0306	combining breve	above	U+02D8	breve
U+0307	combining dot above	above	U+02E
U+0307	combining dot above	above	U+002E	full stop
U+0307	combining dot above	above	U+02D9	dot above
U+0308	combining diaeresis	above	U+00A8	diaeresis
U+030B	combining double acute accent	above	U+02DD	double acute accent
U+030C	combining caron	above	U+02C7	caron
U+0312	combining turned comma above	above	U+0B8
U+0316	combining grave accent below	below	U+0060	grave accent
U+0317	combining acute accent below	below	U+00B4	acute accent
U+031F	combining plus sign below	below	U+002B	plus sign
U+0320	combining minus sign below	below	U+002D	hyphen-minus
U+0323	combining dot below	below	U+002E	full stop
U+0323	combining dot below	below	U+02D9	dot above
U+0324	combining diaeresis below	below	U+00A8	diaeresis
U+0327	combining cedilla	below	U+00B8	cedilla
U+0328	combining ogonek	below	U+02DB	ogonek
U+032C	combining caron below	below	U+02C7	caron
U+032D	combining circumflex accent below	below	U+005E	circumflex accent
U+032E	combining breve below	below	U+02D8	breve
U+0330	combining tilde below	below	U+007E	tilde
U+0330	combining tilde below	below	U+02DC	small tilde
U+0332	combining low line	below	U+002D	hyphen-minus
U+0332	combining low line	below	U+005F	low line
U+0332	combining low line	below	U+2212	minus sign
U+0338	combining long solidus overlay	over	U+02F
U+20D7	combining right arrow above	above	U+2192	rightwards arrow
U+20D7	combining right arrow above	above	U+27F6	long rightwards arrow
U+20EF	combining right arrow below	above	U+2192	rightwards arrow
U+20EF	combining right arrow below	above	U+27F6	long rightwards arrow

This section is non-normative.

The following table provides fallback that user agents may use for stretching a given base character when the font does not provide a MATH.MathVariants table. The algorithms of 5.3 Size variants for operators (MathVariants) work the same except with some adjustments:

Entries are indexed by the base character.
All the glyph IDs and metrics have to be deduced from Unicode code points.
If the glyph construction is horizontal then the entry corresponds to a MathVariants.horizGlyphConstructionOffsets[] item; if it is vertical it corresponds to a MathVariants.vertGlyphConstructionOffsets[] item.
The MathGlyphConstruction.mathGlyphVariantRecord is always empty.
The MathVariants.minConnectorOverlap, GlyphPartRecord.startConnectorLength and GlyphPartRecord.endConnectorLength are treated as 0.
The array of MathGlyphConstruction.GlyphAssembly.partRecords is built from each table row as follows:
1. A (non-extender) bottom/left character
2. Followed by an extender character.
3. Optionally followed by this:
  - Optionally, a (non-extender) middle character and the same extender character previously mentioned.
  - A (non-extender) top/right character.

Base Character	Glyph Construction	Extender Character	Bottom/Left Character	Middle Character	Top/Right Character
U+0028 (	Vertical	U+239C ⎜	U+239D ⎝	N/A	U+239B ⎛
U+0029 )	Vertical	U+239F ⎟	U+23A0 ⎠	N/A	U+239E ⎞
U+003D =	Horizontal	U+003D =	U+003D =	N/A	N/A
U+005B [	Vertical	U+23A2 ⎢	U+23A3 ⎣	N/A	U+23A1 ⎡
U+005D ]	Vertical	U+23A5 ⎥	U+23A6 ⎦	N/A	U+23A4 ⎤
U+005F _	Horizontal	U+005F _	U+005F _	N/A	N/A
U+007B {	Vertical	U+23AA ⎪	U+23A9 ⎩	U+23A8 ⎨	U+23A7 ⎧
U+007C \|	Vertical	U+007C \|	U+007C \|	N/A	N/A
U+007D }	Vertical	U+23AA ⎪	U+23AD ⎭	U+23AC ⎬	U+23AB ⎫
U+00AF ¯	Horizontal	U+00AF ¯	U+00AF ¯	N/A	N/A
U+2016 ‖	Vertical	U+2016 ‖	U+2016 ‖	N/A	N/A
U+203E ‾	Horizontal	U+203E ‾	U+203E ‾	N/A	N/A
U+2190 ←	Horizontal	U+23AF ⎯	U+2190 ←	N/A	U+23AF ⎯
U+2191 ↑	Vertical	U+23D0 ⏐	U+23D0 ⏐	N/A	U+2191 ↑
U+2192 →	Horizontal	U+23AF ⎯	U+23AF ⎯	N/A	U+2192 →
U+2193 ↓	Vertical	U+23D0 ⏐	U+2193 ↓	N/A	U+23D0 ⏐
U+2194 ↔	Horizontal	U+23AF ⎯	U+2190 ←	N/A	U+2192 →
U+2195 ↕	Vertical	U+23D0 ⏐	U+2193 ↓	N/A	U+2191 ↑
U+21A4 ↤	Horizontal	U+23AF ⎯	U+2190 ←	N/A	U+22A3 ⊣
U+21A6 ↦	Horizontal	U+23AF ⎯	U+22A2 ⊢	N/A	U+2192 →
U+21BC ↼	Horizontal	U+23AF ⎯	U+21BC ↼	N/A	U+23AF ⎯
U+21BD ↽	Horizontal	U+23AF ⎯	U+21BD ↽	N/A	U+23AF ⎯
U+21C0 ⇀	Horizontal	U+23AF ⎯	U+23AF ⎯	N/A	U+21C0 ⇀
U+21C1 ⇁	Horizontal	U+23AF ⎯	U+23AF ⎯	N/A	U+21C1 ⇁
U+2223 ∣	Vertical	U+2223 ∣	U+2223 ∣	N/A	N/A
U+2225 ∥	Vertical	U+2225 ∥	U+2225 ∥	N/A	N/A
U+2308 ⌈	Vertical	U+23A2 ⎢	U+23A2 ⎢	N/A	U+23A1 ⎡
U+2309 ⌉	Vertical	U+23A5 ⎥	U+23A5 ⎥	N/A	U+23A4 ⎤
U+230A ⌊	Vertical	U+23A2 ⎢	U+23A3 ⎣	N/A	N/A
U+230B ⌋	Vertical	U+23A5 ⎥	U+23A6 ⎦	N/A	N/A
U+23B0 ⎰	Vertical	U+23AA ⎪	U+23AD ⎭	N/A	U+23A7 ⎧
U+23B1 ⎱	Vertical	U+23AA ⎪	U+23A9 ⎩	N/A	U+23AB ⎫
U+27F5 ⟵	Horizontal	U+23AF ⎯	U+2190 ←	N/A	U+23AF ⎯
U+27F6 ⟶	Horizontal	U+23AF ⎯	U+23AF ⎯	N/A	U+2192 →
U+27F7 ⟷	Horizontal	U+23AF ⎯	U+2190 ←	N/A	U+2192 →
U+294E ⥎	Horizontal	U+23AF ⎯	U+21BC ↼	N/A	U+21C0 ⇀
U+2950 ⥐	Horizontal	U+23AF ⎯	U+21BD ↽	N/A	U+21C1 ⇁
U+295A ⥚	Horizontal	U+23AF ⎯	U+21BC ↼	N/A	U+22A3 ⊣
U+295B ⥛	Horizontal	U+23AF ⎯	U+22A2 ⊢	N/A	U+21C0 ⇀
U+295E ⥞	Horizontal	U+23AF ⎯	U+21BD ↽	N/A	U+22A3 ⊣
U+295F ⥟	Horizontal	U+23AF ⎯	U+22A2 ⊢	N/A	U+21C1 ⇁

Original	italic	Δ_{code point}
A U+0041	𝐴 U+1D434	1D3F3
B U+0042	𝐵 U+1D435	1D3F3
C U+0043	𝐶 U+1D436	1D3F3
D U+0044	𝐷 U+1D437	1D3F3
E U+0045	𝐸 U+1D438	1D3F3
F U+0046	𝐹 U+1D439	1D3F3
G U+0047	𝐺 U+1D43A	1D3F3
H U+0048	𝐻 U+1D43B	1D3F3
I U+0049	𝐼 U+1D43C	1D3F3
J U+004A	𝐽 U+1D43D	1D3F3
K U+004B	𝐾 U+1D43E	1D3F3
L U+004C	𝐿 U+1D43F	1D3F3
M U+004D	𝑀 U+1D440	1D3F3
N U+004E	𝑁 U+1D441	1D3F3
O U+004F	𝑂 U+1D442	1D3F3
P U+0050	𝑃 U+1D443	1D3F3
Q U+0051	𝑄 U+1D444	1D3F3
R U+0052	𝑅 U+1D445	1D3F3
S U+0053	𝑆 U+1D446	1D3F3
T U+0054	𝑇 U+1D447	1D3F3
U U+0055	𝑈 U+1D448	1D3F3
V U+0056	𝑉 U+1D449	1D3F3
W U+0057	𝑊 U+1D44A	1D3F3
X U+0058	𝑋 U+1D44B	1D3F3
Y U+0059	𝑌 U+1D44C	1D3F3
Z U+005A	𝑍 U+1D44D	1D3F3
a U+0061	𝑎 U+1D44E	1D3ED
b U+0062	𝑏 U+1D44F	1D3ED
c U+0063	𝑐 U+1D450	1D3ED
d U+0064	𝑑 U+1D451	1D3ED
e U+0065	𝑒 U+1D452	1D3ED
f U+0066	𝑓 U+1D453	1D3ED
g U+0067	𝑔 U+1D454	1D3ED
h U+0068	ℎ U+0210E	20A6
i U+0069	𝑖 U+1D456	1D3ED
j U+006A	𝑗 U+1D457	1D3ED
k U+006B	𝑘 U+1D458	1D3ED
l U+006C	𝑙 U+1D459	1D3ED
m U+006D	𝑚 U+1D45A	1D3ED
n U+006E	𝑛 U+1D45B	1D3ED
o U+006F	𝑜 U+1D45C	1D3ED
p U+0070	𝑝 U+1D45D	1D3ED
q U+0071	𝑞 U+1D45E	1D3ED
r U+0072	𝑟 U+1D45F	1D3ED
s U+0073	𝑠 U+1D460	1D3ED
t U+0074	𝑡 U+1D461	1D3ED
u U+0075	𝑢 U+1D462	1D3ED
v U+0076	𝑣 U+1D463	1D3ED
w U+0077	𝑤 U+1D464	1D3ED
x U+0078	𝑥 U+1D465	1D3ED
y U+0079	𝑦 U+1D466	1D3ED
z U+007A	𝑧 U+1D467	1D3ED
ı U+0131	𝚤 U+1D6A4	1D573
ȷ U+0237	𝚥 U+1D6A5	1D46E
Α U+0391	𝛢 U+1D6E2	1D351
Β U+0392	𝛣 U+1D6E3	1D351
Γ U+0393	𝛤 U+1D6E4	1D351
Δ U+0394	𝛥 U+1D6E5	1D351
Ε U+0395	𝛦 U+1D6E6	1D351
Ζ U+0396	𝛧 U+1D6E7	1D351
Η U+0397	𝛨 U+1D6E8	1D351
Θ U+0398	𝛩 U+1D6E9	1D351
Ι U+0399	𝛪 U+1D6EA	1D351
Κ U+039A	𝛫 U+1D6EB	1D351
Λ U+039B	𝛬 U+1D6EC	1D351
Μ U+039C	𝛭 U+1D6ED	1D351
Ν U+039D	𝛮 U+1D6EE	1D351
Ξ U+039E	𝛯 U+1D6EF	1D351
Ο U+039F	𝛰 U+1D6F0	1D351
Π U+03A0	𝛱 U+1D6F1	1D351
Ρ U+03A1	𝛲 U+1D6F2	1D351
ϴ U+03F4	𝛳 U+1D6F3	1D2FF
Σ U+03A3	𝛴 U+1D6F4	1D351
Τ U+03A4	𝛵 U+1D6F5	1D351
Υ U+03A5	𝛶 U+1D6F6	1D351
Φ U+03A6	𝛷 U+1D6F7	1D351
Χ U+03A7	𝛸 U+1D6F8	1D351
Ψ U+03A8	𝛹 U+1D6F9	1D351
Ω U+03A9	𝛺 U+1D6FA	1D351
∇ U+2207	𝛻 U+1D6FB	1B4F4
α U+03B1	𝛼 U+1D6FC	1D34B
β U+03B2	𝛽 U+1D6FD	1D34B
γ U+03B3	𝛾 U+1D6FE	1D34B
δ U+03B4	𝛿 U+1D6FF	1D34B
ε U+03B5	𝜀 U+1D700	1D34B
ζ U+03B6	𝜁 U+1D701	1D34B
η U+03B7	𝜂 U+1D702	1D34B
θ U+03B8	𝜃 U+1D703	1D34B
ι U+03B9	𝜄 U+1D704	1D34B
κ U+03BA	𝜅 U+1D705	1D34B
λ U+03BB	𝜆 U+1D706	1D34B
μ U+03BC	𝜇 U+1D707	1D34B
ν U+03BD	𝜈 U+1D708	1D34B
ξ U+03BE	𝜉 U+1D709	1D34B
ο U+03BF	𝜊 U+1D70A	1D34B
π U+03C0	𝜋 U+1D70B	1D34B
ρ U+03C1	𝜌 U+1D70C	1D34B
ς U+03C2	𝜍 U+1D70D	1D34B
σ U+03C3	𝜎 U+1D70E	1D34B
τ U+03C4	𝜏 U+1D70F	1D34B
υ U+03C5	𝜐 U+1D710	1D34B
φ U+03C6	𝜑 U+1D711	1D34B
χ U+03C7	𝜒 U+1D712	1D34B
ψ U+03C8	𝜓 U+1D713	1D34B
ω U+03C9	𝜔 U+1D714	1D34B
∂ U+2202	𝜕 U+1D715	1B513
ϵ U+03F5	𝜖 U+1D716	1D321
ϑ U+03D1	𝜗 U+1D717	1D346
ϰ U+03F0	𝜘 U+1D718	1D328
ϕ U+03D5	𝜙 U+1D719	1D344
ϱ U+03F1	𝜚 U+1D71A	1D329
ϖ U+03D6	𝜛 U+1D71B	1D345

MathML Core

Abstract

Status of This Document

1. Introduction

2. MathML Fundamentals

2.1 Elements and attributes

2.1.1 The Top-Level <math> Element

2.1.2 Types for MathML Attribute Values

2.1.3 Global Attributes

2.1.4 Attributes common to HTML and MathML elements

2.1.5 Legacy MathML Style Attributes

2.1.6 The displaystyle and scriptlevel attributes

2.1.7 Attributes Reserved as Valid

2.2 Integration in the Web Platform

2.2.1 HTML and SVG

2.2.2 CSS styling

2.2.3 DOM and JavaScript

2.2.4 Text layout

2.2.5 Focus

3. Presentation Markup

3.1 Visual formatting model

3.1.1 Box Model

3.1.2 Layout Algorithms

3.1.3 Anonymous <mrow> boxes

3.1.4 Stacking contexts

3.2 Token Elements

3.2.1 Text <mtext>

3.2.1.1 Layout of <mtext>

3.2.2 Identifier <mi>

3.2.3 Number <mn>

3.2.4 Operator, Fence, Separator or Accent <mo>

3.2.4.1 Embellished operators

3.2.4.2 Dictionary-based attributes

3.2.4.3 Layout of operators

3.2.5 Space <mspace>

3.2.5.1 Definition of space-like elements

3.2.6 String Literal <ms>

3.3 General Layout Schemata

3.3.1 Group Sub-Expressions <mrow>

3.3.1.1 Algorithm for stretching operators along the block axis

3.3.1.2 Layout of <mrow>

3.3.2 Fractions <mfrac>

3.3.2.1 Fraction with nonzero line thickness

3.3.2.2 Fraction with zero line thickness

3.3.3 Radicals <msqrt>, <mroot>

3.3.3.1 Radical symbol

3.3.3.2 Square root

3.3.3.3 Root with index

3.3.4 Style Change <mstyle>

3.3.5 Error Message <merror>

3.3.6 Adjust Space Around Content <mpadded>

3.3.6.1 Inner box and requested parameters

3.3.6.2 Layout of <mpadded>

3.3.7 Making Sub-Expressions Invisible <mphantom>

3.4 Script and Limit Schemata

3.4.1 Subscripts and Superscripts <msub>, <msup>, <msubsup>

3.4.1.1 Children of <msub>, <msup>, <msubsup>

3.4.1.2 Base with subscript

3.4.1.3 Base with superscript

3.4.1.4 Base with subscript and superscript

3.4.2 Underscripts and Overscripts <munder>, <mover>, <munderover>

3.4.2.1 Children of <munder>, <mover>, <munderover>

3.4.2.2 Algorithm for stretching operators along the inline axis

3.4.2.3 Base with underscript

3.4.2.4 Base with overscript

3.4.2.5 Base with underscript and overscript

3.4.3 Prescripts and Tensor Indices <mmultiscripts>

3.4.3.1 Base with prescripts and postscripts

3.4.4 Displaystyle, scriptlevel and math-shift in scripts

3.5 Tabular Math

3.5.1 Table or Matrix <mtable>

3.5.2 Row in Table or Matrix <mtr>

3.5.3 Entry in Table or Matrix <mtd>

3.6 Enlivening Expressions

3.7 Semantics and Presentation

4. CSS Extensions for Math Layout

4.1 The display: block math and display: inline math value

4.2 The math-auto transform

4.3 The math-style property

4.4 The math-shift property

2.1.1 The Top-Level `<math>` Element

2.1.6 The `displaystyle` and `scriptlevel` attributes

3.2.1 Text `<mtext>`

3.2.1.1 Layout of `<mtext>`

3.2.2 Identifier `<mi>`

3.2.3 Number `<mn>`

3.2.4 Operator, Fence, Separator or Accent `<mo>`

3.2.5 Space `<mspace>`

3.2.6 String Literal `<ms>`

3.3.1 Group Sub-Expressions `<mrow>`

3.3.1.2 Layout of `<mrow>`

3.3.2 Fractions `<mfrac>`

3.3.3 Radicals `<msqrt>`, `<mroot>`

3.3.4 Style Change `<mstyle>`

3.3.5 Error Message `<merror>`

3.3.6 Adjust Space Around Content `<mpadded>`

3.3.6.2 Layout of `<mpadded>`

3.3.7 Making Sub-Expressions Invisible `<mphantom>`

3.4.1 Subscripts and Superscripts `<msub>`, `<msup>`, `<msubsup>`

3.4.1.1 Children of `<msub>`, `<msup>`, `<msubsup>`

3.4.2 Underscripts and Overscripts `<munder>`, `<mover>`, `<munderover>`

3.4.2.1 Children of `<munder>`, `<mover>`, `<munderover>`

3.4.3 Prescripts and Tensor Indices `<mmultiscripts>`

3.5.1 Table or Matrix `<mtable>`

3.5.2 Row in Table or Matrix `<mtr>`

3.5.3 Entry in Table or Matrix `<mtd>`

4.1 The `display: block math` and `display: inline math` value

4.2 The `math-auto` transform

4.3 The `math-style` property

4.4 The `math-shift` property

4.5 The `math-depth` property

5. OpenType `MATH` table

5.1 Layout constants (`MathConstants`)

5.2 Glyph information (`MathGlyphInfo`)

5.3 Size variants for operators (`MathVariants`)

5.3.1 The `GlyphAssembly` table

C.1 `italic` mappings