W3C Editor's Draft 12 May 2026
More details about this document This version: https://w3c.github.io/mathml-core/ Latest published version: https://www.w3.org/TR/mathml-core/ Latest editor's draft:https://w3c.github.io/mathml-core/ History: https://www.w3.org/standards/history/mathml-core/ Commit history Test suite:https://github.com/web-platform-tests/wpt/tree/master/mathml/ Implementation report: https://wpt.fyi/results/?label=master&label=experimental&aligned&q=math%20%20not%28path%3A%2Fjs%29 Editors: David Carlisle (NAG) Frédéric Wang (Igalia) Former editors: Patrick Ion (Mathematical Reviews, American Mathematical Society) Robert Miner (deceased) (Design Science, Inc.) Feedback: GitHub w3c/mathml-core (pull requests, new issue, open issues)Copyright © 2026 World Wide Web Consortium. W3C® liability, trademark and permissive document license rules apply.
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.
This section describes the status of this document at the time of its publication. A list of current W3C publications and the latest revision of this technical report can be found in the W3C standards and drafts index.
This document was published by the Math Working Group as an Editor's Draft.
Publication as an Editor's Draft does not imply endorsement by W3C and its Members.
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This section is non-normative.
The [MATHML3] specification has several shortcomings that make it hard to implement consistently across web rendering engines or to extend with user-defined constructions, e.g.:
This MathML Core specification intends to address these issues by being as accurate as possible on the visual rendering of mathematical formulas using additional rules from the TeXBook’s Appendix G [TEXBOOK] and from the Open Font Format [OPEN-FONT-FORMAT], [OPEN-TYPE-MATH-ILLUMINATED]. It also relies on modern browser implementations and web technologies [HTML] [SVG] [CSS2] [DOM], clarifying interactions with them when needed or introducing new low-level primitives to improve the web platform layering.
Parts of MathML3 that do not fit well in this framework or are less fundamental have been omitted. Instead, they are described in a separate and larger [MATHML4] specification. The details of which math feature will be included in future versions of MathML Core or implemented as polyfills is still open. This question and other potential improvements are tracked on GitHub.
By increasing the level of implementation details, focusing on a workable subset, following a browser-driven design and relying on automated web platform tests, this specification is expected to greatly improve MathML interoperability. Moreover, effort on MathML layering will enable users to implement the rest of the MathML 4 specification, or more generally to extend MathML Core, using modern web technologies such as shadow trees, custom elements or APIs from [HOUDINI].
The term MathML element refers to any element in the MathML namespace. The MathML elements defined in this specification are called the MathML Core elements and are listed below. Any MathML element that is not listed below is called an Unknown MathML element.
The grouping elements are maction, math, merror, mphantom, mprescripts, mrow, mstyle, semantics and unknown MathML elements.
The scripted elements are mmultiscripts, mover, msub, msubsup, msup, munder and munderover.
The radical elements are mroot and msqrt.
The attributes defined in this specification have no namespace and are called MathML attributes:
MathML specifies a single top-level or root math element, which encapsulates each instance of MathML markup within a document. All other MathML content must be contained in a <math> element.
The <math> element accepts the attributes described in 2.1.3 Global Attributes as well as the following attributes:
The display attribute, if present, must be an ASCII case-insensitive match to block or inline. The user agent stylesheet described in A. User Agent Stylesheet contains rules for this attribute that affect the default values for the display (block math or inline math) and math-style (normal or compact) properties. If the display attribute is absent or has an invalid value, the User Agent stylesheet treats it the same as inline.
This specification does not define any observable behavior that is specific to the alttext attribute.
If the <math> 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 algorithm of the mrow element is used to produce a math content box. That math content box is used as the content for the layout of the element, as described by CSS for display: block (if the computed value is block math) or display: inline (if the computed value is inline math). Additionally, if the computed display property is equal to block math then that math content box is rendered horizontally centered within the content box.
In the following example, a math formula is rendered in display mode on a new line and taking full width, with the math content centered within the container:
<div style="width: 15em;"> This mathematical formula with a big summation and the number pi <math display="block" style="border: 1px dotted black;"> <mrow> <munderover> <mo>∑</mo> <mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow> <mrow><mo>+</mo><mn>∞</mn></mrow> </munderover> <mfrac> <mn>1</mn> <msup><mi>n</mi><mn>2</mn></msup> </mfrac> </mrow> <mo>=</mo> <mfrac> <msup><mi>π</mi><mn>2</mn></msup> <mn>6</mn> </mfrac> </math> is easy to prove. </div>As a comparison, the same formula would look as follows in inline mode. The formula is embedded in the paragraph of text without forced line breaking. The baselines specified by the layout algorithm of the mrow are used for vertical alignment. Note that the middle of sum and equal symbols or fractions are all aligned, but not with the alphabetical baseline of the surrounding text.
Because good mathematical rendering requires use of mathematical fonts, the user agent stylesheet should set the font-family to the math value on the <math> element instead of inheriting it. Additionally, several CSS properties that can be set on a parent container such as font-style, font-weight, direction or text-indent etc are not expected to apply to the math formula and so the user agent stylesheet has rules to reset them by default.
math { direction: ltr; text-indent: 0; letter-spacing: normal; line-height: normal; word-spacing: normal; font-family: math; font-size: inherit; font-style: normal; font-weight: normal; display: inline math; math-shift: normal; math-style: compact; math-depth: 0; } math[display="block" i] { display: block math; math-style: normal; } math[display="inline" i] { display: inline math; math-style: compact; }In addition to CSS data types, some MathML attributes rely on the following MathML-specific types:
unsigned-integer An <integer> value as defined in [CSS-VALUES-4], whose first character is neither U+002D HYPHEN-MINUS character (-) nor U+002B PLUS SIGN (+). boolean A string that is an ASCII case-insensitive match to true or false.The following attributes are common to and may be specified on all MathML elements:
The id, class, style, data-*, autofocus and nonce and tabindex attributes have the same syntax and semantics as defined for id, class, style, data-*, autofocus, nonce and tabindex attributes on HTML elements.
The dir attribute, if present, must be an ASCII case-insensitive match to ltr or rtl. In that case, the user agent is expected to treat the attribute as a presentational hint setting the element's direction property to the corresponding value. More precisely, an ASCII case-insensitive match to rtl is mapped to rtl while an ASCII case-insensitive match to ltr is mapped to ltr.
In the following example, the dir attribute is used to render "𞸎 plus 𞸑 raised to the power of (٢ over, 𞸟 plus ١)" from right-to-left.
<math dir="rtl"> <mrow> <mi>𞸎</mi> <mo>+</mo> <msup> <mi>𞸑</mi> <mfrac> <mn>٢</mn> <mrow> <mi>𞸟</mi> <mo>+</mo> <mn>١</mn> </mrow> </mfrac> </msup> </mrow> </math>All MathML elements support event handler content attributes, as described in event handler content attributes in HTML.
All event handler content attributes noted by HTML as being supported by all HTMLElements are supported by all MathML elements as well, as defined in the MathMLElement IDL.
The mathcolor and mathbackground attributes, if present, must have a value that is a <color>. In that case, the user agent is expected to treat these attributes as a presentational hint setting the element's color and background-color properties to the corresponding values. The mathcolor attribute describes the foreground fill color of MathML text, bars etc while the mathbackground attribute describes the background color of an element.
The mathsize attribute, if present, must have a value that is a valid <length-percentage>. In that case, the user agent is expected to treat the attribute as a presentational hint setting the element's font-size property to the corresponding value. The mathsize property indicates the desired height of glyphs in math formulas but also scales other parts (spacing, shifts, line thickness of bars etc) accordingly.
The displaystyle attribute, if present, must have a value that is a boolean. In that case, the user agent is expected to treat the attribute as a presentational hint setting the element's math-style property to the corresponding value. More precisely, an ASCII case-insensitive match to true is mapped to normal while an ASCII case-insensitive match to false is mapped to compact. This attribute indicates whether formulas should try to minimize the logical height (value is false) or not (value is true) e.g. by changing the size of content or the layout of scripts.
The scriptlevel attribute, if present, must have value +<U>, -<U> or <U> where <U> is an unsigned-integer. In that case the user agent is expected to treat the scriptlevel attribute as a presentational hint setting the element's math-depth property to the corresponding value. More precisely, +<U>, -<U> and <U> are respectively mapped to add(<U>) add(<-U>) and <U>.
displaystyle and scriptlevel values are automatically adjusted within MathML elements. To fully implement these attributes, additional CSS properties must be specified in the user agent stylesheet as described in A. User Agent Stylesheet. In particular, for all MathML elements a default font-size: math is specified to ensure that scriptlevel changes are taken into account.
In this example, an munder element is used to attach a script "A" to a base "∑". By default, the summation symbol is rendered with the font-size inherited from its parent and the A as a scaled down subscript. If displaystyle is true, the summation symbol is drawn bigger and the "A" becomes an underscript. If scriptlevel is reset to 0 on the "A", then it will use the same font-size as the top-level math root.
<math> <munder> <mo>∑</mo> <mi>A</mi> </munder> <munder displaystyle="true"> <mo>∑</mo> <mi>A</mi> </munder> <munder> <mo>∑</mo> <mi scriptlevel="0">A</mi> </munder> </math>The attributes intent and arg are reserved as valid attributes.
This specification does not define any observable behavior that is specific to the intent and arg attributes.
MathML can be mixed with HTML and SVG as described in the relevant specifications [HTML] [SVG].
When evaluating the SVG requiredExtensions attribute, user agents must claim support for the language extension identified by the MathML namespace.
In this example, inline MathML and SVG elements are used inside an HTML document. SVG elements <switch> and <foreignObject> (with proper <requiredExtensions>) are used to embed a MathML formula with a text fallback, inside a diagram. HTML input element is used within the mtext to include an interactive input field inside a mathematical formula. See also 3.8 Semantics and Presentation for an example of SVG and HTML inside an annotation-xml element.
<svg style="font-size: 20px" width="400px" height="220px" viewBox="0 0 200 110"> <g transform="translate(10,80)"> <path d="M 0 0 L 150 0 A 75 75 0 0 0 0 0 M 30 0 L 30 -60 M 30 -10 L 40 -10 L 40 0" fill="none" stroke="black"></path> <text transform="translate(10,20)">1</text> <switch transform="translate(35,-40)"> <foreignObject width="200" height="50" requiredExtensions="http://www.w3.org/1998/Math/MathML"> <math> <msqrt> <mn>2</mn> <mi>r</mi> <mo>−</mo> <mn>1</mn> </msqrt> </math> </foreignObject> <text>\sqrt{2r - 1}</text> </switch> </g> </svg> <p> Fill the blank: <math> <msqrt> <mn>2</mn> <mtext><input onchange="..." size="2" type="text"></mtext> <mo>−</mo> <mn>1</mn> </msqrt> <mo>=</mo> <mn>3</mn> </math> </p>User agents must support various CSS features mentioned in this specification, including new ones described in 4. CSS Extensions for Math Layout. They must follow the computation rule for display: contents.
In this example, the MathML formula inherits the CSS color of its parent and uses the font-family specified via the style attribute.
<div style="width: 15em; color: blue"> This mathematical formula with a big summation and the number pi <math display="block" style="font-family: STIX Two Math"> <mrow> <munderover> <mo>∑</mo> <mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow> <mrow><mo>+</mo><mn>∞</mn></mrow> </munderover> <mfrac> <mn>1</mn> <msup><mi>n</mi><mn>2</mn></msup> </mfrac> </mrow> <mo>=</mo> <mfrac> <msup><mi>π</mi><mn>2</mn></msup> <mn>6</mn> </mfrac> </math> is easy to prove. </div>All documents containing MathML Core elements must include CSS rules described in A. User Agent Stylesheet as part of user-agent level style sheet defaults. In particular, this adds !important rules to force writing mode to horizontal-lr on all MathML elements.
The float property does not create floating of elements whose parent's computed display value is block math or inline math, and does not take them out-of-flow.
The ::first-line and ::first-letter pseudo-elements do not apply to elements whose computed display value is block math or inline math, and such elements do not contribute a first formatted line or first letter to their ancestors.
The following CSS features are not supported and must be ignored:
User agents supporting Web application APIs must ensure that they keep the visual rendering of MathML synchronized with the [DOM] tree, in particular perform necessary updates when MathML attributes are modified dynamically.
All the nodes representing MathML elements in the DOM must implement, and expose to scripts, the following MathMLElement interface, unless otherwise specified.
WebIDL[Exposed=Window] interface MathMLElement : Element { }; MathMLElement includes GlobalEventHandlers; MathMLElement includes HTMLOrSVGOrMathMLElement;The GlobalEventHandlers and HTMLOrSVGOrMathMLElement interfaces are defined in [HTML].
In the following example, a MathML formula is used to render the fraction "α over 2". When clicking the red α, it is changed into a blue β.
<script> function ModifyMath(mi) { mi.style.color = 'blue'; mi.textContent = 'β'; } </script> <math> <mrow> <mfrac> <mi style="color: red" onclick="ModifyMath(this)">α</mi> <mn>2</mn> </mfrac> </mrow> </math>Because math fonts generally contain very tall glyphs such as big integrals, using typographic metrics is important to avoid excessive line spacing of text. As a consequence, user agents must take into account the USE_TYPO_METRICS flag from the OS/2 table [OPEN-FONT-FORMAT] when performing text layout.
MathML provides the ability for authors to allow for interactivity in supporting interactive user agents using the same concepts, approach and guidance to Focus as described in HTML, with modifications or clarifications regarding application for MathML as described in this section.
When an element is focused, all applicable CSS focus-related pseudo-classes as defined in Selectors Level 3 apply, as defined in that specification.
The contents of embedded math elements (including HTML elements inside token elements) contribute to the sequential focus order of the containing owner HTML document (combined sequential focus order).
The default display property is described in A. User Agent Stylesheet:
In order to specify math layout in different writing modes, this specification uses concepts from [CSS-WRITING-MODES-4]:
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:
Block metrics. The block size, first baseline set and last baseline set. The following baselines are defined for MathML boxes:
Given a MathML box, the following offsets are defined:
Here are examples of offsets obtained from line-relative metrics:
Each MathML element has an associated math content box, which is calculated as described in this chapter's layout algorithms using the following structure:
The following extra steps must be performed:
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.
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.
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.
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> if </mtext> <mrow> <mi>x</mi> <mo>≥</mo> <mn>1</mn> </mrow> <mtext> and </mtext> <mn>2</mn> <mtext> 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:
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:
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.
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.
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:
The core operator of an embellished operator is the <mo> element defined recursively as follows:
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:
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:
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:
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 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>.
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> elementA 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:
The same definitions apply for boxes in the visual formatting model where an anonymous <mrow> box is treated as a grouping element.
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>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, …, childN 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> elementThe algorithm for stretching operators along the block axis consists in the following steps:
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.
The min-content inline size (respectively max-content inline size) are calculated using the following algorithm:
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:
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:
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>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.
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> elementThe 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:
DenominatorShift is the maximum between:
The line-ascent of the math content is the maximum between:
The line-descent of the math content is the maximum between:
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 barThe 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:
The line-descent of the math content is the maximum between:
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.
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> elementThe 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-descent of the math content is the maximum between:
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:
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> elementThe 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 the math content is the maximum between:
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.
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.
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:
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> elementThe 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; }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> elementThe 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:
The line-ascent of the math content is the maximum between:
The line-descent of the math content is the maximum between:
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> elementThe 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 line-ascent of the math content is the maximum between:
The line-descent of the math content is the maximum between:
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> elementThe 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.
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:
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.
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:
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.
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> elementThe 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:
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
UnderExtraDescender is 0.
The munder base is an embellished operator with the stretchy property and stretch axis inline. UnderShift is the maximum of:
The line-ascent of the math content is the maximum between:
The line-descent of the math content is the maximum between:
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> elementThe 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:
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
OverExtraAscender is 0.
The mover base is an embellished operator with the stretchy property and stretch axis inline. OverShift is the maximum of:
Otherwise, OverShift is equal to
OverExtraAscender is OverbarExtraAscender.
The line-ascent of the math content is the maximum between:
The line-descent of the math content is the maximum between:
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> elementThe 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.
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:
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> elementThe 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:
For each subscript/superscript pair of mmultiscripts prescripts, increment inline-offset by SpaceAfterScript + the maximum of
For each subscript/superscript pair of mmultiscripts postscripts, modify inline-size to be at least:
Increment inline-offset to the maximum of:
Increment inline-offset by SpaceAfterScript.
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:
For each subscript/superscript pair of mmultiscripts prescripts:
For each subscript/superscript pair of mmultiscripts postscripts:
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; }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".
The <mtd> element generates an anonymous <mrow> box.
The a element is used to group together any number of sub-expressions equivalently to mrow. It's main purpose is to enable the specification fo hyperlinks via the use of the href attribute.
The <a> element accepts the attributes described in 2.1.3 Global Attributes as well as the all the attributes of the corresponding element in HTML. The primary additional attribute is href.
If the href attribute is used then the <a> element creates a hyperlink to the URL specified by the href attribute. The linking behavior is as described for the a element in HTML.
The layout algorithm of the <a> element is the same as the <mrow> element.
The <a> element must implement, and expose to scripts, the following MathMLAnchorElement interface.
WebIDL[Exposed=Window] interface MathMLAnchorElement : MathMLElement { [ReflectSetter] attribute USVString href; [Reflect] attribute DOMString target; }; MathMLAnchorElement includes HyperlinkElementUtils;The href getter steps are:
The set the url algorithm for a MathMLAnchorElement are:
To update href for a MathMLAnchorElement, set the element's href content attribute's value to the element's url, serialized.
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:
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; }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:
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.
The display property from CSS Display Module Level 3 is extended with a new inner display type:
| display |
| <display-outside> || [ <display-inside> | math ] |
For elements that are not MathML elements, if the specified value of display is block math or inline math then the computed value is block flow and inline flow respectively. For the mtable element the computed value is block table and inline table respectively. For the mtr element, the computed value is table-row. For the mtd element, the computed value is table-cell.
MathML elements with a computed display value equal to block math or inline math control box generation and layout according to their tag name, as described in the relevant sections. Unknown MathML elements behave the same as the mrow element.
In the following example, the default layout of the MathML mrow element is overridden to render its content as a grid.
<math> <msup> <mrow> <mo symmetric="false">[</mo> <mrow style="display: block; width: 4.5em;"> <mrow style="display: grid; grid-template-columns: 1.5em 1.5em 1.5em; grid-template-rows: 1.5em 1.5em; justify-items: center; align-items: center;"> <mn>12</mn> <mn>34</mn> <mn>56</mn> <mn>7</mn> <mn>8</mn> <mn>9</mn> </mrow> </mrow> <mo symmetric="false">]</mo> </mrow> <mi>α</mi> </msup> </math>The text-transform property from CSS Text Module Level 4 has a new value math-auto. On text nodes containing a single character, if the computed value is math-auto and the character is present in the "Original" column of C.1 italic mappings then it is converted to the corresponding character from the "italic" column.
A common style convention is to render identifiers with multiple letters (e.g. the function name "exp") with normal style and identifiers with a single letter (e.g. the variable "n") with italic style. The math-auto property is intended to implement this default behavior, which can be overridden by authors if necessary. Note that mathematical fonts are designed with a special kind of italic glyphs located at the Unicode positions of C.1 italic mappings, which differ from the shaping obtained via italic font style. Compare this mathematical formula rendered with the Latin Modern Math font using font-style: italic (left) and text-transform: math-auto (right):
| math-style |
| normal | compact |
| normal |
| All elements |
| yes |
| n/a |
| specified keyword |
| n/a |
| by computed value type |
| visual |
When math-style is compact, the math layout on descendants tries to minimize the logical height by applying the following rules:
The following example shows a mathematical formula rendered with its math root styled with math-style: compact (left) and math-style: normal (right). In the former case, the font-size is automatically scaled down within the fractions and the summation limits are rendered as subscript and superscript of the ∑. In the latter case, the ∑ is drawn bigger than normal text and vertical gaps within fractions (even relative to current font-size) are larger.
These two math-style values typically correspond to mathematical expressions in inline and display mode respectively [TeXBook]. A mathematical formula in display mode may automatically switch to inline mode within some subformulas (e.g. scripts, matrix elements, numerators and denominators, etc) and it is sometimes desirable to override this default behavior. The math-style property allows to easily implement these features for MathML in the user agent stylesheet and with the displaystyle attribute; and also exposes them to polyfills.
| math-shift |
| normal | compact |
| normal |
| All elements |
| yes |
| n/a |
| specified keyword |
| n/a |
| by computed value type |
| visual |
If the value of math-shift is compact, the math layout on descendants will use the superscriptShiftUpCramped parameter to place superscript. If the value of math-shift is normal, the math will use the superscriptShiftUp parameter instead.
This property is used for positioning superscript during the layout of MathML scripted elements. See § 3.4.1 Subscripts and Superscripts <msub>, <msup>, <msubsup>, 3.4.3 Prescripts and Tensor Indices <mmultiscripts> and 3.4.2 Underscripts and Overscripts <munder>, <mover>, <munderover>.
In the following example, the two "x squared" are rendered with compact math-style and the same font-size. However, the one within the square root is rendered with compact math-shift while the other one is rendered with normal math-shift, leading to subtle different shift of the superscript "2".
Per [TeXBook], a mathematical formula uses normal style by default but may switch to compact style ("cramped" in TeX's terminology) within some subformulas (e.g. radicals, fraction denominators, etc). The math-shift property allows to easily implement these rules for MathML in the user agent stylesheet. Page authors or developers of polyfills may also benefit from having access to this property to tweak or refine the default implementation.
A new math-depth property is introduced to describe a notion of "depth" for each element of a mathematical formula, with respect to the top-level container of that formula. Concretely, this is used to determine the computed value of the font-size property when its specified value is math.
| math-depth |
| auto-add | add(<integer>) | <integer> |
| 0 |
| All elements |
| yes |
| n/a |
| an integer, see below |
| n/a |
| by computed value type |
| visual |
The computed value of the math-depth value is determined as follows:
If the specified value of font-size is math then the computed value of font-size is obtained by multiplying the inherited value of font-size by a nonzero scale factor calculated by the following procedure:
The following example shows a mathematical formula with normal math-style rendered with the Latin Modern Math font. When entering subexpressions like scripts or fractions, the font-size is automatically scaled down according to the values of MATH table contained in that font. Note that font-size is scaled down when entering the superscripts but even faster when entering a root's prescript. Also it is scaled down when entering the inner fraction but not when entering the outer one, due to automatic change of math-style in fractions.
These rules from [TeXBook] are subtle and it's worth having a separate math-depth mechanism to express and handle them. They can be implemented in MathML using the user agent stylesheet. Page authors or developers of polyfills may also benefit from having access to this property to tweak or refine the default implementation. In particular, the scriptlevel attribute from MathML provides a way to perform math-depth changes.
This chapter describes features provided by MATH table of an OpenType font [OPEN-FONT-FORMAT]. Throughout this chapter, a C-like notation Table.Subtable1[index].Subtable2.Parameter is used to denote OpenType parameters. Such parameters may not be available (e.g. if the font lacks one of the subtable, has an invalid offset, etc) and so fallback options are provided.
OpenType values expressed in design units (perhaps indirectly via a MathValueRecord entry) are scaled to appropriate values for layout purpose, taking into account head.unitsPerEm, CSS font-size or zoom level.
These are global layout constants for the first available font:
Default fallback constant 0 Default rule thickness post.underlineThickness or Default fallback constant if the constant is not available. scriptPercentScaleDown MATH.MathConstants.scriptPercentScaleDown / 100 or 0.71 if MATH.MathConstants.scriptPercentScaleDown is null or not available. scriptScriptPercentScaleDown MATH.MathConstants.scriptScriptPercentScaleDown / 100 or 0.5041 if MATH.MathConstants.scriptScriptPercentScaleDown is null or not available. displayOperatorMinHeight MATH.MathConstants.displayOperatorMinHeight or Default fallback constant if the constant is not available. axisHeight MATH.MathConstants.axisHeight or half OS/2.sxHeight if the constant is not available. accentBaseHeight MATH.MathConstants.accentBaseHeight or OS/2.sxHeight if the constant is not available. subscriptShiftDown MATH.MathConstants.subscriptShiftDown or OS/2.ySubscriptYOffset if the constant is not available. subscriptTopMax MATH.MathConstants.subscriptTopMax or ⅘ × OS/2.sxHeight if the constant is not available. subscriptBaselineDropMin MATH.MathConstants.subscriptBaselineDropMin or Default fallback constant if the constant is not available. superscriptShiftUp MATH.MathConstants.superscriptShiftUp or OS/2.ySuperscriptYOffset if the constant is not available. superscriptShiftUpCramped MATH.MathConstants.superscriptShiftUpCramped or Default fallback constant if the constant is not available. superscriptBottomMin MATH.MathConstants.superscriptBottomMin or ¼ × OS/2.sxHeight if the constant is not available. superscriptBaselineDropMax MATH.MathConstants.superscriptBaselineDropMax or Default fallback constant if the constant is not available. subSuperscriptGapMin MATH.MathConstants.subSuperscriptGapMin or 4 × default rule thickness if the constant is not available. superscriptBottomMaxWithSubscript MATH.MathConstants.superscriptBottomMaxWithSubscript or ⅘ × OS/2.sxHeight if the constant is not available. spaceAfterScript MATH.MathConstants.spaceAfterScript or 1/24em if the constant is not available. upperLimitGapMin MATH.MathConstants.upperLimitGapMin or Default fallback constant if the constant is not available. upperLimitBaselineRiseMin MATH.MathConstants.upperLimitBaselineRiseMin or Default fallback constant if the constant is not available. lowerLimitGapMin MATH.MathConstants.lowerLimitGapMin or Default fallback constant if the constant is not available. lowerLimitBaselineDropMin MATH.MathConstants.lowerLimitBaselineDropMin or Default fallback constant if the constant is not available. stackTopShiftUp MATH.MathConstants.stackTopShiftUp or Default fallback constant if the constant is not available. stackTopDisplayStyleShiftUp MATH.MathConstants.stackTopDisplayStyleShiftUp or Default fallback constant if the constant is not available. stackBottomShiftDown MATH.MathConstants.stackBottomShiftDown or Default fallback constant if the constant is not available. stackBottomDisplayStyleShiftDown MATH.MathConstants.stackBottomDisplayStyleShiftDown or Default fallback constant if the constant is not available. stackGapMin MATH.MathConstants.stackGapMin or 3 × default rule thickness if the constant is not available. stackDisplayStyleGapMin MATH.MathConstants.stackDisplayStyleGapMin or 7 × default rule thickness if the constant is not available. stretchStackTopShiftUp MATH.MathConstants.stretchStackTopShiftUp or Default fallback constant if the constant is not available. stretchStackBottomShiftDown MATH.MathConstants.stretchStackBottomShiftDown or Default fallback constant if the constant is not available. stretchStackGapAboveMin MATH.MathConstants.stretchStackGapAboveMin or Default fallback constant if the constant is not available. stretchStackGapBelowMin MATH.MathConstants.stretchStackGapBelowMin or Default fallback constant if the constant is not available. fractionNumeratorShiftUp MATH.MathConstants.fractionNumeratorShiftUp or Default fallback constant if the constant is not available. fractionNumeratorDisplayStyleShiftUp MATH.MathConstants.fractionNumeratorDisplayStyleShiftUp or Default fallback constant if the constant is not available. fractionDenominatorShiftDown MATH.MathConstants.fractionDenominatorShiftDown or Default fallback constant if the constant is not available. fractionDenominatorDisplayStyleShiftDown MATH.MathConstants.fractionDenominatorDisplayStyleShiftDown or Default fallback constant if the constant is not available. fractionNumeratorGapMin MATH.MathConstants.fractionNumeratorGapMin or default rule thickness if the constant is not available. fractionNumDisplayStyleGapMin MATH.MathConstants.fractionNumDisplayStyleGapMin or 3 × default rule thickness if the constant is not available. fractionRuleThickness MATH.MathConstants.fractionRuleThickness or default rule thickness if the constant is not available. fractionDenominatorGapMin MATH.MathConstants.fractionDenominatorGapMin or default rule thickness if the constant is not available. fractionDenomDisplayStyleGapMin MATH.MathConstants.fractionDenomDisplayStyleGapMin or 3 × default rule thickness if the constant is not available. overbarVerticalGap MATH.MathConstants.overbarVerticalGap or 3 × default rule thickness if the constant is not available. overbarExtraAscender MATH.MathConstants.overbarExtraAscender or default rule thickness if the constant is not available. underbarVerticalGap MATH.MathConstants.underbarVerticalGap or 3 × default rule thickness if the constant is not available. underbarExtraDescender MATH.MathConstants.underbarExtraDescender or default rule thickness if the constant is not available. radicalVerticalGap MATH.MathConstants.radicalVerticalGap or 1¼ × default rule thickness if the constant is not available. radicalDisplayStyleVerticalGap MATH.MathConstants.radicalDisplayStyleVerticalGap or default rule thickness + ¼ OS/2.sxHeight if the constant is not available. radicalRuleThickness MATH.MathConstants.radicalRuleThickness or default rule thickness if the constant is not available. radicalExtraAscender MATH.MathConstants.radicalExtraAscender or default rule thickness if the constant is not available. radicalKernBeforeDegree MATH.MathConstants.radicalKernBeforeDegree or 5/18em if the constant is not available. radicalKernAfterDegree MATH.MathConstants.radicalKernAfterDegree or −10/18em if the constant is not available. radicalDegreeBottomRaisePercent MATH.MathConstants.radicalDegreeBottomRaisePercent / 100.0 or 0.6 if the constant is not available.These are per-glyph tables for the first available font:
MathItalicsCorrectionInfo The subtable MATH.MathGlyphInfo.MathItalicsCorrectionInfo of italics correction values. Use the corresponding value in MATH.MathGlyphInfo.MathItalicsCorrectionInfo.italicsCorrection if there is one for the requested glyph or 0 otherwise. MathTopAccentAttachment The subtable MATH.MathGlyphInfo.MathTopAccentAttachment of positioning top math accents along the inline axis. Use the corresponding value in MATH.MathGlyphInfo.MathTopAccentAttachment.topAccentAttachment if there is one for the requested glyph or half the advance width of the glyph otherwise.This section describes how to handle stretchy glyphs of arbitrary size using the MATH.MathVariants table.
This section is based on [OPEN-TYPE-MATH-IN-HARFBUZZ]. For convenience, the following definitions are used:
User agents must treat the GlyphAssembly as invalid if the following conditions are not satisfied:
In this specification, a glyph assembly is built by repeating each extender r times and using the same overlap value o between each glyph. The number of glyphs in such an assembly is AssemblyGlyphCount(r) = NNonExt + r NExt while the stretch size is AssembySize(o, r) = SNonExt + r SExt − o (AssemblyGlyphCount(r) − 1).
rmin is the minimal number of repetitions needed to obtain an assembly of size at least T, i.e. the minimal r such that AssembySize(omin, r) ≥ T. It is defined as the maximum between 0 and the ceiling of ((T − SNonExt + omin (NNonExt − 1)) / SExt,NonOverlapping).
omax,theorical = (AssembySize(0, rmin) − T) / (AssemblyGlyphCount(rmin) − 1) is the theorical overlap obtained by splitting evenly the extra size of an assembly built with null overlap.
omax is the maximum overlap possible to build an assembly of size at least T by repeating each extender rmin times. If AssemblyGlyphCount(rmin) ≤ 1, then the actual overlap value is irrelevant. Otherwise, omax is defined to be the minimum of:
The glyph assembly stretch size for a target size T is AssembySize(omax, rmin).
The glyph assembly width, glyph assembly ascent and glyph assembly descent are defined as follows:
The glyph assembly height is the sum of the glyph assembly ascent and glyph assembly descent.
The shaping of the glyph assembly is performed with the following algorithm:
The preferred inline size of a glyph stretched along the block axis is calculated using the following algorithm:
The algorithm to shape a stretchy glyph to inline (respectively block) dimension T is the following:
The algorithm to get a glyph corresponding to a character c given a directionality dir is the following:
The algorithm to set the properties of an operator from its category is as follows:
The algorithm to determine the category of an operator (Content, Form) is as folllows:
| 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, |
| 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 |
| 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 |
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.
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.
| < 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 |
| ⟿ U+27FF | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤀ U+2900 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤁ U+2901 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤂ U+2902 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤃ U+2903 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤄ U+2904 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤅ U+2905 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤆ U+2906 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤇ U+2907 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤈ U+2908 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤉ U+2909 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤊ U+290A | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤋ U+290B | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤌ U+290C | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤍ U+290D | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤎ U+290E | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤏ U+290F | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤐ U+2910 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤑ U+2911 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤒ U+2912 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤓ U+2913 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤔ U+2914 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤕ U+2915 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤖ U+2916 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤗ U+2917 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤘ U+2918 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤙ U+2919 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤚ U+291A | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤛ U+291B | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤜ U+291C | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤝ U+291D | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤞ U+291E | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤟ U+291F | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤠ U+2920 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤴ U+2934 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤵ U+2935 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤶ U+2936 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⤷ U+2937 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥂ U+2942 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥃ U+2943 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥄ U+2944 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥅ U+2945 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥆ U+2946 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥇ U+2947 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥈ U+2948 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥉ U+2949 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥊ U+294A | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥋ U+294B | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥌ U+294C | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥍ U+294D | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥎ U+294E | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥏ U+294F | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥐ U+2950 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥑ U+2951 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥒ U+2952 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥓ U+2953 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥔ U+2954 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥕ U+2955 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥖ U+2956 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥗ U+2957 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥘ U+2958 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥙ U+2959 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥚ U+295A | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥛ U+295B | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥜ U+295C | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥝ U+295D | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥞ U+295E | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥟ U+295F | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥠ U+2960 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥡ U+2961 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥢ U+2962 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥣ U+2963 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥤ U+2964 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥥ U+2965 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥦ U+2966 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥧ U+2967 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥨ U+2968 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥩ U+2969 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥪ U+296A | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥫ U+296B | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥬ U+296C | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥭ U+296D | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥮ U+296E | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥯ U+296F | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥰ U+2970 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥱ U+2971 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥲ U+2972 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥳ U+2973 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥴ U+2974 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥵ U+2975 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥼ U+297C | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥽ U+297D | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥾ U+297E | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⥿ U+297F | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⬄ U+2B04 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⬅ U+2B05 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⬆ U+2B06 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⬇ U+2B07 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⬌ U+2B0C | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⬍ U+2B0D | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⬎ U+2B0E | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⬏ U+2B0F | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⬐ U+2B10 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⬑ U+2B11 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⬰ U+2B30 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⬱ U+2B31 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⬲ U+2B32 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⬳ U+2B33 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⬴ U+2B34 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⬵ U+2B35 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⬶ U+2B36 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⬷ U+2B37 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⬸ U+2B38 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⬹ U+2B39 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⬺ U+2B3A | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⬻ U+2B3B | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⬼ U+2B3C | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⬽ U+2B3D | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⬾ U+2B3E | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⭀ U+2B40 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⭁ U+2B41 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⭂ U+2B42 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⭃ U+2B43 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⭄ U+2B44 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⭅ U+2B45 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⭆ U+2B46 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⭇ U+2B47 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⭈ U+2B48 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⭉ U+2B49 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⭊ U+2B4A | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⭋ U+2B4B | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⭌ U+2B4C | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⭠ U+2B60 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⭡ U+2B61 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⭢ U+2B62 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⭣ U+2B63 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⭤ U+2B64 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⭥ U+2B65 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⭪ U+2B6A | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⭫ U+2B6B | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⭬ U+2B6C | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⭭ U+2B6D | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⭰ U+2B70 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⭱ U+2B71 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⭲ U+2B72 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⭳ U+2B73 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⭺ U+2B7A | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⭻ U+2B7B | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⭼ U+2B7C | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⭽ U+2B7D | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⮀ U+2B80 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⮁ U+2B81 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⮂ U+2B82 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⮃ U+2B83 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⮄ U+2B84 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⮅ U+2B85 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⮆ U+2B86 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⮇ U+2B87 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⮕ U+2B95 | inline | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⮠ U+2BA0 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⮡ U+2BA1 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⮢ U+2BA2 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⮣ U+2BA3 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⮤ U+2BA4 | block | infix | 0.2777777777777778em | 0.2777777777777778em | stretchy |
| ⮥ 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 |
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| ± U+00B1 | block | infix | 0.2222222222222222em | 0.2222222222222222em | N/A |
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| ∨ U+2228 | block | infix | 0.2222222222222222em | 0.2222222222222222em | N/A |
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| ∸ 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 |
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| ⊞ 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 |
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| ➖ 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 |
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| String || U+007C U+007C | block | prefix | 0 | 0 | fence |
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| ” U+201D | block | postfix | 0 | 0 | fence |
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| ∬ 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 |
This section is non-normative.
The following table gives mappings between spacing and non spacing characters when used in MathML accent constructs.
| below | U+002B | plus sign | U+031F | combining plus sign below |
| above | U+002D | hyphen-minus | U+0305 | combining overline |
| below | U+002D | hyphen-minus | U+0320 | combining minus sign below |
| below | U+002D | hyphen-minus | U+0332 | combining low line |
| above | U+002E | full stop | U+0307 | combining dot above |
| below | U+002E | full stop | U+0323 | combining dot below |
| above | U+005E | circumflex accent | U+0302 | combining circumflex accent |
| below | U+005E | circumflex accent | U+032D | combining circumflex accent below |
| below | U+005F | low line | U+0332 | combining low line |
| above | U+0060 | grave accent | U+0300 | combining grave accent |
| below | U+0060 | grave accent | U+0316 | combining grave accent below |
| above | U+007E | tilde | U+0303 | combining tilde |
| below | U+007E | tilde | U+0330 | combining tilde below |
| above | U+00A8 | diaeresis | U+0308 | combining diaeresis |
| below | U+00A8 | diaeresis | U+0324 | combining diaeresis below |
| above | U+00AF | macron | U+0304 | combining macron |
| above | U+00AF | macron | U+0305 | combining overline |
| above | U+00B4 | acute accent | U+0301 | combining acute accent |
| below | U+00B4 | acute accent | U+0317 | combining acute accent below |
| below | U+00B8 | cedilla | U+0327 | combining cedilla |
| above | U+02C6 | modifier letter circumflex accent | U+0302 | combining circumflex accent |
| above | U+02C7 | caron | U+030C | combining caron |
| below | U+02C7 | caron | U+032C | combining caron below |
| above | U+02D8 | breve | U+0306 | combining breve |
| below | U+02D8 | breve | U+032E | combining breve below |
| above | U+02D9 | dot above | U+0307 | combining dot above |
| below | U+02D9 | dot above | U+0323 | combining dot below |
| below | U+02DB | ogonek | U+0328 | combining ogonek |
| above | U+02DC | small tilde | U+0303 | combining tilde |
| below | U+02DC | small tilde | U+0330 | combining tilde below |
| above | U+02DD | double acute accent | U+030B | combining double acute accent |
| above | U+203E | overline | U+0305 | combining overline |
| above | U+2190 | leftwards arrow | U+20D6 | combining left arrow above |
| above | U+2192 | rightwards arrow | U+20D7 | combining right arrow above |
| above | U+2192 | rightwards arrow | U+20EF | combining right arrow below |
| above | U+2212 | minus sign | U+0305 | combining overline |
| below | U+2212 | minus sign | U+0332 | combining low line |
| above | U+27F6 | long rightwards arrow | U+20D7 | combining right arrow above |
| above | U+27F6 | long rightwards arrow | U+20EF | combining right arrow below |
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:
| 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 ⇁ |
This section is non-normative.
As detailed in [xml-entity-names] mathematical alphanumeric symbols with form bold, italic, fraktur, monospace, double-struck etc are available in Unicode.
These alphanumeric symbols should be accessed using their Unicode code points. It is sometimes needed to distinguish between Chancery and Roundhand style for MATHEMATICAL SCRIPT characters. These are notably used in LaTeX for the \mathcal and \mathscr commands. One way to do that is to rely on Chapter 23.4 Variation Selectors of Unicode which describes a way to specify selection of particular glyph variants [UNICODE]. Indeed, the StandardizedVariants.txt file from the Unicode Character Database indicates that variant selectors U+FE00 and U+FE01 can be used on capital script to specify Chancery and Roundhand respectively.
Alternatively, some mathematical fonts rely on salt or ssXY properties from [OPEN-FONT-FORMAT] to provide both styles. Page authors may use the font-variant-alternates property with corresponding OpenType font features to access these glyphs.In addition, the italic math alphanumeric characters may be accessed as described above using the CSS text-transform: math-auto transform which is applied by default to single character <mi> elements. As a convenience the mapping to math italic is shown below.
| 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 |
This section is non-normative.
MathML Core is based on MathML3. See the appendix E of [MathML3] for the people that contributed to that specification.
MathML Core was initially developed by the MathML Community Group, and then by the Math Working Group. Working Group or Community Group members who regularly participated in MathML Core meetings during the development of this specification: Brian Kardell, Bruce Miller, Daniel Marques, David Carlisle, David Farmer, Deyan Ginev, Frédéric Wang, Louis Mahler, Moritz Schubotz, Murray Sargent, Neil Soiffer, Patrick Ion, Rob Buis, Steve Noble and Sam Dooley.
In addition, we would like to extend special thanks to Brian Kardell, Neil Soiffer and Rob Buis for help with the editing.
Many thanks also to the following people for their help with the test suite: Brian Kardell, Frédéric Wang, Neil Soiffer and Rob Buis. Several tests are also based on MathML tests from browser repositories and we are grateful to the Mozilla and WebKit contributors.
We would like to thank the people who, through their input and feedback on public communication channels, have helped us with the creation of this specification: André Greiner-Petter, Anne van Kesteren, Boris Zbarsky, Brian Smith, Elika Etemad, Emilio Cobos Álvarez, ExE Boss, Ian Kilpatrick, Koji Ishii, L. David Baron, Michael Kohlhase, Michael Smith, Ryosuke Niwa, Sergey Malkin, Tab Atkins Jr., Viktor Yaffle and frankvel.
This section is non-normative.
This specification adds script execution mechanisms via the MathML event handler attributes described in 2.1.3 Global Attributes. UAs may decide to prevent execution of scripts specified in these attributes, following the same security restrictions as those applying to HTML or SVG elements.
In [MathML3], it was possible to make any element linkable via href or xlink:href attributes, with an URL pointing to an untrusted resource or even javascript: execution. These attributes are not available in MathML Core. However, as described in 2.2.1 HTML and SVG it is possible to embed HTML or SVG content inside MathML, including HTML or SVG links.
In [MathML3], it was possible to use the maction element with the actiontype value set to "statusline" in order to override the text of the browser statusline. In particular, an attacker could use this to hide the URL text of an untrusted link e.g.
<math> <maction actiontype="statusline"> <mtext><a href="javascript:alert('JS execution')">Click me!</a></mtext> <mtext>./this-is-a-safe-link.html</mtext> </maction> </math>This feature is not available in MathML Core, where the maction element essentially behaves like an mrow container with extra style.
An attacker can try to hang the UA by inserting very large stretchy operators, effectively making the algorithm shaping of the glyph assembly deal with a huge amount of glyphs. UAs may work around this issue by limiting rmin and GlyphAssembly.partCount to maximum values.
As described in CSS Fonts Module, an attacker can try to rely on malformed or malicious fonts to exploit potential security faults in browser implementations. Because the OpenType MATH table is used extensively in this specification, UAs should ensure their font sanitization mechanisms are able to deal with that table.
Finally, in order to reduce attack surface, some UAs expose runtime options to disable part of the web platform. Disabling MathML layout can essentially be achieved by forcing elements in the DOM tree to be put in the HTML namespace and disabling 4. CSS Extensions for Math Layout.
This section is non-normative.
As explained in 2.2.1 HTML and SVG, MathML can be embedded into an SVG image via the <foreignObject> element which can thus be used in a canvas element. UA may decide to implement any measure to prevent potential information leakage such as tainting the canvas and returning a "SecurityError" when one tries to access the canvas' content via JavaScript APIs.
In the following example, the canvas image is set to the image of some MathML content with an HTML link to https://example.org/. It should not be possible for an attacker to determine whether that link was visited by reading pixels via context.getImageData(). For more about links in MathML, see E. Security Considerations.
let svg = ` <svg xmlns="http://www.w3.org/2000/svg" width="100px" height="100px"> <foreignObject width="100" height="100" requiredExtensions="http://www.w3.org/1998/Math/MathML"> <math xmlns="http://www.w3.org/1998/Math/MathML"> <msqrt style="font-size: 25px"> <mtext>■</mtext> <mtext><a href="https://example.org/">■</a></mtext> </msqrt> </math> </foreignObject> </svg>`; let image = new Image(); image.width = 100; image.height = 100; image.onload = () => { let canvas = document.createElement('canvas'); canvas.width = 100; canvas.height = 100; canvas.style = "border: 1px solid black"; document.body.appendChild(canvas); let context = canvas.getContext("2d"); context.drawImage(image, 0, 0); }; image.src = `data:image/svg+xml;base64,${window.btoa(svg)}`;This specification describes layout of DOM elements which may involve system fonts. Like for HTML/CSS layout, it is thus possible to use JavaScript APIs (e.g. context.getImageData() on content embedded in a canvas context, or even just getBoundingClientRect()) to measure box sizes and positions and infer data from system fonts. By combining miscellaneous tests on such fonts and comparing measurements against results of well-known fonts, an attacker can try and determine the default fonts of the user.
The following HTML+CSS+JavaScript document relies on a Web font with exotic metrics to try and determine whether A Well Known System Font is available by default.
<style> @font-face { font-family: MyWebFontWithVeryWideGlyphs; src: url("/fonts/my-web-fonts-with-very-wide-glyphs.woff"); } #container { font-family: AWellKnownSystemFont, MyWebFontWithVeryWideGlyphs; } </style> <div id="container">SOMETEXT</div> <div id="reference">SOMETEXT</div> <script> document.fonts.ready.then(() => { let containerWidth = document.getElementById("container").getBoundingClientRect().width; let referenceWidth = document.getElementById("reference").getBoundingClientRect().width; let isWellKnownSystemFontAvailable = Math.abs(containerWidth - referenceWidth) < 1; }); </script>The following HTML+CSS+JavaScript document tries to determine whether the UI serif font provides Asian glyphs:
<style> @font-face { font-family: MyWebFontWithVeryWideAsianGlyphs; src: url("/fonts/my-web-fonts-with-very-wide-asian-glyphs.woff"); } #container { font-family: ui-serif, MyWebFontWithVeryWideAsianGlyphs } #reference { font-family: MyWebFontWithVeryWideAsianGlyphs; } </style> <div id="container">王</div> <div id="reference">王</div> <script> document.fonts.ready.then(() => { let containerWidth = document.getElementById("container").getBoundingClientRect().width; let referenceWidth = document.getElementById("reference").getBoundingClientRect().width; let uiSerifFontDoesNotContainAsianGlyph = Math.abs(containerWidth - referenceWidth) < 1; }); </script>The following HTML+CSS document contains the same text rendered with text-decoration-thickness set to from-font and 1em (here 100 pixels) respectively. By comparing the heights of the two underlines, one can calculate a good approximation of the underlineThickness value from the PostScript Table [OPEN-FONT-FORMAT].
<style> #test { font-size: 100px; } #container { text-decoration-line: underline; text-decoration-thickness: from-font; } #reference { text-decoration-line: underline; text-decoration-thickness: 1em; } </style> <div id="test"> <div id="container">SOMETEXT</div> <div id="reference">SOMETEXT</div> </div>This specification relies on information from 5. OpenType MATH table to render MathML content. One can get good approximation of most layout parameters from MathConstants and MathGlyphInfo using measurement techniques similar to what is described above for HTML+CSS+JavaScript document. The use of the MathVariants table for MathML rendering can also be observed by putting stretchy operators of different sizes inside a canvas context.
Although none of these parameters taken individually are personal, implementing this specification increases the set of exposed font information that can be used by an attacker to implement fingerprinting techniques. Typically, they could help determine available and preferred math fonts for a user.
Conformance requirements are expressed with a combination of descriptive assertions and RFC 2119 terminology. The key words “MUST”, “MUST NOT”, “REQUIRED”, “SHALL”, “SHALL NOT”, “SHOULD”, “SHOULD NOT”, “RECOMMENDED”, “MAY”, and “OPTIONAL” in the normative parts of this document are to be interpreted as described in RFC 2119. However, for readability, these words do not appear in all uppercase letters in this specification.
All of the text of this specification is normative except sections explicitly marked as non-normative, examples, and notes. [RFC2119]
Examples in this specification are introduced with the words “for example” or are set apart from the normative text with class="example", like this:
This is an example of an informative example.
Informative notes begin with the word “Note” and are set apart from the normative text with class="note", like this:
Note, this is an informative note.
Advisements are normative sections styled to evoke special attention and are set apart from other normative text with <strong class="advisement">, like this: UAs MUST provide an accessible alternative.
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