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W3C

A MathML for CSS Profile

W3C Recommendation 07 June 2011

This version:
http://www.w3.org/TR/2011/REC-mathml-for-css-20110607/
Latest version:
http://www.w3.org/TR/mathml-for-css/
Previous version:
http://www.w3.org/TR/2010/PR-mathml-for-css-20100810/
Editors:
Bert Bos, W3C
David Carlisle, NAG
George Chavchanidze, Opera Software
Patrick D. F. Ion, Mathematical Reviews, American Mathematical Society
Bruce R. Miller, National Institute of Standards and Technology

Please refer to theerratafor this document, which may include some normative corrections.

See alsotranslations.

Copyright © 1998-2011W3C® (MIT,ERCIM,Keio), All Rights Reserved. W3Cliability,trademark anddocument use rules apply.


Abstract

This document describes a profile of MathML 3.0 that admits formatting with Cascading Style Sheets.

Status of this Document

This section describes the status of this document at the timeof its publication. Other documents may supersede this document. Alist of current W3C publications and the latest revision of thistechnical report can be found in theW3C technical reports index athttp://www.w3.org/TR/.

This document is a W3C Recommendation produced by theW3C Math Working Group as part ofW3CMath Activity.The goals of the W3C Math Working Group are discussed in the W3C Math WGCharter. The authors of this document are W3C Math WorkingGroup members.

This document has been reviewed by W3C Members, by softwaredevelopers, and by other W3C groups and interested parties, and isendorsed by the Director as a W3C Recommendation. It is a stabledocument and may be used as reference material or cited from anotherdocument. W3C's role in making the Recommendation is to draw attentionto the specification and to promote its widespread deployment. Thisenhances the functionality and interoperability of the Web.

This is is a mature document that has been widely reviewed and has been shownto be implementable. W3C encourages everybody to implement thisspecification. Comments may be sent to the (archived) public mailinglistwww-math@w3.org.

The previous version of this document was aProposed Recomendation.The only differences between that draft and this are the updated status section, and some updated references.

This Recommendation specifies a profile of the W3C Recommendation, MathML 3.0[mathml], and is intended to accord with current CSS[css].

During the Candidate Recommendation phase, the Working Group tested the MathML for CSS Profile using at least two independent CSS implementations.The Profile contains a suitable CSS stylesheet within the specification itself.The results of testing,MathML for CSS Profile Test Results, have been made public. The testing usedparts of the comprehensiveMathML Test Suite.This is also publicly available. Further details may be found in theMathML3 Implementation Report

This document was produced by a group operating under the5 February 2004 W3C Patent Policy. W3C maintains apublic list of any patent disclosures made in connection with the deliverables of the group; that page also includes instructions for disclosing a patent.An individual who has actual knowledge of a patent which the individual believes containsEssential Claim(s) must disclose the information in accordance withsection 6 of the W3C Patent Policy.

Public discussion of MathML and issues of support through the W3Cfor mathematics on the Web takes place on the public mailing list of the Math WorkingGroup (list archives).To subscribe send an email towww-math-request@w3.orgwith the wordsubscribe in the subject line.

Table of Contents

1Introduction
    1.1Differences in formatting models
2Math Elements
    2.1Root element
    2.2Token elements and layout schemata
    2.3Required Arguments
    2.4Common attributes
3Token Elements
    3.1Identifier <mi>
    3.2Number <mn>
    3.3Operator <mo>
    3.4Text <mtext>
    3.5Space <mspace>
    3.6String Literal <ms>
4General Layout Schemata
    4.1Horizontally Group Sub-Expressions <mrow>
    4.2Fractions <mfrac>
    4.3Radicals <msqrt>, <mroot>
    4.4Error Message <merror>
    4.5Making Sub-Expressions Invisible <mphantom>
    4.6Expression Inside Pair of Fences <mfenced>
    4.7Enclose Expression Inside Notation <menclose>
5Script and Limit Schemata
    5.1Subscript <msub>
    5.2Superscript <msup>
    5.3Subscript-superscript Pair <msubsup>
    5.4Underscript <munder>
    5.5Overscript <mover>
    5.6Underscript-overscript Pair <munderover>
    5.7Prescripts <mmultiscripts>
6Tables and Matrices
    6.1Table or Matrix <mtable>
    6.2Row in a Table or Matrix <mtr>
    6.3Entry in a Table or Matrix <mtd>
7Elementary Math
    7.12D addition, subtraction and multiplication <mstack>
    7.2Horizontal rows <mrow>
    7.3Long division <mlongdiv>
8Annotations
    8.1Bind Action to a Sub-Expression <maction>
    8.2Add semantic mapping <semantics>
9Extensibility and Conformance
    9.1Extensibility
    9.2Conformance
10Differences between MathML presentational markup and present profile
11Document Type Definition
12Default CSS style sheet
13References


1 Introduction

The current profile is intended to be subset of MathML 3.0[mathml] that could be used to capture structure of mathematical formulae in the way suitable for further CSS formatting. This profile is expected to facilitate adoption of MathML in web browsers and CSS formatters, allowing them to reuse existing CSS[css] visual formatting model, enhanced with a few mathematics-oriented extensions, for rendering of the layout schemata of presentational MathML. Development of the CSS profile is assumed to be coordinated with ongoing work on CSS. As specified in this document a restricted part of MathML3 properly used should render well with currently implemented CSS up to CSS 2.1. Some descriptions are offered of what might be done better were a limited set of new properties to be added to CSS3 modules.

It may be useful to note, in connection with the need for this profile, that the CSS2 specification[css2] was developed and refined at about the same time as the first MathML specification[mathml1]. Now new versions of both MathML and CSS are being created. This profile is thus part of the ongoing effort to realize the synergy that W3C Recommendations offer to the Web.

1.1 Differences in formatting models

The Math Working Group has identified the following issues, which are considered to be the main obstacles delaying fully consistent MathML/CSS integration.

  • Insufficient control over vertical alignment of complex inline expressions such as inline tables with multiple rows.

  • Lack of a mechanism to control stretching of glyphs, or any equivalent functionality, that could be used for sizing of mathematical delimiters and stretchy operators.

  • Limited scope in the use of selectors and generation of content, which makes it difficult to apply complex formatting to basic structural markup.

  • The order of children in presentational elements such asmover,munderover,mmultiscripts andmroot does not match their in-flow positions; this makes formatting of such elements more difficult.

  • Handling of operators, delimiters and accents governed by an operator dictionary (that is by element content rather than attribute values) rather than by explicit markup makes matching of such operators using CSS selectors impossible.

  • Usage of some presentational elements such asmpadded,mspace,mstyle might conflict with corresponding CSS formatting properties.

2 Math Elements

2.1 Root element

MathML specifies a single top-level or rootmath element, which encapsulates each instance of MathML markup within a document. All other MathML markup must be contained in amath element, which must always be the outermost element ofa MathML expression and can contain an arbitrary number of children. Themath element carries thedisplay attribute that specifies whether the enclosed MathML expression should be rendered in a display style or an in-line style. Allowed values are "block" and "inline" (default). It also acceptsaltimg andalttext attributes that provide fall-back for User Applications (UAs) that do not support MathML layout schemata. The values ofaltimg andalttext attributes are URI and CDATA respectively. All MathML elements should be in the MathML namespacehttp://www.w3.org/1998/Math/MathML[rec-xmlns]. This can be ensured by adding a default namespace declaration tomath elements, or by using namespace prefixes bound to the MathML namespace.

2.2 Token elements and layout schemata

MathML elements included in the current profile can be divided into two classes.Token elements represent individual symbols, names, numbers, labels, etc. In general, tokens can have only character data as content.Layout schemata build expressions out of parts, and can only have elements as content except for whitespace, which they ignore. There are also a few empty elements used only in conjunction with specific layout schemata.

All individual "symbols" in a mathematical expression should berepresented by MathML token elements. The primary MathML token elementtypes are identifiers (e.g. variables or function names), numbers, andoperators (including fences, such as parentheses, and separators, suchas commas). There are also token elements for representing text orwhitespace that has more aesthetic than mathematical significance,and for representing "string literals" for compatibility withcomputer algebra systems. Note that although a token elementrepresents a single meaningful "symbol" (name, number, label,mathematical symbol, etc.), such symbols may be comprised of more thanone character. For examplesin and24 arerepresented by the single tokens<mi>sin</mi>and<mn>24</mn> respectively.

Token elements included in the current profile are summarized in the table below.

miidentifier
mnnumber
mooperator, fence or separator
mtexttext
mspacespace
msstring literal

In traditional mathematical notation, expressions are recursivelyconstructed out of smaller expressions, and ultimately out of singlesymbols, with the parts grouped and positioned using one of a smallset of notational structures, which can be thought of as "expressionconstructors". In MathML, expressions are constructed in the same way,with the layout schemata playing the role of the expressionconstructors. The layout schemata specify the way in whichsub-expressions are built into larger expressions. The terminologyderives from the fact that each layout schema corresponds to adifferent way of "laying out" its sub-expressions to form a largerexpression in traditional mathematical typesetting.

Basic expression constructions included in the current profile are listed in the table below.

mrowgroups any number of sub-expressions horizontally
mfracforms a fraction from two sub-expressions
msqrtforms a square root (radical without an index)
mrootforms a radical with specified index
merrorencloses a syntax error message from a preprocessor
mphantommakes content invisible but preserve its size
mfencedsurrounds content with a pair of fences
mencloseencloses content with a stretching symbol
msubattaches a subscript to a base
msupattaches a superscript to a base
msubsupattaches a subscript-superscript pair to a base
munderattaches an underscript to a base
moverattaches an overscript to a base
munderoverattaches an underscript-overscript pair to a base
mmultiscriptsattaches prescripts to a base
mtablemarks a table or matrix
mtrmarks a row in a table or matrix
mtdmarks a one entry in a table or matrix
mstackused for elementary math notations such as 2D addition, subtraction and multiplication
mlongdivused for elementary math notations for long division
mslinemarks horizontal line in elementary math layouts
msrowmarks row in elementary math layouts
mactionbinds actions to a sub-expression

2.3 Required Arguments

Some layout schemata require a specific number of arguments, for examplemfrac is supposed to have two child elementsrepresenting numerator and denominator. In the current profile, layout schemata with fixed number of required argumentsaccept only elementsmrow,maction,merror,mphantom and tokensmi,mn,mo,ms,mtext as child elements.This restrictions is imposed to ensure that each part of layout schemata has its own containing block and is uniquely represented in thedocument object model. For example nested fractions where the numerator or denominatorare themselves fractions

<mfrac><mfrac><mi>a</mi><mi>b</mi></mfrac><mfrac><mi>c</mi><mi>d</mi></mfrac></mfrac>

are not allowed in the MathML for CSS profile, although they are allowed inMathML 3.0. It is easy to meet the profile requirements by wrapping nested fractions inmrow elements:

<mfrac><mrow><mfrac><mi>a</mi><mi>b</mi></mfrac></mrow><mrow><mfrac><mi>c</mi><mi>d</mi></mfrac></mrow></mfrac>

The number of arguments required by a particular layout schemata element is specified in the table below.Note that in the current profile, the content model ofmfenced andmaction is stricter compared to what is allowed by MathML 3.0 specification.

ElementRequired argument countArgument roles
mfrac2numeratordenominator
mroot2baseindex
mfenced1base
msub2basesubscript
msup2basesuperscript
msubsup3basesubscriptsuperscript
munder2baseunderscript
mover2baseoverscript
munderover3baseunderscriptoverscript
mmultiscripts4basemprescriptspresubscriptpresuperscript
mtable1+one or moremtr elements
mtr1+one or moremtd elements
mstack4+one or moremn tokens followed bymsrow element,msline and groups consisting of one or moremn tokens followed by optionalmsline
mlongdiv3+result of the division followed bydivisor andgroups consisting of one or moremn tokens followed by optionalmsline
msrow2mo token element followed bymn token
maction2basetooltip

The elementsmrow,msqrt,merror,mphantom,menclose,mtdandmath admit any number of arguments and accept any layout schemata or token elements from current profile as children.

2.4 Common attributes

The attributesid,class andstyle can be used on any element included in the current profile:id provides a mechanism for annotating elements with unique identifiers,class assigns one or more class names to an element andstyle specifies style information for the current element.The attributemathvariant is allowed on nonempty token elements, attribute is included in the profile for interoperability reasons to ensure that font changes are transparent for CSS unaware UAs.

The following table lists common attributes, their values and the elements on which they can be used.

Namevaluesdefaultvalid on
idIDall elements
classNMTOKENSall elements
styleCDATAall elements
mathvariantnormal  | bold | italic | bold‑italic | sans-serif | bold‑sans‑serif | sans‑serif‑italic | sans‑serif‑bold‑italic | monospacenormalmn,mo,ms,mtext
mathvariantnormal  | bold | italic | bold‑italic | sans-serif | bold‑sans‑serif | sans‑serif‑italic | sans‑serif‑bold‑italic | monospaceitalicmi

3 Token Elements

Token elements in presentation markup are, broadly speaking, intended torepresent the smallest units of mathematical notation which carrymeaning. Tokens are roughly analogous to words in text. However,because of the precise, symbolic nature of mathematical notation, thevarious categories and properties of token elements figure prominently inMathML markup. By contrast, in textual data, individual words rarelyneed to be marked up or styled specially.

Frequently tokens consist of a single character denoting amathematical symbol. Other cases, e.g., function names, involvemulti-character tokens. Further, because traditional mathematicalnotation makes extensive use of symbols distinguished by theirtypographical properties, care must be taken to ensure that stylingmechanisms respect typographical properties which carry meaning.Consequently, characters, tokens, and typographical properties ofsymbols are closely related to one another in MathML.

3.1 Identifier <mi>

Anmi element represents a mathematical identifier; its renderingconsists of the text content displayed in a typefacecorresponding to themathvariant attribute.Since the typeface used can distinguish similar identifiers,it often serves an important semantic function.

In MathML 3.0, the default value ofmathvariant depends on the content of the element, it is"italic" for single character content (e.g.,<mi>x</mi>) and"normal" otherwise (e.g.,<mi>sin</mi>).Such behavior does not fit well in the scope of CSS, therefore in current profile "italic" is the default value regardless of the element contentand mathematical identifiers for which a non-italic typeface is desired (e.g., multi-character identifiers), must explicitly specifythemathvariant attribute.

3.2 Number <mn>

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

A typical graphical renderer would render anmn element as the characters of its content, withno extra spacing around them (except spacing from neighboring elements such asmo).

3.3 Operator <mo>

Anmo element represents an operator or anything that should be rendered as an operator. In MathML the list of things that should "render as an operator" is widely inclusive. Besides ordinary operators with infix, prefix, or postfix forms, fence characters such as braces, parentheses, and separators such as comma and semicolon are included.In the current profile themo element is not expected to produce vertically stretchable delimiters; instead themfenced element should be used for vertically stretchy delimiterssuch as stretchy brackets, braces, parentheses and vertical bars.

Note also that this profile does not rely on an operator dictionary, but instead it is recommended to mark fences, separators and large operators explicitly usingfence,separator andlargeop attributes.In addition, prefix, infix and postfix operators may be distinguished using theform attribute. In the present profile, the default value of this attribute is "prefix" if themo element is the first child of a parent element that has many children, and "postfix" ifmo element is the last child of a parent with multiple children; the value is "infix" in all other cases. Thosemo tokens that represent fences such as brackets, braces, parens and vertical bars should be marked using thefence attribute,separators such as comma and semicolon should be marked using theseparator attribute, while large operators such as sums, products and integrals may be labeled using thelargeop attribute.UAs may rely on these attribute to infer default spacing around operators.

In the present profile stretchy operators are defined by thestretchar attribute's specifying a stretchy character to replaces the content of anmo element. The specified character is supposed to stretch to fill the available space (height of line box in case of vertically stretchy delimiters and theavailable width in case of horizontally stretchy delimiters). UAs that do not recognize a character specified by anstretchar attribute as stretchy should ignore the attribute and display the content of themo element instead.

Namevaluesdefault
formprefix | infix | postfixdepends on position ofmo element, see exact rules above
fencetrue | falsefalse
separatortrue | falsefalse
largeoptrue | falsefalse
stretcharcharacternone

3.4 Text <mtext>

Anmtext element is intended to denote commentary text.

3.5 Space <mspace>

Anmspace empty element represents a blank space of any desired size, as set by its attributes. It can also beused to make linebreaking suggestions to a visual renderer.

Namevaluesdefault
widthverythinmathspace | thinmathspace | mediummathspace | thickmathspace | verythickmathspace0
linebreakauto | newline | goodbreakauto

Thewidth attribute defines the width of the space produced by anmspace element. The default value is zero. Named values are described in table below.

Named spacevalue (em)
verythinmathspace1/9
thinmathspace1/6
mediummathspace2/9
thickmathspace5/12
verythickmathspace1/3

Thelinebreak attribute is used to give a linebreaking hint to a visual renderer. Attribute values are defined in table below.

ValueDescription
autodefault linebreaking algorithm (implementation dependent)
newlinestart a new line
goodbreakif a linebreak is needed on the line, here is a good spot

In the case when both thewidth attribute and thelinebreak attribute are set, thelinebreak attribute is ignored.

3.6 String Literal <ms>

Thems element is used to represent "string literals" in expressions meant to be interpreted bycomputer algebra systems or other systems containing "programming languages". By default, string literals are displayed surrounded bydouble quotes.

In visual renderers, the content of anmselement is typically rendered with no extra spacing added around thestring, and quote characters at the beginning and the end of thestring. By default, the left and right quote characters are both thestandard double quote character ". However, these characters can be changed with thelquote andrquote attributes defined below.

Namevaluesdefault
lquotestring"
rquotestring"

4 General Layout Schemata

Besides tokens there are several families of MathML presentationelements. One family of elements deals with various"scripting" notations, such as subscript andsuperscript. Another family is concerned with matrices and tables. Theremainder of the elements, discussed in this section, describe other basicnotations such as fractions and radicals, or deal with general functionssuch as action binding and error handling.

4.1 Horizontally Group Sub-Expressions <mrow>

Anmrow element is used to group together anynumber of sub-expressions, usually consisting of one or moremo elements acting as "operators" on oneor more other expressions that are their "operands".

4.2 Fractions <mfrac>

Themfrac element is used for fractions. It can also be used to mark up the presentation of fraction-like objects such as binomial coefficients and Legendre symbols. The syntax formfrac is:

<mfrac> numerator denominator </mfrac>

In addition to common attributes,mfrac has additional attributes that could be used to control horizontal alignment of numerator and denominator and thickness of fraction bar.

Namevaluesdefault
linethickness0 | 1 | 2 | medium | thick1
numalignleft | center | rightcenter
denomalignleft | center | rightcenter

Thelinethickness attribute indicates the thickness of the horizontal "fraction bar", or "rule", typically used to render fractions. Value "0" indicates that no bar should be rendered, value "1" (the same as "medium") refers to default width of fraction bar and "2" ("thick") produces bold fraction bar.

Thenumalign anddenomalign attributes control the horizontal alignment of the numerator and denominator, respectively. Typically, numerators and denominators are centered.

4.3 Radicals <msqrt>, <mroot>

These elements construct radicals. Themsqrt element isused for square roots, while themroot element is usedto draw radicals with indices, e.g., a cube root. The syntax for theseelements is:

<msqrt> base </msqrt><mroot> base index </mroot>

Themroot element requires exactly 2 arguments. However,msqrt accepts any number of arguments.

4.4 Error Message <merror>

Themerror element displays its contents as an "error message". The contents can be any expression or expression sequence.

4.5 Making Sub-Expressions Invisible <mphantom>

Themphantom element renders its content as invisible, butwith the same size and other dimensions, including baseline position,that its contents would have if they were renderednormally;mphantom can be used to align parts ofan expression by invisibly duplicating sub-expressions.

4.6 Expression Inside Pair of Fences <mfenced>

Themfenced element provides a convenient way of expressing common constructs involving fences (i.e., braces, brackets, and parentheses).The size of the fences depends on the size of the expression enclosed by the fence element. Opening and closing fences are specified using theopen andclose attributes defined below. This profile does not allow anmfenced element to have multiple children; authors are encouraged to group multiple children into onemrow element if this can be done.

Namevaluesdefault
openCDATA(
closeCDATA)

4.7 Enclose Expression Inside Notation <menclose>

Themenclose element renders its content inside the enclosing notation specified by itsnotation attribute,menclose accepts any number of arguments.

The values allowed fornotation are open-ended. Conforming renderers may ignore any value they do not handle, althoughrenderers are supposed to recognize at least the values listed below.

Namevalues
notationbox | left | right | top | bottom | horizontalstrike

The value "box" can be used to enclose content of the element in a frame. The values "left", "right", "top" and"bottom" should result in lines drawn on the corresponding sides ofthe contents, "horizontalstrike" should result in strikeout lines being superimposed over the content of themenclose.

5 Script and Limit Schemata

The elements described in this section position one or more scriptsaround a base. In addition to subscript and superscript elements, MathML has overscriptand underscript elements that place scripts above and below the base.

Because presentation elements should be used to describe the abstractnotational structure of expressions, it is important that the baseexpression in all "scripting" elements (i.e., the firstargument expression) should be the entire expression that is beingscripted, not just, as has been common, the rightmost character.

5.1 Subscript <msub>

The syntax for themsub element is:

 <msub> base subscript </msub>

The element is used to attach a subscript to a base.

5.2 Superscript <msup>

The syntax for themsup element is:

<msup> base superscript </msup>

The element is used to attach a superscript to a base.

5.3 Subscript-superscript Pair <msubsup>

Themsubsup element is used to attach both a subscript and a superscript to a base expression.

The syntax for themsubsup element is:

<msubsup> base subscript superscript </msubsup>

5.4 Underscript <munder>

The syntax for themunder element is:

<munder> base underscript </munder>

The element is used to attach an underscript below a base.

5.5 Overscript <mover>

The syntax for themover element is:

<mover> base overscript </mover>

The element is used to attach an overscript over a base.

5.6 Underscript-overscript Pair <munderover>

The syntax for themunderover element is:

 <munderover> base underscript overscript</munderover>

The element is used to attach both an underscript and an overscript to a base.

5.7 Prescripts <mmultiscripts>

In the current profile the syntax for themmultiscripts element is:

<mmultiscripts> base <mprescripts/> presubscript presuperscript</mmultiscripts>

This element allows adding pairs of prescripts to one base expression. Missing scripts can be represented by the empty elementnone.

The argument sequence consists of the base followed by an empty elementmprescripts and a pair of, vertically aligned, a presubscript and a presuperscript.

6 Tables and Matrices

Matrices, arrays and other table-like mathematical notation are markedup usingmtable,mtr, andmtd elements. These elements are similar to thetable,tr andtd elements of XHTML.

6.1 Table or Matrix <mtable>

A matrix or table is specified using themtable element.

The following attributes may be used to specify alignment and to add frames and rules to the table.

Namevaluesdefault
rowaligntop | bottom | center | baselinebaseline
columnalignleft | center | rightcenter
rowlinesnone | solid | dashednone
columnlinesnone | solid | dashednone
framenone | solid | dashednone

Note that the default value for each ofrowlines,columnlines andframe is the literal stringnone, meaning that the default is to render no lines,rather than that there is no default.

Therowalign attribute specifies how the entries ineach row should be aligned. For example, "top" means that the tops ofeach entry in each row should be aligned with the tops of the otherentries in that row. Thecolumnalign attribute specifieshow the entries in each column should be aligned.

6.2 Row in a Table or Matrix <mtr>

Anmtr element represents one row in a tableor matrix. Anmtr element is only allowed as adirect sub-expression of anmtable element, andspecifies that its contents should form one row of the table. Eachargument ofmtr is placed in a different columnof the table, starting at the leftmost column.

The following attributes may be used to specify alignment

Namevaluesdefault
rowaligntop | bottom | center | baselineinherited
columnalignleft | center | rightinherited

Therowalign andcolumnalign attributes allow a specific row tooverride the alignment specified by the same attributes in thesurroundingmtable element.

6.3 Entry in a Table or Matrix <mtd>

Anmtd element represents one entry, or cell, in atable or matrix. Anmtd element is onlyallowed as a direct sub-expression of anmtr.

The following attributes may be used to specify alignment

Namevaluesdefault
rowaligntop | bottom | center | baselineinherited
columnalignleft | center | rightinherited

Therowalign andcolumnalign attributesallow a specific matrix element to override the alignment specified bya surroundingmtable ormtrelement.

7 Elementary Math

7.1 2D addition, subtraction and multiplication <mstack>

Table like structures in elementary math notations such as 2D addition, subtraction and multiplicationcan be produced usingmstack layout schemata. Vertical alignment ofmstackis specified byalign attribute. In current profile horizontal alignment of numbers withinmstack simply defaults toright, as current CSS implementations are unlikely to handle more sophisticated alignment mechanisms formstack layout schemata.

Namevaluesdefault
aligntop | bottom | center | baselinebaseline
stackalignrightattribute is required

Element contains one or moremn tokens followed bymsrow element,msline and groups consisting of one or moremn tokens followed by optionalmsline.

The syntax for themstack element is:

<mstack stackalign="right">(one or moremn tokens)(msrow element)<msline/>(one or moremn tokens followed by optionalmsline)+</mstack>

7.2 Horizontal rows <mrow>

In the present profilemsrow element is used to add operator before last operand in elementary math notations such as 2D addition, subtraction and multiplication.

Element containsmo token followed bymn token

The syntax for themsrow element is:

<msrow><mo>operator</mo><mn>operand</mn></msrow>

7.3 Long division <mlongdiv>

Elementary math notations for long division can be produced usingmlongdiv layout schemata. Vertical alignment ofmlongdiv is specified byalign attribute. In current profile horizontal alignment of numbers withinmlongdiv simply defaults toleft, as current CSS implementations are unlikely to handle more sophisticated alignment mechanisms formlongdiv layout schemata.

Namevaluesdefault
aligntop | bottom | center | baselinebaseline
stackalignleftattribute is required

Element containsmn token representingresult of the division followed bymn token representingdivisor and groups consisting of one or moremn tokens followed by optionalmsline element.

The syntax for themlongdiv element is:

<mlongdiv stackalign="left">(result of the division)(divisor)(one or moremn tokens followed by optionalmsline)+</mlongdiv>

8 Annotations

8.1 Bind Action to a Sub-Expression <maction>

To provide a mechanism for binding actions to expressions, MathML provides themaction element. The action type is specified by theactiontype attribute. Current profile defines only "tooltip" actiontype.

Namevaluesdefault
actiontypetooltip(required attribute, no default value)

<maction actiontype="tooltip"> base tooltip </maction>

When a mouse cursor is placed over an expression UAs that support this action type should display the content of the second child in a "tooltip" box.

8.2 Add semantic mapping <semantics>

The current profile deals with layout schemata that reflect the visual structure of mathematical formulae. To attach extra semantic information that describes the content of formulae or provide an alternative encoding of a mathematical expression one can use the Content MathMLsemantics element. In current profile content model ofsemantics element is limited to presentational MathML followed byannotation and/orannotation-xml elements.

9 Extensibility and Conformance

9.1 Extensibility

Since the current profile is designed to be suitable for use in an XML/CSS environment, it is relatively easy to extend it by adding new elements or attributes[rec-xml] to a DTD and specifying the default formatting in a style sheet.However any new elements should be placed in their own namespace and any new attributes added to existing MathML elements should have a namespace prefix;authors and implementers are strongly encouraged to use standard markup whenever possible. Similarly, maintainers of documents employing MathML extension mechanisms are encouraged to monitor relevant standards activity and to update documents to use more standardized markup as it becomes available.

9.2 Conformance

Documents that conform to this MathML for CSS profile should be conformant MathML 3.0 documents and should use only those MathML elements and attributes included in the current profile. The content of layout schemata with a fixed number of arguments should match the content model specified in thelist of required arguments and the profile's DTD.

UAs that conform to the MathML for CSS profile should support all MathML elements and attributes included in profile.When a conformant UA encounters an element that it does not recognize it may ignore that element, but should process its content.UAs that support the standard DOM are encouraged to expose such elements through generic DOM Element interface. UAs that support style sheets are encouraged to apply formatting specified in style sheets to such elements.

10 Differences between MathML presentational markup and present profile

The MathML for CSS profile differs from full MathML presentational markup in a number of ways. The present section is intended to highlight the main differences.

11 Document Type Definition

<!ENTITY % common "class NMTOKENS #IMPLIED id ID #IMPLIED style CDATA #IMPLIED"><!ENTITY % math "(maction | menclose | merror | mfenced | mfrac | mi | mlongdiv | mmultiscripts | mn | mo | mover | mphantom | mroot | mrow | ms | mspace | msqrt | mstack | msub | msubsup | msup |mtable | mtext | munder | munderover | semantics)+"><!ENTITY % mrow "(mi | mn | mo | mphantom | maction | merror | mrow | ms | mtext)"><!ATTLIST maction actiontype (tooltip) #REQUIRED %common;><!ELEMENT maction (%mrow;,%mrow;)><!ATTLIST math display (block | inline) #IMPLIED xmlns CDATA #REQUIREDalttext CDATA #IMPLIED altimage CDATA #IMPLIED %common;><!ELEMENT math %math;><!ATTLIST menclose notation (bottom | box | left | right | top | horizontalstrike) #REQUIRED %common;><!ELEMENT menclose %math;><!ATTLIST merror %common;><!ELEMENT merror %math;><!ATTLIST mfenced open CDATA #IMPLIED close CDATA #IMPLIED %common;><!ELEMENT mfenced %mrow;><!ATTLIST mfrac linethickness (0 | 1 | 2 | medium | thick) #IMPLIED numalign (center | left | right) #IMPLIED denalign (center | left | right) #IMPLIED %common;><!ELEMENT mfrac (%mrow;,%mrow;)><!ATTLIST mi mathvariant (normal | bold | italic | bold-italic | sans-serif | bold-sans-serif | sans-serif-italic | sans-serif-bold-italic | monospace) #IMPLIED %common;><!ELEMENT mi (#PCDATA)><!ATTLIST mmultiscripts %common;><!ELEMENT mmultiscripts (%mrow;,mprescripts,((none,%mrow;)|(%mrow;,(none|%mrow;))))><!ATTLIST mn mathvariant (normal | bold | italic | bold-italic | sans-serif | bold-sans-serif | sans-serif-italic | sans-serif-bold-italic | monospace) #IMPLIED %common;><!ELEMENT mn (#PCDATA)><!ATTLIST mo largeop (true | false) #IMPLIED separator (true | false) #IMPLIED fence (true | false) #IMPLIEDform (prefix | infix | postfix) #IMPLIED stretchar CDATA #IMPLIEDmathvariant (normal | bold | italic | bold-italic | sans-serif | bold-sans-serif | sans-serif-italic | sans-serif-bold-italic | monospace) #IMPLIED %common;><!ELEMENT mo (#PCDATA)><!ATTLIST mover %common;><!ELEMENT mover (%mrow;,%mrow;)><!ATTLIST mphantom %common;><!ELEMENT mphantom %math;><!ATTLIST mprescripts %common;><!ELEMENT mprescripts EMPTY><!ATTLIST mroot %common;><!ELEMENT mroot (%mrow;,%mrow;)><!ATTLIST mrow %common;><!ELEMENT mrow %math;><!ELEMENT ms (#PCDATA)><!ATTLIST ms lquote CDATA #IMPLIED rquote CDATA #IMPLIED %common;><!ATTLIST msqrt %common;><!ELEMENT msqrt %math;><!ATTLIST msub %common;><!ELEMENT msub (%mrow;,%mrow;)><!ATTLIST msubsup %common;><!ELEMENT msubsup (%mrow;,%mrow;,%mrow;)><!ATTLIST msup %common;><!ELEMENT msup (%mrow;,%mrow;)><!ATTLIST mtable rowalign (top | bottom | center | baseline) #IMPLIEDcolumnalign (left | center | right) #IMPLIEDrowlines (none | solid | dashed) #IMPLIEDcolumnlines (none | solid | dashed) #IMPLIEDframe (none | solid | dashed) #IMPLIED %common;><!ELEMENT mtable (mtr+)><!ATTLIST mtd rowalign (top | bottom | center | baseline) #IMPLIEDcolumnalign (left | center | right) #IMPLIED %common;><!ELEMENT mtd %math;><!ATTLIST mtext mathvariant (normal | bold | italic | bold-italic | sans-serif | bold-sans-serif | sans-serif-italic | sans-serif-bold-italic | monospace) #IMPLIED %common;><!ELEMENT mtext (#PCDATA)><!ATTLIST mtr rowalign (top | bottom | center | baseline) #IMPLIED columnalign (left | center | right) #IMPLIED %common;><!ELEMENT mtr (mtd+)><!ATTLIST munder %common;><!ELEMENT munder (%mrow;,%mrow;)><!ATTLIST munderover %common;><!ELEMENT munderover (%mrow;,%mrow;,%mrow;)><!ATTLIST mspace width (verythinmathspace | thinmathspace | mediummathspace | thickmathspace | verythickmathspace) #IMPLIED linebreak (auto | newline | goodbreak) #IMPLIED %common;><!ELEMENT mstack (mn+, msrow, msline, (mn+, msline?)+)><!ATTLIST mstack align (top | bottom | center | baseline) #IMPLIED stackalign (right) #REQUIRED %common;><!ELEMENT mlongdiv (mn, mn, (mn+, msline?)+)><!ATTLIST mlongdiv align (top | bottom | center | baseline) #IMPLIED stackalign (left) #REQUIRED %common;><!ATTLIST msrow %common;><!ELEMENT msrow (mo, mn)><!ELEMENT msline EMPTY><!ELEMENT mspace EMPTY><!ATTLIST none %common;><!ELEMENT none EMPTY><!ELEMENT semantics (%math;,(annotation|annotation-xml)*)><!ATTLIST annotation definitionURL CDATA #IMPLIED encoding CDATA #REQUIRED><!ELEMENT annotation (#PCDATA)><!ATTLIST annotation-xml definitionURL CDATA #IMPLIED encoding CDATA #REQUIRED><!ELEMENT annotation-xml ANY>

12 Default CSS style sheet

(this section is non normative)

This profile admits a default CSS style sheet that could be used to render MathML in CSS aware UAs. In the long term perspective it would be appropriate to extend CSS3 with a few math specific properties, until then one can use style sheet enclosed below for formatting of MathML defined in the current profile.

@namespace "http://www.w3.org/1998/Math/MathML";math{line-height:1.3em;text-indent:0;}math[display="block"]{display:block;text-align:center;page-break-inside:avoid;}mfrac{display:inline-table;white-space:nowrap;border-collapse:collapse;text-align:center;vertical-align:0.9em;margin:0 2px;font-size:1em;}mfrac > *{line-height:1.3em;font-size:0.9em;}mfrac > *:first-child{display:inline-table;vertical-align:text-bottom;}mfrac > * + *{border-top:solid thin;display:table-row;}mfrac[linethickness="0"] > * + *{border-top:none;}mfrac[linethickness="2"] > * + *, mfrac[linethickness="thick"] > * + *{border-top:solid medium;}mfrac[numalign="left"] > *:first-child, mfrac[denalign="left"] > * + *{text-align:left;}mfrac[numalign="right"] > *:first-child, mfrac[denalign="right"] > * + *{text-align:right;}msub, msup, msubsup, mmultiscripts{display:inline-table;line-height:0.4em;}msubsup, msup, mmultiscripts{margin-top:0.4ex;table-baseline:2;}msubsup, msub, mmultiscripts{margin-bottom:0.4ex;}msubsup, msup{direction:rtl;}msub > *{display:table-row;}none{content:"\A0";}msubsup > *, msup > *{display:table-row;direction:ltr;text-align:left;}mmultiscripts > *{display:none;}mmultiscripts > *:first-child, mmultiscripts > mprescripts + *{display:table-row;}mmultiscripts > mprescripts + * + *{display:table-header-group;}msub > *:first-child:after, msub > * + *:before, msubsup > *:first-child:before, msup > *:first-child:before,mmultiscripts > *:first-child:before{display:table-cell;content:"\A0";}msubsup > * + * + *, msup > * + *{display:table-header-group;}msub > * + *, msup > * + *, msubsup > * + *, munder > * + *, mover > * + *, munderover > * + *,mmultiscripts > * + *{font-size:0.7em;}munder, munderover, mover{display:inline-table;margin:1px;text-align:center;}munder > *, munderover > *, mover > *{display:table-row;}mover > * + *, munderover > * + * + *{display:table-header-group;}mover, munderover{table-baseline:2;}msqrt{display:inline-block;margin:1px 0 1px 22px;border-top:solid 1px;border-left:groove 2px;padding:2px 5px 0 0;}msqrt:before{display:inline-block;vertical-align:bottom;content:'';width:22px;height:14px;background-repeat:no-repeat;margin:0 3px 0 -22px;}msqrt:before, mroot > * + *:after{background-image:url("data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABYAAAAOCAYAAAArMezNAAAArklEQVR42mNgIAzkgJiRgYpAGIgnAfFvIF4JxKyUGsgOxKVA/ASI5wCxHRBvA+K9QMxHrqGRQLweiDOBmBdJnAWI5wPxeSAWJ8VAPSBOAWJTAuo6gPguEKsQY6gQEPOQ4Ih8IH4JxCYMNABhQPwOiN1pYbgzEL8C4hhaGG4AxM+BuJgWhisB8W0g7qOF4SJAfBqIl1EjI6EDbiDeAcQ7SUxlRAGQa5cA8RkGGoFeACG1GGdqegJfAAAAAElFTkSuQmCC");}mroot{display:inline-table;direction:rtl;}mroot > *{display:table-cell;direction:ltr;text-align:left;}mroot > *:first-child{border-top:solid 1px;border-left:groove 2px;padding:2px 5px 0 3px;}mroot > * + *{vertical-align:bottom;text-align:right;font-size:0.7em;line-height:1em;}mroot > * + *:after{display:block;content:"";width:22px;height:14px;margin-right:-1px;margin-left:auto;}mfenced{display:inline-table;border-collapse:separate;border-spacing:0.2ex 0;white-space:nowrap;margin:1px;}mfenced > *:first-child{display:table-row;}mfenced > * + *{display:none;}mfenced > *:before, mfenced > *:after{display:table-cell;content:"\A0";background-repeat:no-repeat;background-size:100% 100%;}mfenced > *:before{background-image:url("data:image/png;base64,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");}mfenced > *:after{background-image:url("data:image/png;base64,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");}mfenced[open="["] > *:before{border-style:solid;border-width:1px 0 1px 1px;background-image:none;}mfenced[close="]"] > *:after{border-style:solid;border-width:1px 1px 1px 0;background-image:none;}mfenced[open="\2016"] > *:before{border-style:double;border-width:0 0 0 3px;background-image:none;}mfenced[close="\2016"] > *:after{border-style:double;border-width:0 3px 0 0;background-image:none;}mfenced[open="\27e6"] > *:before{border-style:double;border-width:2px 0 2px 3px;background-image:none;}mfenced[close="\27e7"] > *:after{border-style:double;border-width:2px 3px 2px 0;background-image:none;}mfenced[open="|"] > *:before{border-style:solid;border-width:0 0 0 1px;background-image:none;}mfenced[close="|"] > *:after{border-style:solid;border-width:0 1px 0 0;background-image:none;}mfenced[open="\230a"] > *:before{border-style:solid;border-width:0 0 1px 1px;background-image:none;}mfenced[close="\230b"] > *:after{border-style:solid;border-width:0 1px 1px 0;background-image:none;}mfenced[open="\2308"] > *:before{border-style:solid;border-width:1px 0 0 1px;background-image:none;}mfenced[close="\2309"] > *:after{border-style:solid;border-width:1px 1px 0 0;background-image:none;}mfenced[open="{"] > *:before{content:"\A0\A0";background-image:url("data:image/png;base64,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");}mfenced[close="}"] > *:after{content:"\A0\A0";background-image:url("data:image/png;base64,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");}mfenced[open="\27e8"] > *:before, mfenced[open="\2329"] > *:before{background-image:url("data:image/png;base64,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");}mfenced[close="\27e9"] > *:after, mfenced[close="\232A"] > *:after{background-image:url("data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAABZCAYAAAA+TwS/AAAByElEQVR42s2ZPSjFURiH/z4XkZvIZpFQJFaLslDqdkvdVQYjqZuFyWq6JXUH3TJZpW4WyWA0mSS6yWCQ8hGDr9+pdzid7vY+g1PP+vSe//89H+97sizLOjN4jNDCCdFHS5dp4aZoI4WzokgKW8UxPe0DMUkKC6JKCjvEs+glpUf2x7GxJO5FCyXsEV9ikYzyTJyTwlXxa2scGQMm3CejvBQf9k2RsWVRblDCMRPWyRS6MWmBEu6Y8IwSTpswME4Im8SjCStUlBUTvoscIZyPpl0ihO3ixYR3opmQHkZR5glhMRKeEsIu8WnCHzFKSGtRlHuEcCUSvolur7BffEfSdSLKi0h4ayvJNUqRMLDgFQ4mwhNi2leRMKTQsFe4nUS56xVOJcJXS3zXqCfSNa+wnAivvSk0kwgDcx5hOFafEmHNO+1qIgwpNOQR5htMu+wR5hoIH/5VhOg3xP8ynof4SkHXMr7b4PshumPjZwp+6qHnMn5zwO826O0Lvx/iN1j0jo1XAXidglZSeK2HV6N4vYxW9HjPAe+KoH0bvLOE975CmmDdObx/iHc40R4s3iXG+9hopx1/C8BfK/D3FPTFB3+Twl/N0He9P0bV3S+iamc2AAAAAElFTkSuQmCC");}mfenced[open=""] > *:before, mfenced[close=""] > *:after{content:normal;}mover > * + mo[fence="true"], munder > * + mo[fence="true"]{content:"\A0";line-height:1ex;background-size:100% 100%;background-image:url("data:image/png;base64,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");}munder > * + mo[fence="true"]{background-image:url("data:image/png;base64,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");}menclose{display:inline-table;border-collapse:separate;border-spacing:0.4ex 0;}menclose[notation="top"]{border-top:solid thin;}menclose[notation="bottom"]{border-bottom:solid thin;}menclose[notation="right"]{border-right:solid thin;}menclose[notation="left"]{border-left:solid thin;}menclose[notation="box"]{border:solid thin;}menclose[notation="horizontalstrike"]{text-decoration:line-through;}mtable{display:inline-table;line-height:1.5em;text-align:center;vertical-align:middle;}mtr{display:table-row;}mtd{display:table-cell;padding:0 0.5ex;}mtable[columnalign="left"], mtr[columnalign="left"], mtd[columnalign="left"]{text-align:left;}mtable[columnalign="right"], mtr[columnalign="right"], mtd[columnalign="right"]{text-align:right;}mtable[rowalign="top"] mtd, mtable mtr[rowalign="top"] mtd, math mtable mtr mtd[rowalign="top"]{vertical-align:top}mtable[rowalign="bottom"] mtd, mtable mtr[rowalign="bottom"] mtd, math mtable mtr mtd[rowalign="bottom"]{vertical-align:bottom}mtable[rowalign="center"] mtd, mtable mtr[rowalign="center"] mtd, math mtable mtr mtd[rowalign="center"]{vertical-align:middle}mtable[frame="solid"]{border:solid thin;}mtable[frame="dashed"]{border:dashed thin;}mtable[rowlines="solid"], mtable[rowlines="dashed"], mtable[columnlines="solid"], mtable[columnlines="dashed"]{border-collapse:collapse;}mtable[rowlines="solid"] > mtr + mtr{border-top:solid thin;}mtable[rowlines="dashed"] > mtr + mtr{border-top:dashed thin;}mtable[columnlines="solid"] > mtr > mtd + mtd{border-left:solid thin;}mtable[columnlines="dashed"] > mtr > mtd + mtd{border-left:dashed thin;}mspace[linebreak="goodbreak"]:before{content:"\200B";white-space:normal;}mspace[linebreak="newline"]:before, mspace[linebreak="indentingnewline"]:before {content:"\000A";white-space:pre;}mspace[width]:before{content:normal;}mspace[width="verythinmathspace"]{padding:0 0.05em;}mspace[width="thinmathspace"]{padding:0 0.08em;}mspace[width="mediummathspace"]{padding:0 0.11em;}mspace[width="thickmathspace"]{padding:0 0.14em;}mspace[width="verythickmathspace"]{padding:0 0.17em;}mo[largeop="true"]{font-size:1.3em;vertical-align:-0.1ex;}mo[form="infix"], * + mo{padding:0 0.3ex;}mo[form="prefix"]{padding:0 0 0 0.5ex;}mo[form="postfix"]{padding:0 0.5ex 0 0;}mo[fence="true"], mo[separator="true"]{padding:0;}mi[mathvariant="bold"], mi[mathvariant="bold-italic"], mi[mathvariant="bold-sans-serif"], mi[mathvariant="sans-serif-bold-italic"],mn[mathvariant="bold"], mn[mathvariant="bold-italic"], mn[mathvariant="bold-sans-serif"], mn[mathvariant="sans-serif-bold-italic"],mo[mathvariant="bold"], mo[mathvariant="bold-italic"], mo[mathvariant="bold-sans-serif"], mo[mathvariant="sans-serif-bold-italic"],ms[mathvariant="bold"], ms[mathvariant="bold-italic"], ms[mathvariant="bold-sans-serif"], ms[mathvariant="sans-serif-bold-italic"],mtext[mathvariant="bold"], mtext[mathvariant="bold-italic"], mtext[mathvariant="bold-sans-serif"], mtext[mathvariant="sans-serif-bold-italic"]{font-weight:bold;font-style:normal;}mi[mathvariant="monospace"], mn[mathvariant="monospace"],mo[mathvariant="monospace"], ms[mathvariant="monospace"],mtext[mathvariant="monospace"]{font-family:monospace;font-style:normal;}mi[mathvariant="sans-serif"], mi[mathvariant="bold-sans-serif"], mi[mathvariant="bold-sans-serif"], mi[mathvariant="sans-serif-italic"], mi[mathvariant="sans-serif-bold-italic"],mn[mathvariant="bold-sans-serif"],mn[mathvariant="sans-serif"], mn[mathvariant="bold-sans-serif"], mn[mathvariant="sans-serif-italic"],mn[mathvariant="sans-serif-bold-italic"], mo[mathvariant="sans-serif"], mo[mathvariant="bold-sans-serif"], mo[mathvariant="bold-sans-serif"], mo[mathvariant="sans-serif-italic"], mo[mathvariant="sans-serif-bold-italic"], ms[mathvariant="sans-serif"], ms[mathvariant="bold-sans-serif"], ms[mathvariant="bold-sans-serif"], ms[mathvariant="sans-serif-italic"], ms[mathvariant="sans-serif-bold-italic"], mtext[mathvariant="sans-serif"], mtext[mathvariant="bold-sans-serif"], mtext[mathvariant="bold-sans-serif"], mtext[mathvariant="sans-serif-italic"], mtext[mathvariant="sans-serif-bold-italic"]{font-family:sans-serif;font-style:normal;}mi, mi[mathvariant="italic"], mi[mathvariant="bold-italic"],mi[mathvariant="sans-serif-italic"], mi[mathvariant="sans-serif-bold-italic"],mn[mathvariant="italic"], mn[mathvariant="bold-italic"],mn[mathvariant="sans-serif-italic"], mn[mathvariant="sans-serif-bold-italic"],mo[mathvariant="italic"], mo[mathvariant="bold-italic"],mo[mathvariant="sans-serif-italic"], mo[mathvariant="sans-serif-bold-italic"],ms[mathvariant="italic"], ms[mathvariant="bold-italic"],ms[mathvariant="sans-serif-italic"], ms[mathvariant="sans-serif-bold-italic"],mtext[mathvariant="italic"], mtext[mathvariant="bold-italic"],mtext[mathvariant="sans-serif-italic"], mtext[mathvariant="sans-serif-bold-italic"]{font-style:italic;}mi[mathvariant="normal"], mn[mathvariant="normal"], mo[mathvariant="normal"], ms[mathvariant="normal"], mtext[mathvariant="normal"]{font-style:normal;}ms:before, ms:after {content:"\0022"}ms[lquote]:before {content:attr(lquote)}ms[rquote]:after {content:attr(rquote)}mphantom {visibility:hidden}merror{outline:solid thin red}merror:before{content:"Error: "}mrow{white-space:nowrap;}math[display='block']{display:block;margin:1em 0 1em 3em;}mstack, mlongdiv{display:inline-table;font-family:monospace;}mstack{text-align:right;border-collapse:collapse;}mstack[align='top'], mlongdiv[align='top']{vertical-align:top;}mstack[align='bottom'], mlongdiv[align='bottom'] {vertical-align:bottom;}mstack[align='center'], mlongdiv[align='center']{vertical-align:middle;}msline{display:block;border-bottom:solid thin;}mstack > *, mlongdiv > mn:first-child{display:table-row;}mlongdiv > *:first-child + *{display:table-cell;}mlongdiv > *:first-child + * + *{border-top:solid thin;}mlongdiv > *:first-child:before{display:table-cell;content:'\a0';}mlongdiv > *:first-child + *:after{content:')';}mlongdiv > *{display:block;}mscarry{display:none;}maction > * + *{display:none;}maction[actiontype="tooltip"]:focus > * + *,maction[actiontype="tooltip"]:hover > * + *{position:fixed;display:block;top:0;left:0;background-color:InfoBackground;color:InfoText;padding:0.5ex;border:solid 1px;}annotation, annotation-xml{display:none;}

13 References

css
Cascading Style Sheets, level 2 revision 1,Bert Bos, Tantek Çelik, Ian Hickson, Håkon Wium Lie. W3C Recommendation 7 June 2011.
css2
Cascading Style Sheets, level 2CSS2 Specification, Bert Bos, Håkon Wium Lie, Chris Lilley, Ian Jacobs. May 1998.
rec-xml
Extensible Markup Language (XML) 1.0 (Fifth Edition),Tim Bray, Jean Paoli, C. M. Sperberg-McQueen, Eve Maler, and François Yergeau (editors). W3C Recommendation 26 November 2008.
rec-xmlns
Namespaces in XML 1.0 (Third Edition),Tim Bray, Dave Hollander, Andrew Layman, Richard Tobin, Henry S. Thompson. W3C Recommendation 8 December 2009.
mathml
Mathematical Markup Language (MathML) Version 3.0,David Carlisle, Patrick Ion, Robert Miner. W3C Recommendation, 21 October 2010.
mathml1
Mathematical Markup Language (MathML) 1.0 Specification, Patrick Ion, Robert Miner. April 1998.
roadmap
Math Working Group Roadmap 2007/8, Patrick Ion, Robert Miner. March 2007, document subject to update. [See especially2.2.1]

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