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.
This document describes a profile of MathML 3.0 that admits formatting with Cascading Style Sheets.
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.
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
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.
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.
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.
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.
mi | identifier |
mn | number |
mo | operator, fence or separator |
mtext | text |
mspace | space |
ms | string 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.
mrow | groups any number of sub-expressions horizontally |
mfrac | forms a fraction from two sub-expressions |
msqrt | forms a square root (radical without an index) |
mroot | forms a radical with specified index |
merror | encloses a syntax error message from a preprocessor |
mphantom | makes content invisible but preserve its size |
mfenced | surrounds content with a pair of fences |
menclose | encloses content with a stretching symbol |
msub | attaches a subscript to a base |
msup | attaches a superscript to a base |
msubsup | attaches a subscript-superscript pair to a base |
munder | attaches an underscript to a base |
mover | attaches an overscript to a base |
munderover | attaches an underscript-overscript pair to a base |
mmultiscripts | attaches prescripts to a base |
mtable | marks a table or matrix |
mtr | marks a row in a table or matrix |
mtd | marks a one entry in a table or matrix |
mstack | used for elementary math notations such as 2D addition, subtraction and multiplication |
mlongdiv | used for elementary math notations for long division |
msline | marks horizontal line in elementary math layouts |
msrow | marks row in elementary math layouts |
maction | binds actions to a sub-expression |
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.
Element | Required argument count | Argument roles |
mfrac | 2 | numeratordenominator |
mroot | 2 | baseindex |
mfenced | 1 | base |
msub | 2 | basesubscript |
msup | 2 | basesuperscript |
msubsup | 3 | basesubscriptsuperscript |
munder | 2 | baseunderscript |
mover | 2 | baseoverscript |
munderover | 3 | baseunderscriptoverscript |
mmultiscripts | 4 | basemprescripts presubscriptpresuperscript |
mtable | 1+ | one or moremtr elements |
mtr | 1+ | one or moremtd elements |
mstack | 4+ | one or moremn tokens followed bymsrow element,msline and groups consisting of one or moremn tokens followed by optionalmsline |
mlongdiv | 3+ | result of the division followed bydivisor andgroups consisting of one or moremn tokens followed by optionalmsline |
msrow | 2 | mo token element followed bymn token |
maction | 2 | basetooltip |
The elementsmrow
,msqrt
,merror
,mphantom
,menclose
,mtd
andmath
admit any number of arguments and accept any layout schemata or token elements from current profile as children.
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.
Name | values | default | valid on |
id | ID | all elements | |
class | NMTOKENS | all elements | |
style | CDATA | all elements | |
mathvariant | normal | bold | italic | bold‑italic | sans-serif | bold‑sans‑serif | sans‑serif‑italic | sans‑serif‑bold‑italic | monospace | normal | mn ,mo ,ms ,mtext |
mathvariant | normal | bold | italic | bold‑italic | sans-serif | bold‑sans‑serif | sans‑serif‑italic | sans‑serif‑bold‑italic | monospace | italic | mi |
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.
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.
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
).
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.
Name | values | default |
form | prefix | infix | postfix | depends on position ofmo element, see exact rules above |
fence | true | false | false |
separator | true | false | false |
largeop | true | false | false |
stretchar | character | none |
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.
Name | values | default |
width | verythinmathspace | thinmathspace | mediummathspace | thickmathspace | verythickmathspace | 0 |
linebreak | auto | newline | goodbreak | auto |
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 space | value (em) |
verythinmathspace | 1/9 |
thinmathspace | 1/6 |
mediummathspace | 2/9 |
thickmathspace | 5/12 |
verythickmathspace | 1/3 |
Thelinebreak
attribute is used to give a linebreaking hint to a visual renderer. Attribute values are defined in table below.
Value | Description |
auto | default linebreaking algorithm (implementation dependent) |
newline | start a new line |
goodbreak | if 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.
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 anms
element 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.
Name | values | default |
lquote | string | " |
rquote | string | " |
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.
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".
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.
Name | values | default |
---|---|---|
linethickness | 0 | 1 | 2 | medium | thick | 1 |
numalign | left | center | right | center |
denomalign | left | center | right | center |
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.
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.
Themerror
element displays its contents as an "error message". The contents can be any expression or expression sequence.
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.
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.
Name | values | default |
open | CDATA | ( |
close | CDATA | ) |
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.
Name | values |
notation | box | 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
.
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.
The syntax for themsub
element is:
<msub> base subscript </msub>
The element is used to attach a subscript to a base.
The syntax for themsup
element is:
<msup> base superscript </msup>
The element is used to attach a superscript to a base.
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>
The syntax for themunder
element is:
<munder> base underscript </munder>
The element is used to attach an underscript below a base.
The syntax for themover
element is:
<mover> base overscript </mover>
The element is used to attach an overscript over a base.
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.
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.
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.
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.
Name | values | default |
rowalign | top | bottom | center | baseline | baseline |
columnalign | left | center | right | center |
rowlines | none | solid | dashed | none |
columnlines | none | solid | dashed | none |
frame | none | solid | dashed | none |
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.
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
Name | values | default |
rowalign | top | bottom | center | baseline | inherited |
columnalign | left | center | right | inherited |
Therowalign
andcolumnalign
attributes allow a specific row tooverride the alignment specified by the same attributes in thesurroundingmtable
element.
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
Name | values | default |
rowalign | top | bottom | center | baseline | inherited |
columnalign | left | center | right | inherited |
Therowalign
andcolumnalign
attributesallow a specific matrix element to override the alignment specified bya surroundingmtable
ormtr
element.
Table like structures in elementary math notations such as 2D addition, subtraction and multiplicationcan be produced usingmstack
layout schemata. Vertical alignment ofmstack
is 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.
Name | values | default |
align | top | bottom | center | baseline | baseline |
stackalign | right | attribute 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>
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>
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.
Name | values | default |
align | top | bottom | center | baseline | baseline |
stackalign | left | attribute 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>
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.
Name | values | default |
actiontype | tooltip | (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.
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.
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.
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.
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.
The profile drops several formatting oriented elements and attributes, includingmstyle
(an element explicitly formatting oriented and which duplicates some CSS functionality is a CSS-incompatible way),mpadded
(also now duplicating CSS functionality is CSS incompatible way),mglyph
(might be included in future versions of profile),mlabeledtr
(which does not fit in the CSS table model),malign
,maligngroup
,malignmark
,malignscope
,msgroup
,mscarry
andmscarries
elements.The list of dropped presentational attributes includesaccent
,accentunder
,align
,alignmentscope
,columnspacing
,columnspan
,columnwidth
,depth
,displaystyle
,equalcolumns
,equalrows
,fontfamily
,fontsize
,fontstyle
,fontweight
,framespacing
,groupalign
,height
,indentalign
,indentalignfirst
,indentalignlast
,indentshift
,indentshiftfirst
,indentshiftlast
,indenttarget
,longdivstyle
,lspace
,mathbackground
,mathcolor
,mathsize
,maxsize
,minlabelspacing
,minsize
,mode
,movablelimits
,rowspacing
,rowspan
,rspace
,side
,subscriptshift
,superscriptshift
,symmetric
,width (on mtable)
. Also list of supported named spaces is limited.
The changes affect the handling of anmi
token element. In this MathML for CSS profile, the default value of themathvariant
attribute is "italic",regardless of the content of the element. For interoperability reasons, authors should specify the value of this attribute explicitly if anmi
token contains more then one character.
The MathML for CSS profile does not rely on an operator dictionary because CSS selectors can not differentiate betweenmo
tokens based on their content.Therefore authors are encouraged to use more explicit markup when applicable: for example, stretchy vertical delimiters are better markedusing themfenced
construction, and stretchy over or under bars and strikes are better marked using themenclose
element.In addition, there areform
,fence
,separator
,largeop
,stretchar
attributes thatcan be used to specify the class of an operator.
In the MathML for CSS profile themfenced
schema is simplified. In particular, theseparators
attribute of anmfenced
element is dropped,as there is no way to handle theseparator
attribute in the present CSS framework. For interoperability reasons, since the attribute does not have an empty default value, the content model was restricted to allow only one child element.
Multiscripts schemata is included in the profile but number of scripts is limited to at most two prescripts. It is difficult to handle mmultiscripts construction as the order of child elements inside ammultiscripts
element does not match their in-flow order.
The table model is simplified: themlabeledtr
element is dropped as it does not fit in the CSS table model, and many attributes have been removed.
The 2D elementary math layoutsmstack
andmlongdiv
are significantly simplified.Horizontal alignment options are limited andmscarries
construction is dropped.
Layout schemata with fixed number of required arguments accept 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 document object model.
<!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>
(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,iVBORw0KGgoAAAANSUhEUgAAABQAAABQCAYAAAAZQFV3AAABtElEQVR42s2ZK0hEURCGr8UiPhYVRJAFoxssFtsafDXRKLogNpNNDDazTSxiMYhoMdtWsAibtKhssCj4ALWIoM4s58Awdb7gD3+45eO8z5z/FgWnfnEfAWoTz4tHCJhCdsQDBGxKXBd3EbBl8a14kIBtiF+pMdsS/4pnCNic+Ed8SMAq4g/xM7HWetIEaFdrROtOEuySgE0kmHqB2FKNBLtP3yGtmtatRWGd4scEexF3RIHrpnV7xGRcG+BsFDZuYO/i9ihw3wCPicn4NMDFKHDJwNS9UeCBgTWJ2W0a4GkUVnbd3YwCaw44TY6fOnyQ3hjYE3FUfRngVRQ45Lp7FgVWHXA3Clyhl8y2A4ZvtyMHnIwCzx1wLAq8cMDRKLDhgMNR4J0DlqPABwcsRYFvDtgdBX47YPHvgHiX8UnBlw2+sPGthx8O+PGFH7D4FVAt4EsKv0bxi16FliIqvFjCyzm84FShJbEfR6Rox58V+MNHhT7NVPjjUYU+b1X4AxyPCFRoiKHCYxYVGgRloVGVCg/TVGjcl4UGklloZJqFhrpZaOychQbjWWh0b7co9nPBqvX74w/Kju1j59IjnwAAAABJRU5ErkJggg==");}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,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");}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 > * + 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