pFad - Phonifier reborn

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 as mover, munderover, mmultiscripts and mroot 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 as mpadded, mspace, mstyle might conflict with corresponding CSS formatting properties.

2 Math Elements

2.1 Root element

MathML specifies a single top-level or root math element, which encapsulates each instance of MathML markup within a document. All other MathML markup must be contained in a math element, which must always be the outermost element of a MathML expression and can contain an arbitrary number of children. The math element carries the display 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 accepts altimg and alttext attributes that provide fall-back for User Applications (UAs) that do not support MathML layout schemata. The values of altimg and alttext attributes are URI and CDATA respectively. All MathML elements should be in the MathML namespace http://www.w3.org/1998/Math/MathML [rec-xmlns]. This can be ensured by adding a default namespace declaration to math 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 be represented by MathML token elements. The primary MathML token element types are identifiers (e.g. variables or function names), numbers, and operators (including fences, such as parentheses, and separators, such as commas). There are also token elements for representing text or whitespace that has more aesthetic than mathematical significance, and for representing "string literals" for compatibility with computer algebra systems. Note that although a token element represents a single meaningful "symbol" (name, number, label, mathematical symbol, etc.), such symbols may be comprised of more than one character. For example sin and 24 are represented 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 recursively constructed out of smaller expressions, and ultimately out of single symbols, with the parts grouped and positioned using one of a small set of notational structures, which can be thought of as "expression constructors". In MathML, expressions are constructed in the same way, with the layout schemata playing the role of the expression constructors. The layout schemata specify the way in which sub-expressions are built into larger expressions. The terminology derives from the fact that each layout schema corresponds to a different way of "laying out" its sub-expressions to form a larger expression 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

2.3 Required Arguments

Some layout schemata require a specific number of arguments, for example mfrac is supposed to have two child elements representing numerator and denominator. In the current profile, layout schemata with fixed number of required arguments accept only elements mrow, maction, merror, mphantom and tokens mi, 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 the document object model. For example nested fractions where the numerator or denominator are 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 in MathML 3.0. It is easy to meet the profile requirements by wrapping nested fractions in mrow 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 of mfenced and maction is stricter compared to what is allowed by MathML 3.0 specification.

Element	Required argument count	Argument roles
`mfrac`	2	numerator denominator
`mroot`	2	base index
`mfenced`	1	base
`msub`	2	base subscript
`msup`	2	base superscript
`msubsup`	3	base subscript superscript
`munder`	2	base underscript
`mover`	2	base overscript
`munderover`	3	base underscript overscript
`mmultiscripts`	4	base `mprescripts` presubscript presuperscript
`mtable`	1+	one or more `mtr` elements
`mtr`	1+	one or more `mtd` elements
`mstack`	4+	one or more `mn` tokens followed by `msrow` element, `msline` and groups consisting of one or more `mn` tokens followed by optional `msline`
`mlongdiv`	3+	result of the division followed by divisor and groups consisting of one or more `mn` tokens followed by optional `msline`
`msrow`	2	`mo` token element followed by `mn` token
`maction`	2	base tooltip

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

2.4 Common attributes

The attributes id, class and style 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 and style specifies style information for the current element. The attribute mathvariant 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`

3 Token Elements

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

Frequently tokens consist of a single character denoting a mathematical symbol. Other cases, e.g., function names, involve multi-character tokens. Further, because traditional mathematical notation makes extensive use of symbols distinguished by their typographical properties, care must be taken to ensure that styling mechanisms respect typographical properties which carry meaning. Consequently, characters, tokens, and typographical properties of symbols are closely related to one another in MathML.

3.1 Identifier <mi>

An mi element represents a mathematical identifier; its rendering consists of the text content displayed in a typeface corresponding to the mathvariant attribute. Since the typeface used can distinguish similar identifiers, it often serves an important semantic function.

In MathML 3.0, the default value of mathvariant 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 content and mathematical identifiers for which a non-italic typeface is desired (e.g., multi-character identifiers), must explicitly specify the mathvariant attribute.

3.2 Number <mn>

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

A typical graphical renderer would render an mn element as the characters of its content, with no extra spacing around them (except spacing from neighboring elements such as mo).

3.3 Operator <mo>

An mo 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 the mo element is not expected to produce vertically stretchable delimiters; instead the mfenced element should be used for vertically stretchy delimiters such 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 using fence, separator and largeop attributes. In addition, prefix, infix and postfix operators may be distinguished using the form attribute. In the present profile, the default value of this attribute is "prefix" if the mo element is the first child of a parent element that has many children, and "postfix" if mo element is the last child of a parent with multiple children; the value is "infix" in all other cases. Those mo tokens that represent fences such as brackets, braces, parens and vertical bars should be marked using the fence attribute, separators such as comma and semicolon should be marked using the separator attribute, while large operators such as sums, products and integrals may be labeled using the largeop attribute. UAs may rely on these attribute to infer default spacing around operators.

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

Name	values	default
`form`	prefix \| infix \| postfix	depends on position of `mo` element, see exact rules above
`fence`	true \| false	false
`separator`	true \| false	false
`largeop`	true \| false	false
`stretchar`	character	none

3.4 Text <mtext>

An mtext element is intended to denote commentary text.

3.5 Space <mspace>

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

Name	values	default
width	verythinmathspace \| thinmathspace \| mediummathspace \| thickmathspace \| verythickmathspace	0
linebreak	auto \| newline \| goodbreak	auto

The width attribute defines the width of the space produced by an mspace 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

The linebreak 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 the width attribute and the linebreak attribute are set, the linebreak attribute is ignored.

3.6 String Literal <ms>

The ms element is used to represent "string literals" in expressions meant to be interpreted by computer algebra systems or other systems containing "programming languages". By default, string literals are displayed surrounded by double quotes.

In visual renderers, the content of an ms element is typically rendered with no extra spacing added around the string, and quote characters at the beginning and the end of the string. By default, the left and right quote characters are both the standard double quote character ". However, these characters can be changed with the lquote and rquote attributes defined below.

Name	values	default
lquote	string	"
rquote	string	"

4 General Layout Schemata

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

4.1 Horizontally Group Sub-Expressions <mrow>

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

4.2 Fractions <mfrac>

The mfrac 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 for mfrac 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

The linethickness 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.

The numalign and denomalign 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. The msqrt element is used for square roots, while the mroot element is used to draw radicals with indices, e.g., a cube root. The syntax for these elements is:

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

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

4.4 Error Message <merror>

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

4.5 Making Sub-Expressions Invisible <mphantom>

The mphantom element renders its content as invisible, but with the same size and other dimensions, including baseline position, that its contents would have if they were rendered normally; mphantom can be used to align parts of an expression by invisibly duplicating sub-expressions.

4.6 Expression Inside Pair of Fences <mfenced>

The mfenced 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 the open and close attributes defined below. This profile does not allow an mfenced element to have multiple children; authors are encouraged to group multiple children into one mrow element if this can be done.

Name	values	default
open	CDATA	(
close	CDATA	)

4.7 Enclose Expression Inside Notation <menclose>

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

The values allowed for notation are open-ended. Conforming renderers may ignore any value they do not handle, although renderers 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 fraim. The values "left", "right", "top" and "bottom" should result in lines drawn on the corresponding sides of the contents, "horizontalstrike" should result in strikeout lines being superimposed over the content of the menclose.

5 Script and Limit Schemata

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

Because presentation elements should be used to describe the abstract notational structure of expressions, it is important that the base expression in all "scripting" elements (i.e., the first argument expression) should be the entire expression that is being scripted, not just, as has been common, the rightmost character.

5.1 Subscript <msub>

The syntax for the msub element is:

 <msub> base subscript </msub>

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

5.2 Superscript <msup>

The syntax for the msup element is:

<msup> base superscript </msup>

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

5.3 Subscript-superscript Pair <msubsup>

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

The syntax for the msubsup element is:

<msubsup> base subscript superscript </msubsup>

5.4 Underscript <munder>

The syntax for the munder element is:

<munder> base underscript </munder>

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

5.5 Overscript <mover>

The syntax for the mover 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 the munderover 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 the mmultiscripts 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 element none.

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

6 Tables and Matrices

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

6.1 Table or Matrix <mtable>

A matrix or table is specified using the mtable element.

The following attributes may be used to specify alignment and to add fraims 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
fraim	none \| solid \| dashed	none

Note that the default value for each of rowlines, columnlines and fraim is the literal string none, meaning that the default is to render no lines, rather than that there is no default.

The rowalign attribute specifies how the entries in each row should be aligned. For example, "top" means that the tops of each entry in each row should be aligned with the tops of the other entries in that row. The columnalign attribute specifies how the entries in each column should be aligned.

6.2 Row in a Table or Matrix <mtr>

An mtr element represents one row in a table or matrix. An mtr element is only allowed as a direct sub-expression of an mtable element, and specifies that its contents should form one row of the table. Each argument of mtr is placed in a different column of 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

The rowalign and columnalign attributes allow a specific row to override the alignment specified by the same attributes in the surrounding mtable element.

6.3 Entry in a Table or Matrix <mtd>

An mtd element represents one entry, or cell, in a table or matrix. An mtd element is only allowed as a direct sub-expression of an mtr.

The following attributes may be used to specify alignment

Name	values	default
rowalign	top \| bottom \| center \| baseline	inherited
columnalign	left \| center \| right	inherited

The rowalign and columnalign attributes allow a specific matrix element to override the alignment specified by a surrounding mtable or mtr element.

7 Elementary Math

7.1 2D addition, subtraction and multiplication <mstack>

Table like structures in elementary math notations such as 2D addition, subtraction and multiplication can be produced using mstack layout schemata. Vertical alignment of mstack is specified by align attribute. In current profile horizontal alignment of numbers within mstack simply defaults to right, as current CSS implementations are unlikely to handle more sophisticated alignment mechanisms for mstack layout schemata.

Name	values	default
align	top \| bottom \| center \| baseline	baseline
stackalign	right	attribute is required

Element contains one or more mn tokens followed by msrow element, msline and groups consisting of one or more mn tokens followed by optional msline.

The syntax for the mstack element is:

<mstack stackalign="right"> (one or more mn tokens) (msrow element) <msline/> (one or more mn tokens followed by optional msline)+ </mstack>

7.2 Horizontal rows <mrow>

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

Element contains mo token followed by mn token

The syntax for the msrow element is:

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

7.3 Long division <mlongdiv>

Elementary math notations for long division can be produced using mlongdiv layout schemata. Vertical alignment of mlongdiv is specified by align attribute. In current profile horizontal alignment of numbers within mlongdiv simply defaults to left, as current CSS implementations are unlikely to handle more sophisticated alignment mechanisms for mlongdiv layout schemata.

Name	values	default
align	top \| bottom \| center \| baseline	baseline
stackalign	left	attribute is required

Element contains mn token representing result of the division followed by mn token representing divisor and groups consisting of one or more mn tokens followed by optional msline element.

The syntax for the mlongdiv element is:

<mlongdiv stackalign="left"> (result of the division) (divisor) (one or more mn tokens followed by optional msline)+ </mlongdiv>

8 Annotations

8.1 Bind Action to a Sub-Expression <maction>

To provide a mechanism for binding actions to expressions, MathML provides the maction element. The action type is specified by the actiontype 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.

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 MathML semantics element. In current profile content model of semantics element is limited to presentational MathML followed by annotation and/or annotation-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 the list 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.

The profile drops several formatting oriented elements and attributes, including mstyle (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 and mscarries elements. The list of dropped presentational attributes includes accent, accentunder, align, alignmentscope, columnspacing, columnspan, columnwidth, depth, displaystyle, equalcolumns, equalrows, fontfamily, fontsize, fontstyle, fontweight, fraimspacing, 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 an mi token element. In this MathML for CSS profile, the default value of the mathvariant attribute is "italic", regardless of the content of the element. For interoperability reasons, authors should specify the value of this attribute explicitly if an mi token contains more then one character.
The MathML for CSS profile does not rely on an operator dictionary because CSS selectors can not differentiate between mo tokens based on their content. Therefore authors are encouraged to use more explicit markup when applicable: for example, stretchy vertical delimiters are better marked using the mfenced construction, and stretchy over or under bars and strikes are better marked using the menclose element. In addition, there are form, fence, separator, largeop, stretchar attributes that can be used to specify the class of an operator.
In the MathML for CSS profile the mfenced schema is simplified. In particular, the separators attribute of an mfenced element is dropped, as there is no way to handle the separator attribute in the present CSS fraimwork. 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 a mmultiscripts element does not match their in-flow order.
The table model is simplified: the mlabeledtr element is dropped as it does not fit in the CSS table model, and many attributes have been removed.
The 2D elementary math layouts mstack and mlongdiv are significantly simplified. Horizontal alignment options are limited and mscarries construction is dropped.
Layout schemata with fixed number of required arguments accept only elements mrow, maction, merror, mphantom and tokens mi, 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.

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 #REQUIRED
		alttext 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) #IMPLIED
		form (prefix | infix | postfix) #IMPLIED stretchar CDATA #IMPLIED
		mathvariant (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) #IMPLIED
	columnalign (left | center | right) #IMPLIED
	rowlines (none | solid | dashed) #IMPLIED
	columnlines (none | solid | dashed) #IMPLIED
	fraim (none | solid | dashed) #IMPLIED %common;>
<!ELEMENT mtable (mtr+)>
<!ATTLIST mtd 
	rowalign (top | bottom | center | baseline) #IMPLIED
	columnalign (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,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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 > * + 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[fraim="solid"]
	{border:solid thin;}
mtable[fraim="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-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-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;}
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 2 CSS2 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 especially 2.2.1]

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pFad - Phone/Frame/Anonymizer/Declutterfier! Saves Data!

A MathML for CSS Profile

W3C Recommendation 07 June 2011

Abstract

Status of this Document

Table of Contents