MathML 3
MathML 2 was first adopted in 2001. Experience with MathML has
accumulated over the years and the web environment has changed somewhat since
then. MathML 3 is an update to MathML 2 that includes several requested
features and some changes to update the recommendation to the current and
emerging standards. MathML 3 also contains lots of smaller changes to clarify
the spec and unify attribute values so that compatibility between
implementations is more likely. With the exception of a few very minor changes
for features not widely implemented, MathML 3 is backwards compatible with
MathML 2.
The big changes are:
Some of the smaller changes are:
MathML 3 introduces several attributes for controlling line breaks and
indentation after line breaks. The new controls can be used for both automatic
line breaks when the renderer determines that there is not enough room to display
an expression in a given width and for manual (forced) line breaks. In MathML 3,
linebreaking and indentation are specified on operators (mo). The controls include:
- whether a line break should or should not happen at an operator;
- whether the break should be before or after the operator;
- what character to use (if any) in place of an "⁢"
character at a line break
- the amount of vertical space to be used after the line break
MathML 3 offers lots of control over how to indent after a line break. This allows for many different styles of linebreaking and also makes it possible
to align the new line with previous point in the expression (e.g., at an "=").
Alignment at a particular point is done by marking the element you want to align
to with an id attribute and then telling MathML to indent to that id
value.
The indenting controls include:
- alignment – left/center/right/automatic/id
- shift amount – amount to shift it from the aligned point
These options can be set for all of the lines or specifically for either the
first or last line to override the indentation behavior for those lines. This flexibility accommodates many different styles of indenting.
For some examples, see Linebreaking of Expressions. For details, see
Section 3.2.5.2.2 and
Section 3.2.5.2.3 of the MathML 3 recommendation.
MathML has long been useful for notations used in algebra and higher math,
but describing the two-dimensional layout used in elementary math required
tedious layout using mtable, with each digit in its own
column and clever tricks to get the lines to come out correctly. This was both difficult to do and the result was inaccessible. MathML 3 adds support for a wide variety of notations used in lower grade math
for:
- addition, subtraction, and multiplication (with carries/borrows)
- long division
- repeating digits in decimal numbers
Here are some examples:
| Subtraction with Borrows |
Long Division (US, etc., style) |
Repeating Decimal |
 |
 |
 |
The support for these notations is very flexible in MathML 3 to handle the
wide variety of notations that are used around the world. The flexibility
allows for:
- different positions for the operator in addition, subtraction, and
multiplication problems
- different positions for the carries
- different styles of cross outs
- control over the length, position, and thickness of lines
- different notations for long division
- different notations for showing repeating decimals
For more examples, including a video showing how MathPlayer will speak these
for accessibility, see our
elementary math examples page. For complete details about the elements and
attributes used for elementary math, see
Section 3.6 of the MathML 3 recommendation.
Mathematical notation is mostly consistent around the world. However, there are some notations that differ
depending upon the language/locale such as "." versus "," for a decimal
separator and "tan" (English) versus "tg" (French) for the tangent function. For
people who want to produce language-independent MathML, content MathML smoothes
over these differences and presentation MathML allows these specific notations
to be encoded.
In Arabic countries, mathematical notation is written right-to-left using the
same alphabetic characters. MathML 3 now makes it possible to encode
right-to-left notations in presentation MathML. MathML 3 adds a
dir attribute to control whether layout is left-to-right or right-to-left
(see
Section 3.1.5 of the MathML 3 recommendation for details). MathML 3 also
introduces some mathvariant values for handling different styles of Arabic characters
(see Section
3.2.2).
Here's two examples of Arabic math that use right-to-left notation (note:
numbers are still left-to-right in Arabic math notation):
| Square root |
Long division |
 |
 |
The chapter on content MathML was completely rewritten for MathML 3. Content MathML is used when the semantics of the math are more important than
the visual display (the presentation) of the math. In MathML 3, a subset of content
MathML is defined with semantics specified by OpenMath.
This subset of content MathML is called Strict Content MathML and each
element in strict content MathML is associated with a specific OpenMath
Content Dictionary entry. OpenMath Content Dictionaries are
extensible and permit a more precise definition of the semantics of each
element. The
meaning of most content MathML elements remains basically unchanged, although a
mapping for each element into strict content MathML is given.
In order to accomplish alignment with OpenMath, the following changes were
made to the elements:
-
New content elements were added:
bind, share,
cerror, cs and cbytes
-
Deprecated content elements:
reln, fn, and declare
Additional attributes were added to the math element. Probably
the biggest difference is that any attribute that can be specified for
mstyle can now be specified for math. Other additions
include the ability to set the width for linebreaking, control over the
altimg size and alignment, and the ability to set the cdgroup
(used for content MathML). See
Section 2.2.1 of the MathML 3 recommendation for full details.
In MathML 2, linking was done via
XLink. However, XLink did not catch on and HTML5 doesn't use it. In MathML 3, all
elements accept an href attribute to allow for hypertext links. Note that what should happen for hypertext links depends on the environment in
which the MathML resides. In MathPlayer, links can not point to places
inside of a MathML expression. See
Section 2.1.6
and Section
6.4.3
of the MathML 3 recommendation for full details on linking and href.
mglyph was extended to support general image inclusion (sort of
like a img element in HTML). In earlier versions of MathML, the
idea was that mglyph was a way of including characters from a
non-standard font. This was not used much and the old usage of specifying a font
and index into that font is deprecated in MathML 3. mglyph
now takes attributes to specify the source of the image, size, and alignment.
For accessibility reasons, an
alt attribute value is required. For complete details on
mglyph, see
Section 3.2.1.2 of the MathML 3 recommendation.
mpadded is used to adjust the spacing around its children. The
allowed attribute values have been extended and new attributes for positioning
the children within the specified spacing have been added. See
Section 3.3.6
of the MathML 3 recommendation for full details.
This element was previously grouped with content MathML, but properly spans
both presentation and content MathML and should be implemented by any system
that implements only content or only presentation MathML. It is now in
Chapter 5, which
discusses mixing content and presentation MathML. annotation
and
annotation-xml both take the content MathML attributes cd
and name, and also take a src attribute to specify the
location of an external source for semantic information.
MathML 3 adds a new
Chapter 6 that discusses how MathML should interact with its host
environment. There is an emphasis on MathML in web pages, but there is
discussion with embedding MathML in other environments. Among the topics covered
are:
- names and "flavors" to use for encodings on the clipboard and the format
to use for data in those encodings
- how MathML can be mixed with other markup, including embedding SVG in
MathML
- using CSS with MathML
In a step forward into today's web environment, the
normative version of the
grammar is now expressed in Relax NG, not as a DTD. A DTD and XSD
version still exist and are derived from the Relax NG grammar.
The Operator Dictionary
table has been greatly expanded (and cleaned up) to include lots of new
characters and attributes. The format is new and includes the ability to sort on
different columns.
Most of the information about entities has been moved from chapter 6 and is
now its own recommendation:
XML Entity Definitions for
Characters. That new recommendation includes changes made to Unicode
characters along with a discussion of some problematic characters.
HTML5 updates HTML4 to help meet the needs of modern web architecture. One of those updates is to bring math support into HTML5 via MathML. Most MathML
will work just fine in HTML5, but here are a few things to watch out for:
HTML5 normally doesn't care
about namespaces and puts all of the elements in the HTML namespace; MathML and
SVG are the two exceptions to this rule. For compatibility with XTHML 1.x
and XHTML5, the math tag should include the MathML namespace as shown below:
<math xmlns="http://www.w3.org/1998/Math/MathML">
...
</math>
Another namespace issue arises with the use of annotation-xml
inside of
semantics. Inside of MathML, all elements are placed in the
MathML namespace with two exceptions: inside some annotation-xml
elements and inside of mtext elements.
The first exception allows you to include an HTML alternative encoding inside
of a semantics elements. The exception happens when the
encoding attribute for annotation-xml is either "text/html" or
"application/xhtml+xml". In these cases, the elements are
placed inside the HTML namespace and can be manipulated by script or styled by
CSS if made visible. For other encodings, the non-HTML5 elements are placed in the MathML
namespace even if they are declared to be in another namespace (eg,
http://www.openmath.org/OpenMath ). If you use XHTML5 which is namespace
aware, namespaces inside of MathML should be handled properly.
The second exception is inside of mtext. HTML5 extends
MathML by allowing HTML5 elements inside of mtext. These elements are placed in
the HTML namespace. It is not recommended that you make use of this
extension because it is unlikely to work in other environments.
If HTML tags occur elsewhere inside of a MathML element (with the two
exceptions above), the MathML element is terminated (closed off) by the HTML5
parser at that point. That is almost certainly not what most authors intend, so
care should be taken when adding HTML5 in MathML.
MathML 3 is a new recommendation and besides MathPlayer 3, there are not any
complete implementations of it yet. Many other implementations, such as Firefox
and MathJax have implemented some of MathML 3; we expect more and more of the
features of MathML 3 will be implemented over the next year or two in those and
other implementations.
|
