HTML Math

The <MATH> element is used to include math expressions in the current line. HTML math is powerful enough to describe the range of math expressions you can create in common word processing packages, as well as being suitable for rendering to speech. When rendering to fixed pitch text-only media, simple text graphics can be used for math symbols such as the integration sign, while other symbols can be rendered using their entity names. The SGML SHORTREF capability is used to provide abbreviations for hidden brackets, subscripts and superscripts.

The design of HTML math owes a lot to LaTeX's math mode, which has been found to be effective for a wide variety of mathematical typesetting. Where practical, HTML math uses tag names matching LaTeX commands, e.g. ATOP, CHOOSE and SQRT act in the same way as their LaTeX namesakes. Of course, SGML and LaTeX have quite different syntactical conventions. As a result, HTML math uses the ISO entity names for symbols rather than the TeX names. In LaTeX, the character command ^ sets the next character as an exponent, while the character command _ sets it as an index. If the exponent or index contains more than one character then the group of characters must be enclosed in curly brackets { }. This syntax is inappropriate for SGML, so HTML math instead treats _ and ^ as shortref characters for the SUB and SUP elements which are used for indices and exponents, respectively.

I can't find the ISO entity names for the _ and ^ chararacters!

HTML math has been designed to be both concise and comparatively easy to read. In practice, formulae will be a little longer than in LaTeX, but much shorter than with other math proposals for SGML, for instance EuroMath or ISO 12083. This simplification has been achieved through the power of the BOX element, which replaces many elements in other proposals, as well as the simple conventions for binding the SUB and SUP elements and their use as generic raising and lowering operators. HTML math differentiates terms e.g. binary operators, variables, constants, integral signs, delimiters and so on. This simplifies rendering and reflects the assumptions adopted by LaTeX. It further allows the same raising and lowering operators to be used for many different roles according to the term they apply to. HTML math doesn't provide direct support for multi-line equations, as this can be effectively handled by combining math with the TABLE element.

Example - the integral from a to b of f(x) over 1+x

    <MATH>&int;_a_^b^{f(x)<over>1+x} dx</MATH>

which can be rendered on a fixed pitch text-only medium as:

         b
         /   f(x)
         | ------- dx
         /  1 + x
         a

The example uses { and } as shortrefs for <BOX> and </BOX> respectively. This is used for invisible brackets, stretchy delimiters and integral signs, and placing one thing over another. The shortref characters "_" and "^" are used for subscripts and superscripts respectively.

HTML math follows general practice in mathematical typesetting by rendering functions, numbers and other constants in an upright font, while variables are rendered in an italic font. You can set particular terms in a bold face, and for chemical formulae, you can force the use of an upright font. Limits for symbols like the integral and summation signs are placed directly above (below) the symbol or to the immediate right depending on the symbol.

Spacing between constants, variables and operators is determined automatically. Additional spacing can be inserted with entities such as &thinsp; &sp; and &quadsp;. White space in the markup is used only to delimit adjacent variables or constants. You don't need spaces before or after binary operators or other special symbols, as these are recognised by the HTML math tokeniser. White space can be useful, though, for increased legibility while authoring.
I need to check on the ISO entity names for spacing!

Math Markup

The following elements are permitted within MATH elements:

BOX

Used for hidden brackets, stretchy delimiters, and placing one expression over another (e.g. numerators and denominators).

SUB, SUP

Subscripts and superscripts. Also used for limits.

ABOVE

Used to draw an arrow, line or symbol above an expression.

BELOW

Used to draw an arrow, line or symbol below an expression.

VEC, BAR, DOT, DDOT, HAT, TILDE

These are convenience tags for common accents as an alternative to using ABOVE.

SQRT, ROOT

For square roots and other roots of an expression.

ARRAY

For matrices and other kinds of arrays.

TEXT

Used to include a short piece of text within a math element, and often combined with SUB or SUP elements.

B, T, BT

These elements are used override the default rendering. B renders the enclosed expression in an bold face. T designates a term to be rendered in an upright font, while BT designates a term to be rendered in a bold upright font. The class attribute can be used to describe the kind of term, e.g. vector, tensor, or matrix.

HTML Math Entities

The following links are underconstruction ...

• Functions
• Operators
• Continuation dots
• Greek letters
• Relations
• Accents, arrows and pointers
• Delimiters
• Other symbols.
• Spacing entities.

Rendering HTML Math

The expression is rendered in three steps:

1. The first step recursively parses expressions building up a matching hierarchy of data structures (with bounding boxes) corresponding to sequences of nested expressions. The math tokeniser needs to be able to distinguish constants, variables, functions, operators, delimiters, and special symbols such as integrals, which can take limits and may be stretchy.
2. The next step sets the size of the innermost expressions based on the size of available fonts. If possible subscript and superscript expressions should be set in a smaller font. The size and relative positioning of neighboring and enclosing expressions is then propagated up the hierarchy from the innermost outwards, as the procedure stack formed in step (1) unwinds.
3. The final step is to render the hierarchy of expressions to the output medium. This is now straight forward as all the positioning and sizes of special symbols and text strings are now fixed.

Note: In practice, only a limited range of font sizes are suitable, as a result, deeply nested expressions like continued fractions can't use ever smaller fonts. This is simply handled by a parameter to the ParseExpression routine that sets the font size to be used for that expression. ParseExpression is called recursively for nested expressions and uses the next smaller font until it bottoms out with the smallest font available. The size parameter corresponds to an enumeration of the available font sizes.

Permitted Attributes

ID

An SGML identifier used as the target for hypertext links or for naming particular elements in associated style sheets. Identifiers are NAME tokens and must be unique within the scope of the current document.

CLASS

This a space separated list of SGML NAME tokens and is used to subclass tag names. By convention, the class names are interpreted hierarchically, with the most general class on the left and the most specific on the right, where classes are separated by a period.

For the MATH element, CLASS can be used to describe the kind of math expression involved. This can be used to alter the way formulae are rendered, and to support exporting the expression to symbolic math software. The class "chem" is useful for chemical formulae which use an upright font for variables rather than the default italic font. For example:

    <math class=chem> Fe_2_^2+^Cr_2_O_4_</math>

                        2+
which is rendered as  Fe  Cr  O
                        2   2  4

Otherwise, the conventions for choosing class names are outside the scope of this specification.

BOX

The presence of this attribute causes the user agent to draw a rectangular box around the formulae.