Mathematics has need for a number of Latin and Greek alphabets that on first thought appear to be font variations of one another, e.g., normal, bold, italic and script H.  However in any given document, these characters have distinct mathematical semantics.  For example, a normal H represents a different variable from a bold H, etc.  If one drops these distinctions in plain text, one gets gibberish.  Instead of the well-known Hamiltonian formula

            H = òdt(eE² + mH²),

you’d get the integral equation (!)

H = òdt(eE² + mH²).

Accordingly, the STIX project requests adding normal, bold, italic, script, etc., Latin and Greek alphabets.  Straight encoding leads to 1209 characters and loses some useful common information, such as all variants of H might not be trivially recognizable as H’s.  But it does allow plain text to retain the proper character semantics and it allows simple (nonrich) search methods to work.

The proposal considers two possible ways to encode mathematical alphabetic symbols in ways that allow simple search algorithms to work.  One encodes them all outright in one of the surrogate planes.  This is the approach the UTC recommended informally in the UTC Meeting 79.  For reference, the other uses “math variant tags”, which act in some ways like nonspacing combining marks.  For example, a math script H would be encoded as H<math script>.  Encountering such a combination, a rendering engine should choose some script font to render the H.  Which script font is beyond the scope of plain text.

The alphabetic symbols encountered in mathematics are given in the following table:

a-w also includes a glyph variant of f, e, and q, since both glyphs for each of these can appear in the same document with different semantics.  In addition there is the partial derivative sign ¶ and the upper-case Greek letters have the del Ñ. This gives 24+4 lowercase characters, and 24+1 upper-case Greek characters. 

Outright Encoding Approach

Outright encoding stores the alphabets in plane 1 for a total of 1209 characters as currently entered.  No accented characters are included.  Accented mathematical symbols are always represented by combining character sequences.

Math Variant Tag Approach

Math variant tags could be defined for each of the categories above.  If this approach is used, the tags should have the following properties:

1. no effect at start of line
2. combining class 255
3. affect entire previous combining character sequence
4. only the first of consecutive tags is used (others are ignored)

Discussion

Rendering mathematics requires a fairly sophisticated 2D layout engine.  Compared to the complexity needed in this engine, handling either math variant tags or surrogate pairs is straightforward.  The outright encoding approach is simpler conceptually, since it doesn’t require any additional rules.  It only requires the ability of the display engine to handle surrogate pairs.  Both approaches require multicode navigation, e.g., the text caret must not end up inside a multicode sequence.  Such navigation is easy to implement if combining-mark sequences are implemented.  Since combining mark sequences are required in mathematics, this navigation shouldn’t be difficult to implement.  Similarly it is anticipated that handling surrogate pairs will be easy, partly because they will be handled by computer operating systems thanks to the strong business case for supporting East Asian characters in plane 2.