Re: math alphabets, WAS: Proprietary Card Decks

From: Hans Aberg (
Date: Thu Apr 14 2011 - 10:59:36 CDT

  • Next message: Murray Sargent: "RE: math alphabets, WAS: Proprietary Card Decks"

    On 14 Apr 2011, at 16:13, Doug Ewell wrote:

    >>>> Unicode does not have characters for say superscripts and
    >>>> subscripts, which are essential to math. My guess it would be too
    >>>> complicated to require it for current text-only renderers, but in
    >>>> the future that might change.
    >>> No, because in math, superscript is not a character attribute but a
    >>> formatting style that is applied to any term or formula and that can
    >>> be fully (and infinitely) nested.
    >>> That abstraction is better handled in markup than in plain text.
    >>> (Unlike the mathalphanumerics, such markup is still independent of
    >>> the font).
    >> That is so in rendering programs like TeX, because one does not enter
    >> the math so that it can be parsed semantically. One enters
    >> superscripts how they should be rendered and not by the logical
    >> structure of the formula.
    >> That is different if one has say a theorem prover. Then one can enter
    >> a formula, let the program parse it into an AST, and from that infer
    >> how it should be rendered, for example, where to put parenthesizes.
    > I don't follow this. Asmus' point is that superscript can be applied,
    > not only to any arbitrary character that can be used in a math
    > expression, but also at any arbitrary level of nesting. After Unicode
    > has finished adding superscript versions of every imaginable math
    > character, including all of the math alphanumerics, it would then have
    > to add second-level, third-level, etc. versions of every character, so
    > that one could enter "a to the b to the c to the (d times square root of
    > 2)" in plain text. And don't forget subscripts of superscripts, and
    > vice versa.

    One way would be to enter a^b^c^(d·√2), only that '^' would be a special superscript symbol. If the parser is intelligent enough, it can infer that the parenthesizes are not needed in the rendering.

    > A counterargument that this is going too far, that Unicode wouldn't need
    > to encode arbitrary levels of superscript/subscript nesting but only
    > one, is basically an agreement with Asmus that this problem is best
    > solved by (semantic) markup.

    I'm not sure there is much difference with modern text rendering, as it it would call some library that can render it. In TeX, the first few levels are diminished, but not after that.

    This would move down some of the rendering that now is on a level above Unicode. But I'm not sure there is much difference from have combining characters.


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