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Subject: comments re draft version 2.0 (David Eppstein)

From: Stan Devitt <jsdevitt@radicalflow.com>
Date: Mon, 10 Apr 2000 08:05:51 -0400
Message-ID: <004601bfa2e5$1dc4a3e0$6561a8c0@devitt.local>
To: <www-math@w3.org>
While the "Big-Oh" notation is not explicitly included in the MathML content
definitions, it is a good example of how the content definitions can be
extended.

1)  O-Notation, etc.

    Answer:
    O(x)   could be written.
    <apply><csymbol definitionURL="CRCStandardMath_30"
        encoding="text">O</csymbol>
        <ci>x</ci>
    <apply>

The csymbol allows the author to be precise about the definition, and the
presentation.  The xml content of the csymbol element is treated as a
presentation
mo element, or if needed, can be a full presentation expression.

(2) How would you represent an expression like $\lfloor (n+1)/6\rfloor$ in
content markup style?

    Answer:

    <apply><csymbol definitionURL="...">floor</csymbol> ...</apply>
    <apply><csymbol definitionURL="...">ceiling</csymbol> ...</apply>

    In general, where a new element requires a special presentation, this
can be
    done by providing  a suitable XSLT transformation, perhaps in
conjunction
    with the semantics tag so that both the presentation and the meaning
remain
    in the rendered document. (See chapter 5.)

(3) How does one represent chains of inequalities in content markup?  You
list the equalities and inequalities as n-ary but what about chains that
mix the two, e.g. (from some of my course notes)

Answer:

    A content expression for   a = b <= c   is

            <apply><and/>
                <apply><eq/><ci>a</ci><ci>b</ci></apply>
                <apply><leq/><ci>b</ci><ci>c</ci></apply>
            </apply>

    This could be combined with a better
    presentation using a syntax element.

    The spec stops short of longer chains of relations unless they are
    homogeneous.  The difficulty was in deciding how to handle the meaning
    of  arbitrary  chains.  e.g.    a < b != c,    or a < b > c,  as then
    spelling out the allowable content got complicated.

    A definition could be added as an extension using csymbol and an XSLT
    transformation.

    e.g.     <apply> <csymbol definitionURL="...">relationchain</csymbol>
                <ci>a</ci><eq/><ci>b</ci><leq/><ci>c</ci>
               </apply>
Received on Monday, 10 April 2000 09:03:22 GMT

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