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Re : importance of tie bars

From: Frederic WANG <fwsmail35@aol.com>
Date: Sun, 06 Jan 2008 12:37:55 +0100
Message-ID: <4780BD93.6000303@aol.com>
To: www-math@w3.org

    I believe this is the occasion to study the more general issue of 
mixing graphics and MathML, otherwise you would have to add new MathML 
tags for each specific notation. Michael Kohlhase and David Carlisle 
wrote a W3C note 5 years ago about the graphics in MathML ( see 
http://www.w3.org/Math/Documents/Notes/graphics.xml ).

    In the section "Non-Hierarchical Mixing of Formulae and Graphics", 
they studied a case quite similar to the tie bars, except that they did 
not think about the label. At the end of the page, they proposed a "SVG 
in MathML" representation, using the "annotation-xml" tag. I think it 
would not be too difficult to apply this to the tie bar notation, using 
for example something like :

<math xmlns="http://www.w3.org/1998/Math/MathML">
  <semantics>
    <mrow>
        <msub>    <mi>x</mi>    <mn>1</mn>  </msub>
        <mo>+</mo>
        <mo>...</mo>
        <msub id="starttie">    <mi>x</mi>    <mi>i</mi>  </msub>
        <mo>+</mo>
        <mo>...</mo>
        <msub>    <mi>x</mi>    <mi>n</mi>  </msub>
        <mo>=</mo>
        <msub>    <mi>y</mi>    <mn>1</mn>  </msub>
        <mo>...</mo>
        <mo>+</mo>
        <msub id="endtie">    <mi>y</mi>    <mi>i</mi>  </msub>
        <mo>+</mo>
        <mo>...</mo>
        <msub>    <mi>y</mi>    <mi>n</mi>  </msub>
    </mrow>

    <annotation-xml encoding="image/svg" definitionURL="embellishments">
      <svg:connection from="starttie" to="endtie" shape="undertiebar" 
label="i-th summand" />
    </annotation-xml>
  </semantics>
</math>

Of course, the structure of the "connection" element should be adapted 
(and include the foreignObject element) if we want to write the label 
with MathML.

 >
 > Hi all.
 >
 > I've been talking to some people using MathML for chemistry lately, 
and got a question about tie bars, which can't usually be represented in 
MathML.  If I understand correctly, tie bars look like a horizontal 
bracket (i.e. '[') under an equation, and seem to be primarily used to 
point to two terms in an equation that are related in some way.  I'm not 
sure of this, but there is also probably a requirement to label the 
horizontal part of the notation.  E.g.
 >
 > (x_0 + ... + x_i + ... x_n)^a = (x_0 + ... + x_i + ... x_n)^b
 >               |                               |
 >                -------------------------------
 >                        ith summand
 >
 > I hope this comes out okay as ASCII art.
 >
 > However, by their nature, they do not respect the equation nesting 
structure, and so are tricky in MathML.  Something like a <starttie/> 
... <endtie/> type construct would be necessary.  There might also need 
to be an id, since presumably one can have several tie bars in an 
equation, and one would need to match the starts and ends.
 >
 > I'm interested in hearing if lack of tie bars in MathML has been an 
issue for others.
 >
 >
 > --Robert

-- 
Frederic WANG
http://www.maths-informatique-jeux.com/international/
Received on Sunday, 6 January 2008 11:35:57 GMT

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