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Re: Spacing and formatting across multiple math tags

From: Robert Miner <RobertM@dessci.com>
Date: Tue, 28 Oct 2003 10:17:48 -0600
Message-Id: <200310281617.h9SGHm921828@wisdom.geomtech.com>
To: silverbanana@gmx.de
Cc: www-math@w3.org


Hi.

> I'm trying to write some proofs in MathML on my homepage. Some of them
> look like this:
> 
> <math><=> Term1 = Term2 |+2 |*3 |()^2</math>
> <math><=> Term3 = Term4 |/(x+4)</math>
> <math><=> Term5 = Term6</math>
> Some explanatory text in XHTML:
> <math> => Term7 = Term8</math>
> <math><=> Term9 = Term10</math>
> q.e.d
> 
> Now I'd like to ask: Is it possible to instruct MathML to put all <=>
> and =>, all Term1,3,5,7,9, all Term2,4,6,8,10, and all |+3 and so on in
> one column to improve readability and if so how?

I have a couple of comments.  

First, from a mathematical point of view, this is just one long row of
implications with linebreaks.  The explanatory text isn't really there
in the mathematical assertion.  So, if you the author choose to break
up your single math assertion into two assertions with text
explanation providing the bridge, then naturally the markup no longer
reflects the logical structure, since you intentionally moved some of
that logical structure into text.  There is nothing at all wrong with
that.  Similarly, no doubt there are variables, short equations, etc
in the text at the top of the page which are logically related to
mathematical constructs at the bottom of the page, and that isn't
reflected in markup either.  Such compromises are inevitable (and the
correct choice) when authoring for both human readers and machine
readers. 

Next, as to the MathML mechanics of representation, I think the
best markup would be a single row with linebreaks as I suggested.
Unfortunately, the WebEQ Viewer Control applet is the only widely
available browser rendering technology that implements linebreaking
today, and it isn't appropriate here.  So, it isn't MathML 2 that is
at fault here, it is the state of rendering technology.  Today, your
only choice is to fake it with tables.  Obviously that is less than
optimal, but so are the alternatives.

Third, XHTML + MathML is the wrong markup vehicle for you if what you
are aiming at is capturing semantics of high-level constructs such at
proofs.  That, I believe, was the point of Stan Devitt's analogy with
PostScript.  XHTML + MathML is a very general markup language, whose
main focus is really display in browsers.  You would probably be
better served by a more semantic markup language, and specifically one
aimed at capturing the semantics of mathematical argumentation.  A
good candidate is OMDoc.  I believe there are even XSL stylesheets for
transforming OMDoc into XHTML + MathML.

--Robert

------------------------------------------------------------------
Dr. Robert Miner                                RobertM@dessci.com
MathML 2.0 Specification Co-editor                    651-223-2883
Design Science, Inc.   "How Science Communicates"   www.dessci.com
------------------------------------------------------------------
Received on Tuesday, 28 October 2003 11:14:41 GMT

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