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Re: Questions about MathML 3.0 domainofapplication

From: David Carlisle <davidc@nag.co.uk>
Date: Sun, 24 Jul 2011 16:45:56 +0100
Message-ID: <4E2C3E34.1000900@nag.co.uk>
To: www-math@w3.org
On 24/07/2011 15:36, Christian Lerch wrote:
> Hello www-math@w3.org,
> I have a few questions regarding the following piece from the MathML 3.0
> spec (section 4.3.3.1 Uses of <domainofapplication>, <interval>,
> <condition>, <lowlimit> and <uplimit>)
> ----
> The general technique of using a condition element together with
> domainofapplication is quite powerful. For example, to extend the
> previous example to a multivariate domain, one may use an extra bound
> variable and a domain of application corresponding to a cartesian product:
>
> <apply><int/>
> <bvar><ci>x</ci></bvar>
> <bvar><ci>y</ci></bvar>
> <domainofapplication>
> <set>
> <bvar><ci>t</ci></bvar>
> <bvar><ci>u</ci></bvar>
> <condition>
> <apply><and/>
> <apply><leq/><cn>0</cn><ci>t</ci></apply>
> <apply><leq/><ci>t</ci><cn>1</cn></apply>
> <apply><leq/><cn>0</cn><ci>u</ci></apply>
> <apply><leq/><ci>u</ci><cn>1</cn></apply>
> </apply>
> </condition>
> <list><ci>t</ci><ci>u</ci></list>
> </set>
> </domainofapplication>
> <apply><times/>
> <apply><power/><ci>x</ci><cn>2</cn></apply>
> <apply><power/><ci>y</ci><cn>3</cn></apply>
> </apply>
> </apply>
>
> Note that the order of the inner and outer bound variables is significant.
> ----
> My questions:
>
>  1. Does this exaple try to denote a double integral ?

yes

>  If yes, is this
>     the recommended way to do it ?

well it's a way, probably the recommended way if it is over an arbitrary 
domain


>  2. Why is the <set> wrapper inside <domainofapplication> necessary at
>     all?  Only because the later happens to just take a single argument ?

well because it doesn't take the qualifiers, in particular condition, 
used here. One could always extend the set of elements that take 
qualifiers but  it doesn't always make things clearer and here I think 
having an extended version of domainofapplication that took qualifiers 
wouldn't really make things clearer would it?

>     In a set, however, I could put arbitrary elements. From the example
>     I conclude that this use of <set> is very specific to the
>     <domainofapplication> parent and hence requires a very specific
>     element list. I could not find any specification about the required
>     structure of this <set>.
Not sure I understand this question, perhaps the answer to the next 
question will make it clearer.


>  3. What purpose serves the last <set> element <list>... ? We already
>     have declared <bvar> t and u (in that order) as set element 1 and 2.
>     Why list them again ? Does the final note of this section refer in
>     any way to the use of the <list> element ?

In MathML1 there were a few examples given that used constructors 
without the final clause but it's ambiguous (and was never I think 
allowed by the text of the specification), so at MathML2 (and so 3) we 
made sure all the examples of set and similar constructs had the main 
body (not just teh bvar and condition qualifiers).

<set>
bvars
condition
term
</set>

Is the subset of the set of all terms (over an implied domain) 
restricted by the condition.

So here the <set> is constructing a list of pairs (ie its a subset of 
R^2). The bvars and the condition specify the restriction that 
determines the subset.
>
> Any comments or expalantions would be greatly appreciated.
>
> Thank you in advance,
> Chris
>
> <http://km-works.eu>
>

David



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Received on Sunday, 24 July 2011 15:46:17 GMT

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