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Re: MathML Content and Operators

From: Paul Libbrecht <paul@activemath.org>
Date: Tue, 14 Jun 2005 22:41:28 +0200
Message-Id: <c1129834ff486b8db3825263874a0b67@activemath.org>
To: www-math@w3.org, maths@mathsonly.com

Charles,

Dare I suggest that MathML is definitely better replaced by OpenMath 
when talking about standardized extensibility ?
At least in this language you do have something at the end of a 
definitionURL (if using MathML-content) or referenced by an OMS 
element.
What's at the end is a somewhat informal description which has 
appearances of a dictionary.
http://openmath.org/ is the host of these dictionaries and many 
contributed are already presented.

Now coming to the "d" symbol... trying to find a mathematical meaning.
The only one I heard about was that d is an operator from n-forms to 
(n+1)-forms of a manifold's tangent-bundle... I haven't seen enough 
material in semantically encoded math to see this yet... sadly!

As far as I know the >>notations<< df/dx are just notations for a 
partial derivative which are inspired by this n-form definition of d.

Any reason not to encode your content directly using partialldiff ??

paul



Le 14 juin 05, à 20:50, Mathematics (General) a écrit :

>
> I can see the use of the <csymbol> element in defining new symbolic 
> operators, although I'm put off using it a little by the spec. saying 
> <csymbol> can be used for "unknown or *user-defined* functions and 
> symbols". The phrase 'user-defined function' puts me off its use, 
> since differential operators (a) are widely used and should not be 
> 'defined' by any one user (unless they are being 'redefined' in a 
> particular context), (b) they aren't functions or really symbols, but 
> instead operators (and as such require things like bound variables?).
>
> As I see it, operators and constructs are defined by (empty) elements, 
> while functions and symbols are defined by the contents of other 
> elements (like <ci> and <csymbol>).
>
> As a result, the way I would like to extend the Content ML is to use a 
> new operator *empty element* in an <apply> - operators like <diff /> 
> and <partialdiff /> already exist, so why can I not use <differential 
> /> as a new child of <apply>? Since an unknown first child of <apply> 
> is interpreted as being a user-defined function, is there any way to 
> link this completely new element to a definition?
>
> For example:
>
> <apply>
>   <differential /> <!-- with a definition URI somewhere in the doc. -->
>   <ci>x</ci>
> </apply>
>
> where "<ci>x</ci>" can be replaced with any expression.
>
> What concerns me a little about the "definitionURL" attribute is that 
> the syntax or encoding of the target are completely undefined. 
> Additionally, most of the examples given in the spec. point to 
> human-readable URIs and resources. This means that any operator 
> defined by a MathML document using <csymbol> almost certainly cannot 
> be interpreted by a computer algebra system correctly - although I see 
> no easy way round this problem.
>
> Just one comment on the example syntax you provided: the spec. states 
> that "The diff element is the differentiation operator element for 
> functions of a single variable." (section 4.4.5.2). Since 'f' is a 
> function of both 'x' and 'y', it is clearly not a function of just one 
> variable (assuming 'x' and 'y' are independent). Therefore, according 
> to the specification, it would be erroneous to use <diff /> in this 
> case (although I agree totally with the use of <partialdiff /> here).
>
> I'm not worried in the slightest about presentation (or the conversion 
> of Content ML to presentation), but I want to get the semantics right 
> so they can be interpreted by an algebraic system.
>
>
> Any further thoughts?
>
> Best regards,
> Charles Lyons.
>
>
> P.S. I've taken on-board your comments about my sloppy Presentation 
> syntax and use of the &InvisibleTimes; - I agree, it was incorrect. 
> However, it is also important for the &dd; and the following character 
> not to line-break...
>
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Received on Tuesday, 14 June 2005 20:41:38 GMT

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