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

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 ⁢ - I agree, it was incorrect. > However, it is also important for the ⅆ and the following character > not to line-break... > > _____________________________________________________________ > http://www.easypost.com Anti-Virus & Anti-Spam Web Mail thats hotter > than hot > >Received on Tuesday, 14 June 2005 20:41:38 GMT

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