Re: rendering entities

This discussion touches on some  very important issues.

Presentation MathML is to a large extent about providing information needed
to support  the visual / aural rendering of a mathematical expression.  The
"information" that must be provided for rendering includes:

-   choice of characters.
-   grouping.  (mrow)
-   relative positioning of the groups. (superscripting / over/ under etc.)

It is very much like a printer driver language.

If you assume a 1-1 mapping from mathematical expressions to presentations
you can read the code generated for the printer.  That is, if you are
extremely disciplined (as in  generating the renderings by machine) about
how you construct your presentations using these tools then by mapping
selected characters to one particular mathematical meaning  and inferring
specific functional relationships from the grouping and positioning you can
read the markup back in and reconstruct the original mathematical
expression.  The ⁢ was introduced to make this kind of
reverse engineering easier.

However, in general this 1-1 mapping (expression to rendering) assumption
fails in for two reasons:

1.  Different (mathematical) cultures render the same mathematical concept
in different ways.
2.  Different mathematical disciplines re-use the same characters and
notations in different ways.

This is true right down at the character level.  All you really know about
the &differentialD; is that it is just a character that has a recognizable
appearance taking into account choice of fonts, etc.   Its actual meaning
still depends on the mathematical context in which it is being used and is
far from being specified by (say) Unicode.

Once you have chosen to use &differentialD; you have already decided how you
want it to appear.  The particular layout has already been chosen, including
the characters, once you use Presentation MathML

Of course, you can reverse engineer the presentation under the right
assumptions and then map it to a different presentation, but the right place
to decide this is at the point where you decide to map a mathematical
expression to a particular presentation - not afterwards.  And one of the
roles of Content MathMl is to provide a way to capture the mathematical
expression in this presentation independent way.

Stan Devitt



On 4/20/06, Stephan.Semirat@ac-grenoble.fr <Stephan.Semirat@ac-grenoble.fr>
wrote:
>
>
> Hi,
>
> > > i'd like to know if there's a way to change the default rendering of
> > > mathml entities (e.g. rendering &DifferentialD; as a roman d instead
> > > of a blackboard d) under FireFox and IE+MathPlayer.
> >
> > Possibly it's possible to set up the font choices to select a font
> > witha d rather than a d| but I tend to do it a simpler way, just
> > use d in the source file. Thw blackboard bold operators are there if you
> > want to use them but there is no obligation to use them if you don't
> want to,
> > you can use whatever name you want for any operator.
>
> Thank you. Is that what you mean : &DifferentialD; and d are just
> characters with no "content" meaning ?
>
> However, if for instance i want to translate my xhtml+mathml files to tex,
> then &DifferentialD will be translated to \dd while d will be translated to
> d.
> So i need to encode these two letter differently, no ?
>
> (i could also use roman mstyle for d,e,i instead of DifferentialD,
> exponentialE, imaginaryI but in fact, these entities are usefull and
> meaningfull (to the end user i am) ; it's just that their rendering is not
> very conventionnal...)
>
> Regards,
> Stéphan
>
>