[om] comments on documents

David Carlisle davidc at nag.co.uk
Sat May 18 14:39:04 CEST 2002

> But a/b and a*b^(-1), given the usual algebraic domain are
> the same. 

have the same value but are different terms, just as 4 = 2+2 which was I
think your previous example. An application can (and some do) do
arbitrary manipulation on the expression once it is received so might
store those two in the same form but normally (especially a rendering
application) you might expect to keep them distinct. This is in
distinction to yor example of 

and a/b which is purely a presentation matter over which openmat, as I
said before, hives no clue as to teh desired rendering.

> If there is a natural encoding in OM then this should come out
> as  foo + foo + foo  

I'm sorry but I think you have missed the point of openmath, you
repeatedly give incorrect descriptions of how openmath (or mathml) works
and then give valid reasons why a system following that description
might have problems.

Openmath essentially represents the expression as a tree of
application/binding terms, as such exp(x)*exp(-y) and exp(x-y)
would have differnt OM encodings, You might expect that some OM
applications might be able to tell these were equal, but not all, in
particular OM applications mapping to a rendering agent like TeX or
presentation MathML probably would not identify these two terms.

>    My conclusion is that the OM content must give essential
> hints on how to display the expression.
A conclusion from a false premise.

>   I suppose one could
> put presentation tags on each of the 3 items within the semantics,
> but would your XSL translator be ready for that?
As a matter of fact yes you can annotate terms with presentation MathML
but that doesn't seem particularly relevant here.

> Your heuristics might not be the same as mine or those in documents
> I have been manipulating which use both  invisible space and \cdot
> for multiplication, but with different precedence.

Yes that's exactly my point. The presentation rules are built into the
stylesheet not into the openmath object as you claimed. You may have
different desired presentation, and your system would show the same
object in an entirely different notation. That's all as it should be.

> I think that your logic and heuristics, regardless of how careful
> you are, will not be what everyone wants.

As above, we are in agreement here.

>   Can one say, in the
> MathML... "in this expression map all multiplications to \cdot for
> display"? I hope so.

MathML has two sides, in Presenattion MathML you ask for 
"a binary operator displayed as a cdot" but don't identify it as

In Content MathML you ask for the multiplication operator (which you
then apply prefix style, not as an infix operator) You can annotate
individual operations with presentation mml to force a particular
display although that's a bit tiresoe or you just use the unadorned
content markup and take the presentation form that your rendering
systemuses for that markup. Some systems may allow you to customise the
default presentation but whether or how they allow such customisation is
out of scope for the mathml specification. One difference between
content mathml and OM though is that each content expression does have a
default presentation, as shown in the spec.


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