[Om] getting started with openMath

[Lars Hellström]

ken skrev 2012-10-09 17.22:
> Hello, Lars Hellström
>
> I was thinking of using OpenMath as a command language to access the CAS,
> not as a standard for encoding mathematical objects

I see. Yes, that would be trickier.

> in the CAS.

It needn't be /in/ the CAS (indeed, a mature CAS would internally often use 
various optimised representations for mathematical objects that can be quite 
different from what OM has defined), but rather for allowing two different 
pieces of software both working with not entirely trivial mathematical 
objects to talk to each other.

> Like a
> explained to Alberto I was think of using openMath to abstract the CAS I use
> from the rest of my application so I could change the CAS. It seems like it
> is turning out to be a lot of work and may not be worth it.

It could still be feasible if there only is some specific domain of 
computations that you want the CAS to do for you, but it is certainly 
starting to look difficult.

> Are you saying
> that openMath is better suited for use inside a CAS and not for a way to
> pass things between different applications or components?

No, OM is very much about making /communication/ feasible. As mentioned 
above, a CAS may internally employ quite different representations.

> So I am confused about this arcsin thing. Does not arcsin always output the
> same thing for a given input, so why would anyone ever want to define it
> differently? If I enter arcsin(1) into a calculator I expect to always get
> back pi/2 rad or 90 deg. The unites and whether it is exact would need to be
> defined but they are all equivalent and I should be able to get it in any
> form needed and change between any of them as I like depending on the CAS,
> so that is out side the definition of arcsin.

The catch is that not everyone makes the same choices when one gets to the 
edge cases in definitions of the elementary functions, and (as I recall it) 
there is a classical example that at least one of the inverse 
trigonometrical functions (it might have been arccos or arccot rather than 
arcsin, though) had slightly different definitions in different CASes, 
because it was taken as the inverse of restrictions to different intervals 
of the underlying trigonometric function. Much of the text in e.g.
   http://www.openmath.org/cd/transc1.xhtml
serve specifically to nail down exactly which of the plausible definitions 
of these elementary functions should be taken as authorative for the symbols 
defined there.

> That brings up another question. Is there any way to specify unites in

(I suspect you mean "units", which is plural of the noun "unit". "Unites" is 
present tense of the verb "unite".)

> openMath. That becomes a big thing if physics? If I ever get that far (I
> doubt I will) I would like my calculator to be smart enough that it would
> change everything to si units before solving an equation where units are
> specified.

Here you may be in luck, because it has been one of the more active areas in 
recent years. If you take a look through the list archives 
(http://openmath.org/pipermail/om/), you will surely find more information. 
Some of it may be concerned mostly with linked data interoperability, 
though. Also, you might be interested in
http://www.openmath.org/cd/contrib/cd/SI_BaseUnits1.xhtml
http://www.openmath.org/cd/contrib/cd/SI_NamedDerivedUnits1.xhtml

Lars Hellström