[om] DefMP elements

[Bill Naylor]

> > Excuse me for appearing a bit ignorant here. The signature for sin in STS
> > is defined as sin: NumericalValue -> NumericalValue, where NumericalValue
> > is defined as:
> >
> > "NumericalValue
> >
> > Denotes an OpenMath object that is to be thought of as something that
> > represents a numerical value, or a numerical value."
> >
> > this seems very circular to me, where do we define a 'numerical value'? I
> > mean integers are clearly numerical values, so are reals. Almost as
> > clearly complex numbers are numerical values. What about Quaternions? I
> > would have thought so? What is it that makes them numerical and matrices
> > not?
> We don't, and this is a weakness of a system like STS. Now that the Pisa
> meeting has approved multiple signatures, we could tidy this up a little.
> I had thought of NumericalValue as being substes of C or Z/(n).
> James

And I believe exp (and log, sin, cos, tan etc.) can be extended to the
quaternions. Though I'm not sure whether all of the properties in transc1
will still hold. I know for sure the sin=1/2i (exp(ix)-exp(-ix)) property
(similarly for tan) does hold as that is how it is defined in this case.
Not so sure for the inverse functions.

Are these then the most general type of Numerical Value? (though I guess
you don't get the same sort of structure as Z/(n))

Bill.

--
om at openmath.org  -  general discussion on OpenMath
Post public announcements to om-announce at openmath.org
Automatic list maintenance software at majordomo at openmath.org
Mail om-owner at openmath.org for assistance with any problems