Re: [Axiom-developer] Re: Units and dimensions

[Ralf Hemmecke]

> > > So Length, Length*Time^(-1) etc. are examples for such 
> > > monomials.
> > That's where I get in trouble.  (Well, one of the places.)  Length IS
> > basic in the SI system, but Length/Time is a different dimension from
> > Length OR Time and is not basic.  It's COMPOSED of basic dimensions,
> > but that could be said of every derived dimension in a complete system.
>
> I think what Ralf meant is that the *derived* dimensions form a group, not the
> basic dimensions.

Right, and as such they must form a domain where all the group 
operations are implemented. Informally, one can think of that domain (of 
"derived dimension") as a container that has as its elements 
powerproducts (negative powers allowed) of BasicDimensions.

I somehow have a slight feeling that the trouble comes when the design 
should be such that the compiler is doing the dimension analysis. For 
that we have to think a bit whether it is possible at all.

> > However, Length/Time^2 * Time^2 is composed of two derived dimensions -
> > Length/Time^2 and Time^2 - but will simplify to a basic dimension.  I was
> > thinking some kind of conditional definition of type output for those
> > operators - if the resulting dimensional expression is in the basic
> > dimensions list for the system, return type BasicDimension, else the result
> > is a DerivedDimension.
>
> No, the concept here is called "retract". You'd have an operation

> retractIfCan: DerivedDimension -> Union("failed", BasicDimension)

Sorry, but I really don't quite understand, why one would need such a 
retract at all. But maybe I'll learn more while implementing something 
and getting feedback.

> (I know, Ralf, that you hate that return type, but so far we don't have
> Partial...)

Martin, you are right. ;-)

Ralf