[Om] usage of OM symbols for physical units

[W Naylor]

On Mon, 29 May 2006, Christian Groß wrote:

> Hello everybody,
> 
> I have a question on the OpenMath symbols for physical units, in combination
> with their prefixes, i.e., on the cd's
> units_metric1 and units_siprefix1.
> In units_metric1 you have symbols metre and metre_sqrd and in units_siprefix1
> you find prefixes like centi and milli.
> 
> I guess this works well in order to express cm = centi-metre or mm =
> milli-metre. But what about cm^2 as a small unit for area?
> One could construct "(centi-metre)^2" of course, using the usual power symbol,

I had corespondance with Professor Davenport in 2002, we finally resolved 
that the arith1 symbols would be used, there is a discussion document on 
this at:
http://www.openmath.org/cocoon/openmath/documents/Units.pdf

> etc. But if it is intended that for defining physical symbols
> one needs the power symbol anyway, then which sense has the symbol metre_sqrd?

the symbol metre_sqrd is defined in the Description and FMP as 
metre × metre
I think there is no ambiguity here

> It should be (metre)^2 in this case, if the whole system has a systematic. On
> the other hand, I could also use centi-metre_sqrd, but in my opinion this
> would mean 10^(-2)*m^2, whereas cm^2 is 10^(-4)*m^2.
> 

I suppose if you wanted cm^2 you would have to go (prefix(centi,metre))^2, 
whilst prefix(centi,metre_sqrd) would mean 10^(-2)*m^2 

> Similar questions arise for the units of volumes. Why is there a "litre"
> symbol but no "metre_cubic"?
> 
> Finally, without giving any reference to the special case "kilo", the
> description of "prefix" in units_ops1 doesn't make much sense:
> 

This is clearly a bug, (which I raised about a year ago), that needs to be 
fixed!

Bill

> prefix
> 
> Description:
>    "This symbol represents the fact that the subsequent unit has been
> effectively multiplied by 1,000 ($10^{3}$)"
> 
> Commented Mathematical property (CMP):     This is unit multiplication by
> 1,000
> 
> Thanks for any help and comments,
> 
> regards,
> Christian Gross
> 
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> 
> 
> 

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-                  Dr. W.A. Naylor
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-                  http://www.cs.bath.ac.uk/~wn
-                  http://orcca.on.ca/~bill
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