[Om] questions on the OM symbols for physical units and their prefixes

[Michael Kohlhase]

Dear all,

Note that there is a W3C note [1] in the  MathML group that is also 
relevant here. we should try to be compatible with that in our practices 
in OM.

A paper that also touches on the units question is our proposal for a 
Physics Markup Language to be presented at the MKM Conference. That 
proposes to equip units  with types in a dimension type sytem. We are in 
the process of developing OMDoc Content Dictionaries for these based on 
the MathML note above.

Michael

[1] http://www.w3.org/TR/mathml-units/
[2] 
https://svn.mathweb.org/repos/mathweb.org/trunk/omdoc/projects/physml/doc/mkm06/paper.pdf

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   Prof. Dr. Michael Kohlhase,         Office: Research 1, Room 62 
   Professor for Computer Science      Campus Ring 12, 
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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 cm2 as a small unit for area?
> One could construct "(centi-metre)2" of course, using the usual power 
> symbol, 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? 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)*m2, 
> whereas cm2 is 10^(-4)*m2.
>
> 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:
>
> 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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