# [Om] usage of OM symbols for physical units

Paul Libbrecht paul at activemath.org
Tue May 30 15:44:44 CEST 2006

```Dear OpenMathers,

It's a shame that there is no link from the CD pages to such a document!
as that indicated by Bill! We'd need to make such links appear.
Here, a simple link on the top of the CD presentation would have lead me
and Christian into exploring how and why arith1/times for units.

I discovered another issue which seems harder with the usage of the
times symbol: rendering of notation-times is typically different than
rendering of normal multiplications... so we need either to write
conditions for just about any possible unit-usage (so, one for X*m^2,
one for X*m^3, X*(cm)^2...) or need to have another way to know that the
right-hand-side is a unit... The only reliable mechanism is see is types
which... mmmh... is expensive and beyond XSLT!
So I would be in favor of a dedicated times.

As to the Occam's razor, the law of parsimony, I will always suggest my
"rephrases" which are translation rules expected to be operated to
convert an expression with symbols in one CD-group to an expression with
symbols in another. Conversion to the MathML CD of X•m^2 (with m a
symbol in units_metric1) would be X*m^2 (with m a variable!).

paul

W Naylor wrote:
> 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
>>
>>

```