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Hello Michael, hello all,

On Friday 01 June 2007 23:07:29 Michael Hucka wrote:
> RG> Lets assume you want to multiply 2.0 * 10^-3 m^2 with
> RG> 3.0 * 10^-5 m^3. The result should be 6.0 * 10^-8
> RG> m^5.
>
> I don't understand which is the unit and which is the
> quantity. E.g., In the case of the "2.0 * 10^-3 m^2", are
> you trying trying to define a single unit equal to "two
> square millimetres"? (10^-3 m^2 would be square
> millimetres, I think?)

Yes, I think Ralph was only talking about units, no values involved. Actually
the units Ralph used as an example are quite arbitrary and would not
reallistically be used. 2*10^-3 m^2 is not 2 square mm but rather 0.002 sqare
meters.
Your example about square feet is valid: I you want to express square feet
with meter as base unit, the new way is more intuitive. On the other side, if
you want to express gallons with meter as base unit, the old way was more
intuitive.

Ralph´s point (as I understand it) is that with the old unit definition the
multiplication of two units is almost trivial. (Multiplication of units is an
operation that occurs frequently when checking/converting/handling units).
With the new unit definition (from the errata) multiplication of units is more
complicated, less efficient, and probably looses more accuracy.

As far as I can see, in principle both ways to handle units can do everything
that is needed. I just cannot see why the old way was wrong, and I agree with
Ralph that the old way is probably easier to handle.

To illustrate:
Multiplication of two unit definitions (base on the same base unit) in the old
schema:
(a * 10^b *u^c) * (d * 10^e * u^f)
= (a*d) * 10^(b+e) * u^(c+f)

In the new schema the solution would be:
(a * 10^b *u)^c * (d * 10^e * u)^f
= [ (a^c*d^f)^(1/(c+f)) * 10^((b*c+e*f)/(c+f)) * u ]^(c+f),
and this is not yet normalized (the scale part needs to be integer), so
another step is needed.

In some cases this will not be a problem. a and d will often be 1.0, and
((b*c+e*f)/(c+f)) will quite often be an integer, in which case evrything is
fine. In the general case, however, we may have to use floating point
operations for exponents, which looses accuracy and makes the exact
comparison of units difficult, or, we should use exact rational numbers as
exponents, which is much more complicated from a developers point of view.


> If you do indeed mean to use strange multipliers, I think
> here again you would pull out the part that's the actual
> unit of measurement from the part that's the fraction of the
> measurement, and use the unit-composition trick to define
> the fraction separately from the unit of measurement, as in
> the following:
>
> unitDefinition id="funky_new_unit"
> unit kind="dimensionless" multiplier=".002"
> unit kind="metre" exponent="2"
>
> or something along those lines. But I think I'm not
> understand the intended units in that example.

OK. I see. Using this trick you can force to more or less use the old way of
handling units. I didn´t think of this.

Sven


--
Sven Sahle
Bioquant, Universität Heidelberg
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