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Dear Upi,

bhalla> Dear Mike, Did you consider the possibility of
bhalla>
bhalla> 1. defining a 'dimensionless' unit, and

Indeed, SBML already defines "dimensionless".

bhalla> 2. requiring that _every_ number have a unit
bhalla> attached, even if it is only 'dimensionless'?

Just as background, to clarify the situation (you may
already have this in mind; sorry if this is stating the
obvious), most fields taking numbers in SBML do have units
defined (along with defaults). Those units are associated
with the overall expression or overall value of the field.

The problem here involves numbers appearing within MathML
expressions, for example in reaction rate formulas. MathML
does not have a standard scheme for attaching unit and
dimensionality information to <cn>. There some suggestions,
e.g. at http://www.w3.org/TR/mathml-units/; they involve
using either <csymbol> or <semantics> and wrapping numbers
inside <apply></times>...</apply> to attach the unit
information. An alternative approach is taken in CellML,
where they allow the use of a "units" attribute in the
CellML namespace to be added to MathML <cn> elements, as in
for example

<math xmlns="http://www.w3.org/1998/Math/MathML">
....
<cn cellml:units="dimensionless"> -1.0 </cn>
...
</math>

Of the schemes I've seen, the CellML one is the simplest and
easiest. The MathML proposal at the URL mentioned above,
involving <semantics> or <csymbol>, results in much more
complicated expressions and probably a lot of opportunities
for errors.

It could be considered a failure of SBML that it does not
define a scheme for associating units with numbers.

Should such a facility be added?

MH

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