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Re: An approach to describing the relationships between units-

• To: costello@m...
• Subject: Re: An approach to describing the relationships between units-of-measure
• From: David Carlisle <davidc@n...>
• Date: Mon, 21 Jul 2003 13:21:35 +0100
• Cc: xml-dev@l...
• In-reply-to: <3F1BCFC6.D23FEA71@m...> (costello@m...)
• References: <3F1BCFC6.D23FEA71@m...>

>   {k, m | k = m * 1.62}
here and elsewhere
you mean
  {(k, m) | k = m * 1.62}
   ^    ^
I think, that is you want sets of pairs.
(Which is why you have the <list> connstructor in the MathML
representation of this)


> expressed as xPath(???)

Xpath could express the constraint that something=1.62* something else
eg
($1/cartesian-coordinate/x/kilometer =
$2/cartesian-coordinate/x/kilometer
or
$1/cartesian-coordinate/x/kilometer =
$2/cartesian-coordinate/x/mile * 1.62
)
would return true if the x coordiunates of the locations in $1 and $2
were true, using XSLT2 you could define a function that retuned true or
false with this (and a simliar expression for y coordinate).


> If someone more skilled
> with MathML than I would care to do so, I would greatly appreciate it.)

In your first version you were building sets of pairs of real numbers
for which there is really only one mathml representation.

For this set, again the MathML set construction is fairly automatic
following on from your {} notation which, again is missing the pair
constructor

{ (c, p) | ....
  ^    ^

However your problem now is not to represent the set but rather the
objects in the set which you have use  c.y.kilometer notation.
You could build a mathematical representation of the structired object,
and represent that in MathML, but I'm not sure that is really what you
want to do.


I think I'd be inclined to model everything as a function mapping on to
a canonical representation (say cartesian coordinates in met[re][er]s).

so 

<cartesian-coordinate>
            <x>
              <kilometers>
...


is the mapping (x,y) -> (x/1000,y/1000)

and
  <polar-coordinate>
            <r>
                <kilometer>..
            </r>
            <theta>
...

is the mapping

  (x,y) -> (r/1000 * cos theta, r/1000 * sin theta)

Then instances are equivalent if evaluating the specified function of
the supplied arguments results in teh same canonical form.


>   (6340 k, 3914) in S
          ^
You mean (6340 , 3914) in S, I think. S consists of pairs of numbers not
dimensions.

David

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• References:
  • An approach to describing the relationships between units-of-measure
    • From: "Roger L. Costello" <costello@m...>

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