[Om] [Om3] Math in office documents/Providing an implementation for a symbol
Paul Libbrecht
paul at activemath.org
Tue Dec 16 11:35:49 CET 2008
Le 16-déc.-08 à 11:10, Professor James Davenport a écrit :
>> My concern with the
>> <FMP> element is that is a tool used to describe the properties of a
>> black box, where the symbol is any object satisfying all of the
>> <FMP>s. As I understand it, additional <FMP>s are not
>> equivilent to "alternative implementations"; in my understanding,
>> they
>> are additional constraints on the symbol, and ALL constraints must be
>> jointly satisfied.
> Correct.
That gives freedom, true, and it's a good thing!
>> I want to directly define what the black box contains, without
>> necessarily describing any of its properties.
> But, if you are defining what it contains, aren't you therefore ALSO
> defining its properties?
erm... an FMP of the style:
function(x) = {do-bla-bla-in-a-concrete-way}
is a valid FMP, quite a constraining one, but a valid one which does
specify the value everywhere this equality holds!
The only bit you are missing compared to an implementation spec is the
contraint that says that not only this property holds but that this is
the way it's implemented! That's a useless constraint to my taste.
(and a good machine should be able to know, by theorems, that this FMP
is valid even though it uses it's own,
I wonder how NAG library or Maple could solve this challenge, for
example, a nice one)
>> For instance, I want a function called
>> Planck_bb_freq(nu, T), to compute an object's blackbody radiance at
>> the
>> given frequency and temp. Given SI units, there is only one
>> correct
>> implementing expression.
I don't agree there's a single one even though there is probably only
one found on earth a of today.
paul
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