[Om] [Om3] Math in office documents/Providing an implementation for a symbol

[Paul Libbrecht]

Hello Bryce,

Le 16-déc.-08 à 03:12, Bryce L Nordgren a écrit :
> I posted to OM3 mostly because it seemed that MathML3 was tooling up  
> to directly reference OM3 content dictionaries.  Also, I may have  
> missed something, but from what I can tell, the only way to define  
> new symbols for use with either MathML or OM is to define it within  
> an OM content dictionary.

OM3 is a fine discussion for that, it is indeed slightly more followed  
by the W3C-math-wG but much less from OpenMath veterans. I'll allow  
myself to cross-post even though it's not really elegant.

> Asking here seemed the appropriate place, especially if discussion  
> risked articulating a new requirement of the system.

This is true indeed.
A new requirement of the "standard" and not "system", right?

The below mail seems indeed to express a wish to specify symbols with  
a single way to interprete them. I feel it is a bad practice but  
still, it can be achieved today, with zero DEFMP or extra  
implementation element: your symbol declaration  should contain a  
single FMP, that specifying the implementation.

The only freedom you leave to receivers of such a symbol declaration  
is to take the freedom to consider an own interpretation of that  
symbol to be equivalent to that symbol satisfying the prescribed  
function equality.

Do you want to even avoid that freedom?
I really don't see a reason and it shows a global mistrust to  
mathematics.
As far as I know, a system "implements FMPs" by just having their  
developers "knowing" that their implementations satisfy the FMP in a  
theoretical way. That knowledge may be wrong but that would be a bug  
of them.

  (please note: there's more than evaluating to a "implementing" a  
function, inverting or solving equations with it are examples of it).

paul


> 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.  I want to directly  
> define what the black box contains, without necessarily describing  
> any of its properties.
>
> 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 want to describe the properties of this  
> function (peak described by the frequency form of the Wien  
> displacement law, falls off exponentially at higher freqs and  
> polynomially at lower; integral over all wavelengths is the Stephan- 
> Boltzmann law).  I have the one and only defining equation of the  
> symbol, so I want to associate it with the name.  What's more, I  
> want to ensure that whenever I reference the symbol in a context  
> where it is evaluated, it always computes the expression I've  
> specified (example OMA given at end of email).   I want to  
> explicitly forbid any mathematical system from taking liberties with  
> the expression, inferring anything extra, or fiddling with the  
> units.  :)
>
> The processing system is allowed to supply implementations for  
> times, divide, minus, power, exp, speed_of_light, Planck_constant,  
> and Boltzmann_constant (unless I get paranoid about these last three  
> and just type in values in the correct unit system). It may  
> precompute constant terms if it desires or perform any other  
> computational optimization which does not affect the result.
>
> How does one express this sentiment in a content dictionary?  And if  
> there is no means of doing it, could such a facility possibly be  
> added to OM3?
>
> Thanks,
> Bryce
>
>     <om2:OMA>
>         <om2:OMS name="times" cd="arith1"/>
>         <!-- First term (2 h nu^3)/(c^2) -->
>         <om2:OMA>
>             <om2:OMS name="divide" cd="arith1"/>
>             <!-- 2 h nu^3 -->
>             <om2:OMA>
>                 <om2:OMS name="times" cd="arith1"/>
>                 <om2:OMI>2</om2:OMI>
>                 <om2:OMS name="Planck_constant"  
> cd="physical_consts1"/>
>                 <!-- nu cubed -->
>                 <om2:OMA>
>                     <om2:OMS name="power" cd="arith1"/>
>                     <om2:OMV name="ʋ"/>
>                     <om2:OMF dec="3"/>
>                 </om2:OMA>
>             </om2:OMA>
>             <!-- c^2 -->
>             <om2:OMA>
>                 <om2:OMS name="power" cd="arith1"/>
>                 <om2:OMS name="speed_of_light" cd="physical_consts1"/>
>                 <om2:OMI>2</om2:OMI>
>             </om2:OMA>
>         </om2:OMA>
>
>         <!-- Second Term: 1 / (e^((h nu)/(k T)) -1 )-->
>         <om2:OMA>
>             <om2:OMS name="divide" cd="arith1"/>
>             <om2:OMF dec="1"/>
>
>             <!-- e^((h nu)/(k T)) -1 -->
>             <om2:OMA>
>                 <om2:OMS name="minus" cd="arith1"/>
>                 <!-- e^((h nu)/(k T)) -->
>                 <om2:OMA>
>                     <om2:OMS name="exp" cd="transc1"/>
>                     <om2:OMA>
>                         <om2:OMS name="divide" cd="arith1"/>
>                         <!-- h nu -->
>                         <om2:OMA>
>                             <om2:OMS name="times" cd="arith1"/>
>                             <om2:OMS name="Planck_constant"  
> cd="physical_consts1"/>
>                             <om2:OMV name="ʋ"/>
>                         </om2:OMA>
>                         <!-- k T -->
>                         <om2:OMA>
>                             <om2:OMS name="times" cd="arith1"/>
>                             <om2:OMS name="Boltzmann_constant"  
> cd="physical_consts1"/>
>                             <om2:OMV name="T"/>
>                         </om2:OMA>
>                     </om2:OMA>
>                 </om2:OMA>
>                 <om2:OMF dec="1"/>
>             </om2:OMA>
>         </om2:OMA>
>     </om2:OMA>
>

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