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Re: Rule-based programming: declare variables to be a number

• To: mathgroup at smc.vnet.net
• Subject: [mg80853] Re: Rule-based programming: declare variables to be a number
• From: David Bailey <dave at Remove_Thisdbailey.co.uk>
• Date: Tue, 4 Sep 2007 03:45:49 -0400 (EDT)
• References: <fb83lf$82d$1@smc.twtelecom.net> <200709020651.CAA25850@smc.twtelecom.net> <fbgmuq$9d7$1@smc.vnet.net>

Andrzej Kozlowski wrote:
> On 2 Sep 2007, at 08:51, David Bailey wrote:
> 
>> As others have commented, it is not a good idea to write code like
>> NumericQ[g]=True because this changes the basic operation of
>> Mathematica. For example, such code might work OK until you try to
>> combine it with some more code that needs NumericQ for something else!
>>
>> David Bailey
>> http://www.dbaileyconsultancy.co.uk
> 
> 
> Who are the "others"?
> Anyway, I completely disagree with this statement in this particular  
> context.
> 
>   NumericQ has clearly been designed with this in mind. Note, for  
> example, that althou NumericQ is Protected, a definition like
> 
> NumericQ[a]=True
> 
> does not require unprotecting NumericQ. Moreover, it does not add a  
> DownValue to NumericQ.
> 
> NumericQ[g] = True;
> DownValues[NumericQ]
> {}
> 
> 
> There are plenty of other reasons to believe that all all  
> theseproperties of NumericQ are designed precisely for this type of  
> use. Besides, I have another reason to think that no probems of the  
> kind you are imagining would happen in this case: I have been using  
> NumericQ inprecisly this way for about 10 years in numerous notebooks  
> without any problems.
> 
> Note alo the post from Carl Woll which, I think, can be regarded as  
> an "offcial" WRI authorization for this kind of usage ;-)
> 
> (However, note also that using Carl's definition:
> 
> In[19]:= g /: NumericQ[g] = True;
> 
> Dos not actually add an UpValue to g:
> 
> UpValues[g]
> {}
> 
> and I don't think it has any advantage over the more straightforward
> 
> NumericQ[g] = True;
> 
> 
> I am sure all this is deliberate design, and even though it may not  
> be easy to explain, it is very convenient.
> 
> Andrzej Kozlowski
> 
Lets not quarrel about this - but my point was that it is probably 
easier to specify the set of objects that don't commute rather than 
specify everything else that is an ordinary variable!

In general, I don't like to extend the built-in functions unless 
absolutely necessary (as dh mentioned) - it just creates trouble when 
you combine several pieces of code together. Why not just define a 
spinMatrixQ predicate?

Also, it is not clear from the original question, if 'multiplication' is 
represented by Times - if it is, the expressions will get sorted 
regardless of NumericQ!

David Bailey
http://www.dbaileyconsultancy.co.uk

• References:
  • Re: Rule-based programming: declare variables to be a number
    • From: David Bailey <dave@Remove_Thisdbailey.co.uk>