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MathGroup Archive 2004

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Re: Attributes and behaviors?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg46606] Re: Attributes and behaviors?
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Wed, 25 Feb 2004 13:07:00 -0500 (EST)
  • Organization: The University of Western Australia
  • References: <c1c9kk$atc$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In article <c1c9kk$atc$1 at smc.vnet.net>,
 "Fred Klingener" <flush at BitBucket.com> wrote:

> I've built a toy function:  kSin[x_] :=Sin[x], and here are a few
> observations about it:
> 
> - In:-> Attributes[Sin] Out:-> {Listable, NumericFunction,...}
> - In:-> Attributes[kSin] Out:-> {}
> - a few tests show that kSin[] has full listable behavior, that is, it
> produces the same
>   output as Sin[] when fed a List as an input argument.

Because Sin is Listable:

   kSin[{a,b,c}] --> Sin[{a,b,c}] --> {Sin[a],Sin[b],Sin[c]}

> - My 'serious' function kDualNumberSin[] relies on Series[] for its
> operation.
> - Series[] has no Listable attribute.
> - a few primitive tests show that Series[] in fact has Listable capability.

This is, I think, more subtle. The documentation on Series says that

  Series[f, {x, 0, n}] constructs Taylor series for any function f   
  according to the formula f[0] + f'[0] +  ...

Now if f happens to be {g[x], h[x]} then you see that f[0] = 
{g[0],h[0]}, f'[0] = {g'[0],h'[0]}, and so on. 

You can also write

   {g[x], h[x]} + O[x]^4

and, since Plus is Listable, the behaviour is more obvious.

Note that D does not have the Listable attribute either but it works in 
the same fashion as Series (for the same reason).

> - What's the nature of the relationship between attributes and behavior?

Generally, an Attribute is required before the behaviour occurs. 
However, there is the possibility of inheritance (your kSin) or from a 
fundamental mathematical property. 

> - Is the attribute used in some inscrutable inner workings of the kernal?

No.

> - What are the costs and benefits of simply setting the Listability
> attribute in my function?

Very little cost -- but if it's not necessary there is no need to set it.

> - How certain do I have to be that my function really IS Listable before I
> set the attribute?

A simple test should suffice.

> - Does the absence of the Listability attribute of Series[] mean that its
> current listable behavior is an undocumented feature subject to future
> abandonment?

No.

Cheers,
Paul

-- 
Paul Abbott                                   Phone: +61 8 9380 2734
School of Physics, M013                         Fax: +61 8 9380 1014
The University of Western Australia      (CRICOS Provider No 00126G)         
35 Stirling Highway
Crawley WA 6009                      mailto:paul at physics.uwa.edu.au 
AUSTRALIA                            http://physics.uwa.edu.au/~paul


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