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MathGroup Archive 2004

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Re: Attributes and behaviors?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg46565] Re: Attributes and behaviors?
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Mon, 23 Feb 2004 22:33:49 -0500 (EST)
  • Organization: Universitaet Leipzig
  • References: <c1c9kk$atc$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

if you introduce a new data type like DualNumber[] you have to
add the rules for the build in functions to
handle this.

DualNumber /: Sin[d_DualNumber]:= kSin[d]

Mathematica is a functional language and you have to setup
the new behaviour  of the *function* for the data.

Regards
  Jens

Fred Klingener wrote:
> 
> Please help me understand better the relationship between attributes and
> behaviors.
> 
> Background:  I'm a Mathematica (5.0.0) newbie who's trying to build a
> package for dual numbers.  In the package, ultimately I want to overwrite
> the System numeric functions to handle dual numbers without affecting the
> handling of the native (atomic) types.
> 
> Progress so far:  I have some sample functions working pretty well.
> Functions I've named things like kDualNumberSin[] seem to work numerically
> and symbolically on dual numbers and to drop through (via an explicit call)
> to System`Sin[] on Real arguments.  Now I'm ready to think about overwriting
> System`Sin[], for example, and I'm having trouble getting my head around
> atttributes.
> 
> 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.
> 
> - 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.
> - kDualNumberSin[] also seems to have listable capability.
> 
> All of this is confusing.
> 
> - What's the nature of the relationship between attributes and behavior?
> - Is the attribute used in some inscrutable inner workings of the kernal?
> - What are the costs and benefits of simply setting the Listability
> attribute in my function?
> - How certain do I have to be that my function really IS Listable before I
> set the attribute?
> - Does the absence of the Listability attribute of Series[] mean that its
> current listable behavior is an undocumented feature subject to future
> abandonment?
> 
> TIA for any help,
> 
> Fred Klingener
> Brock Engineering


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