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MathGroup Archive 2004

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question: override Multiply[]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg50163] question: override Multiply[]
  • From: darrk at bolt.com (dark)
  • Date: Wed, 18 Aug 2004 01:20:17 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Dear all,
I am analysing complexly symmetrical patterns (such as atmospheric
turbulence). To remove symmetries I study the following group

eg. X(X+X(X+X))

+ is communicative
. is non-communicative
+ & . are assocciative

(similar to trees)

Since the astmospheric turbulence dynamics is similar to a natural
selection of macroscopic structures, we can use associative rules to
understand and mimic the patterns. (However I am not sure it's up to
which level)

For compatibility with the data (in 3-d space) I need to redefine '.'
as follows

. = |associate 2 neighbor vectors (depending on positions)
    |associate 2 similar vectors (depending on magnitudes)

(spatial associativity)

ie. eg. x1+x2=x1.x2 if x1 is adjacent to x2

The motivation of this overriding is the factorization and problem
solving engine of Mathematica. Could you let me know whether
Mathematica has this capability? Is ther another factorization engine
support complex associativity like above?

(This approach is very computational exhausive however I want to make
simple analysis first)

BTW, if you are interested in
- complex patterns (<-- non-dynamical patterns)
- associative algebra (<-- morphology)
- syntatic/semantic analysis (<- numerical analysis)
(similar classical subjects in brackets)

please email me, I would be very glad to know you.

Thanks very much.


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