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.