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MathGroup Archive 2005

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symbolic quaternionic analysis

  • To: mathgroup at smc.vnet.net
  • Subject: [mg55480] symbolic quaternionic analysis
  • From: danieldaniel at gmail.com (Daniel Alayon Solarz)
  • Date: Fri, 25 Mar 2005 05:48:21 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

At the end of this message is my code to handle what the title refers to.

I have two questions, 

1) is there any other? and
2) I am interested in functional analysis, is Mathematica capable of handle that?
 
<< Calculus`VectorAnalysis`

p[t_, x_, y_, z_] := {t, {x, y, z}}
m[p[t1_, x1_, y1_, z1_], 
    p[t2_, x2_, y2_, z2_]] := {t1*t2 - Dot[{x1, y1, z1}, {x2, y2, z2}], 
    t1*{x2, y2, z2} + t2*{x1, y1, z1} + Cross[{x1, y1, z1}, {x2, y2, z2}]}
Pwr[p[t_, x_, y_, z_], 0] := { 1, {0, 0, 0}}
Pwr[p[t_, x_, y_, z_], 1] := p[t, x, y, z]
Pwr[p[t_, x_, y_, z_], n_] := m[Pwr[p[t, x, y, z], n - 1], p[t, x, y, z]]
RFueter[{a_, {b_, c_, d_}}] := 
  m[D[{a, {b, c, d}}, t], p[1, 0, 0, 0]] + 
    m[D[{a, {b, c, d}}, x], p[0, 1, 0, 0]] +
    m[D[{a, {b, c, d}}, y], p[0, 0, 1, 0]] +
    m[D[{a, {b, c, d}}, z], p[0, 0, 0, 1]]
LFueter[{a_, {b_, c_, d_}}] := 
  m[p[1, 0, 0, 0], D[{a, {b, c, d}}, t]] + 
    m[p[0, 1, 0, 0], D[{a, {b, c, d}}, x]] +
    m[p[0, 0, 1, 0], D[{a, {b, c, d}}, y]] +
    m[p[0, 0, 0, 1], D[{a, {b, c, d}}, z]]


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