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Function parameterization guess

  • To: mathgroup at smc.vnet.net
  • Subject: [mg132640] Function parameterization guess
  • From: Narasimham <mathma18 at gmail.com>
  • Date: Sun, 27 Apr 2014 02:07:08 -0400 (EDT)
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Using excellent function capabilities of Mathematica is it not possible to generally guess or propose some standard parameterizations of components given functions?
 
For two variables and single parameter. Given x^2 + y^2 =1 we have {x,y}= {Cos[t],Sin[t]} and its variants {Sech[t],Tanh[t]}among others are solutions.

For three variables and two parameters. Given x^2 + y^2 - z^2 =1 we have Cosh[u] Cos[v], Cosh[u] Sin[v], Sinh[u] and variants..

The number of parametric set variations for component variables is not infinite, can be indicated with an arbitrary constant. A general or possible sub parameterization may be considered for each functional relationship.

Regards
Narasimham



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