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Function parameterization guess
Posted:
Apr 27, 2014 2:07 AM


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



