On Friday, August 29, 2014 6:46:39 PM UTC+2, Chris Corio wrote:
>
> Can anyone point me at the functions that I can use to solve these 
> equations or have any suggestions for the solutions?  I appreciate the help.
>
>
Sage's "solve" is explicit, I don't know if it gives you a solution.
What you probably actually need is a numerical approximation. There is
http://www.sagemath.org/doc/reference/numerical/sage/numerical/optimize.html#sage.numerical.optimize.minimize_constrained
although SLSQP in SciPy
http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.fmin_slsqp.html
is maybe best for you. In eq1 to eq3, subtract the right hand side from the 
left hand side, as lambda functions, and that list is eqcons. The bounds on 
k and h are in "bounds".
Also, set the objective function function to lambda : 1, what does count 
are the constraints.
That's a general answer, I hope I really understood what you want.

Make sure to check which version of scipy there is in Sage and which one 
the documentation refers to. It could be outdated.

-- H

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