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I am looking for a numerical method that can solve a system of non-linear equations. The non-linear equations are polynomials that are in one of the following forms:

$$ c_1x_1+c_2x_2+\ldots+c_nx_n=C \\ d_1x_1^2+d_2x_2^2+\ldots+d_nx_n^2=D $$

(The variables are $x_1,x_2,\ldots x_n$.)

I can't get initial guesses that are close to the root. Is there a good numerical method to solve the system of equations?

Thank you in advance

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    Have you tried MATLab or SAGE? You'll have to do a little scripting magic, but it's nothing too complicated ;-) If you need help with that, though, edit your question to reflect that and/or ask on StackOverflow.2012-05-28

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