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I have a set of nonlinear equations [tex]f_i(x_1,x_2,x_3...)[/tex] and I want to find their solutions.

After doing some reading I have come across commutative algebra. So to simplify my problem I have converted my nonlinear equations into a set of polynomials [tex]p_i(x_1,x_2,x_3...,y_1,y_2...)[/tex] by introducing new variables (the y's) defined in the [tex]\Re[/tex].

How can I find the answer to:

1) whether a solutions exists?

2) if so what is it?

To tackle these two questions I have used mathematica to find solutions with no luck...

I then used mathematica to search for a Groebner Basis which is a new set of polynomials with the same solution space also with no luck....

Is there a way to study the equations analytically to answer at least question 1)

(I could only find theorems for equations defined over the Complex field)....Or if not an answer to 1) some thing I can state about this set of polynomials?

Any help would be greatly appreciated

cheers

M

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# Solutions to a set of polynomials (Commutative Algebra)

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