As far as your last point that amounts to checking whether or not the system generates the unit ideal. You can do that with a Groebner basis calculation which is souped up linear algebra. Victor Sent from my iPhone On Nov 30, 2009, at 1:15 PM, Dan Asimov <dasimov@earthlink.net> wrote:
We know that there exists a formula that may use roots (and arithmetic operations) for solving polynomials for each degree through 4, and no higher.
I. What's known about finding such a formula for solving *several polynomial equations in several variables* ?
(The polynomials can be of different degrees in general, and the coefficients can be any complex numbers.)
II. Wait! Let's go back a step and ask when such a system of polynomial equations is even *known to have a solution*.
--Dan
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