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5

If you are looking at intersecting the zero sets of two polynomials in two variables, then by Bezout's theorem you should anticipate that the number of solutions will be equal to the product of the degrees of the polynomials. So in general, you will not get unique solutions. You will need to be very careful to hide these extra solutions "at infinity&...


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Generating systems. The same method that works for linear equations works also for polynomial equations. Starting with a solution in mind (in mathematics and computer science, we call this a planted solution), generate in some way left-hand sides of equations, and then compute the corresponding right-hand sides. If you use more than one equation per variable ...


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