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3
votes
2answers
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Checking if a System of Polynomial Equations is Consistent

I'm trying to determine whether any solutions exist to a system of $(n+1)$ polynomial equations in $n$ unknowns. For example: $$ \begin{align*} xy&=-2\\ x^2-1&=0\\ y^3-3y^2+2y&=0 ...
0
votes
0answers
204 views

4th degree nonlinear simultaneous equations with 3 unknowns

What method should be used to solve the following nonlinear simultaneous equations for $z_1, z_2, z_3$ $$a_2z_1^2 + a_1z_2^2 - (z_1z_2 \tan(t))^2 - z_1z_2 2b_1/\cos(t)^2 = b_1/\cos(t)^2 - a_1a_2$$ ...