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2
votes
1answer
109 views
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:
$$
\begin{align*}
xy&=-2\\
x^2-1&=0\\
y^3-3y^2+2y&=0
...
0
votes
0answers
166 views
4th degree nonlinear simultaneous equations with 3 unknowns
What method should be used to solve the following nonlinear simultaneous equations for $z_1, z_2, z_3$
$$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$$
...
