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Consider a polynomial in two variables $(z,w)\in \mathbb {C}$ given by the expression

$F(z,w)=a_{0}(z)+a_{1}(z)w+a_{2}(z)w^{2}+\cdots +a_{n}(z)w^{n}$ where $a_{i}(z)$ is a polynomial with rational coefficients. The zero set $F(z,w)=0$ defines an algebraic curve in $\mathbb {C} ^{2}$. These curves are often quite complicated consisting of interleaved sheets twisting around singular points of $F(z,w)$ and although we cannot graph directly the curve in $\mathbb {C} ^{2}$, we can obtain a very precise plot of the real or imaginary component of the curve. For example, consider the expression $F(z,w)=$

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