# A Simple Arithmetic Circuit

Let $$\mathbb{F}$$ be some finite field. We would like to show in this section the transformation from the program computing polynomial $$f(u, v) = u^2 + 3uv + v + 5$$ where $$u, v \in \mathbb{F}$$. With inputs $$u, v \in \mathbb{F}$$, the arithmetic circuit for this polynomial is equivalently represented by topologically following the sequence of computations below.

1. Compute $$u^2$$.
2. Compute $$uv$$.
3. Compute $$3uv$$.
4. Compute $$u^2 + 3uv$$.
5. Compute $$u^2 + 3uv + v$$.
6. Compute $$u^2 + 3uv + v + 5$$.