Let $(F,+,\cdot)$ be an ordered field. The signum $\operatorname{sign}:F\to F$ is a function defined for all $x\in F$ by $$\operatorname{sign}(x):=\begin{cases} 1&\text{if }x > 0,\\ 0&\text{if }x = 0,\\ -1&\text{if }x < 0,\\ \end{cases}$$
for $1,-1,0\in F.$
