Definition:Continued Fraction Expansion of Laurent Series

Definition
Let $k$ be a field.

Let $k((t^{-1}))$ be the field of formal Laurent series in the variable $t^{-1}$.

Irrational Laurent series
Let $f \in k((t^{-1}))$ be an irrational formal Laurent series.

The continued fraction expansion of $f$ is the infinite continued fraction $(\lfloor \alpha_n \rfloor)_{n\geq0}$ where $\alpha_n$ is recursively defined as:
 * $\alpha_n = \displaystyle \begin{cases} f & : n = 0 \\

\dfrac 1 {f - \lfloor f \rfloor} & : n \geq 1 \end{cases}$ where $\lfloor \cdot \rfloor$ denotes the polynomial part.