compose division ops for `ContinuedFraction`

[sr-murthy]

All division operations in ContinuedFraction:

• continuedfraction.ContinuedFraction.__truediv__
• continuedfraction.ContinuedFraction.__rtruediv__
• continuedfraction.ContinuedFraction.__floordiv__
• continuedfraction.ContinuedFraction.__rfloordiv__

can be refactored by composing the division-free algorithms for the negation and inversion of simple continued fractions of positive rational numbers, which are described in the documentation.

A new __invert__ operation is required for the composition, which implements the following algorithm for the inversion of a positive rational number $\frac{a}{b}$ with simple continued fraction $[a_0; a_1,\ldots, a_n]$: the positive inversion $+\frac{b}{a}$ is given by:

$$ +\frac{b}{a} = \begin{cases} [a_1; a_2,\ldots, a_n], \hskip{3em} & \text{if } 0 < a < b \iff a_0 = 0 \\ [0; a_0, a_1,\ldots, a_n], \hskip{3em} & \text{if } 0 < b < a \iff a_0 \geq 1 \end{cases} $$

This makes it possible to implement negative inversion $-\frac{b}{a}$ as the composition:

$$ -\frac{b}{a} = \frac{1}{-\frac{a}{b}} = -\left(\frac{1}{\frac{a}{b}}\right) = \begin{cases} [-1; a_0 - 1], \hskip{3em} & n = 0 \text{ and } a_0 \geq 1 \\ [-1; 1, a_0 - 1, 2], \hskip{3em} & n = 1 \text{ and } a_0 \geq 2 \\ [-1; 2, a_2, \ldots, a_n], \hskip{3em} & n \geq 2 \text{ and } a_0 = 1 \\ [-1; 1, a_0 - 1, 1, a_2, \ldots, a_n], \hskip{3em} & n \geq 2 \text{ and } a_0 > 1 \end{cases} $$

In applying this algorithm there is an assumption that the last element $a_n &gt; 1$, as any simple continued fraction of type $[a_0; a_1,\ldots, a_{n} = 1]$ can be reduced to the simple continued fraction $[a_0; a_1,\ldots, a_{n - 1} + 1]$.