### Implementing new CF class advice

My goal is to implement Gosper's algorithm for algebraic operations on continued fractions into Sage. To begin with, I would like to implement a functionality to perform a homographic transformation

$$x \rightarrow \frac{ax + b}{cx + d}$$

where $x$ is a CF.

The easiest way to do this is probably to create a new class in `sage.rings.continued_fraction`

that would on inicialization accept the integer constants $a, b, c, d$ and a descendant of `ContinuedFraction_base`

class. The most important method of this class would be `next()`

or `_iter_()`

, which would read the input $x$ until it can output new term using Gosper's algorithm.

How do I create an instance of this class with proper arguments, when for example $(3*x + 1)/2$, where $x$ is a CF, is called from Sage? (Instead of `_mul_()`

being called, than `_add_()`

and so on...)

Simplifying using inbuilt Sage methods and then evaluating the expression as a string using regular expressions somehow (like this) might be a solution, but I am not sure if the best one.

Thank you very much for any advice on this!

EDIT: I have found this promising link, but haven't found anything useful in there so far...