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### Coercion on continued fractions

Currently, when user types

sage: x = continued_fraction(pi)
sage: y = 3*x


an TypeError is raised saying

TypeError: unsupported operand parent(s) for '*': 'Integer Ring' and '<class 'sage.rings.continued_fraction.ContinuedFraction_real'>'


I understand that Sage tries to find common parent of Integer element and ContinuedFraction_real and fails. It seems that continued fractions in Sage are not implemented as elements of any particular field, and are derived directly from SageObject.

I am implementing an algorithm for arithmetical operations on continued fractions. Is it possible to make Sage call a particular method when the user tries to perform an arithmetical binary operation, where one of the operands is a continued fraction?

I have found those 1, 2, 3 links, but it seems that the topic of coercion is rather extensive and I don't know what to look for, as I don't know what the correct solution to the problem is.

Thank you for any response!