Transform a continued fraction representation into a real : dfc2f

### 2.8.8 Transform a continued fraction representation into a real : `dfc2f`

`dfc2f` takes as argument a list, a continued fraction representation

- a list of integers for a rational number
- a list whose last element is a list for an ultimately periodic representation, i.e. a quadratic number, that is a root of a second order equation with integer coefficients.
- or a list with a remainder r as last element (a=a0+1/....+1/an+1/r).

`dfc2f` returns the rational number or the quadratic number with the argument as continued fraction representation.
Input :

`dfc2f([1,2,[2]])`

Output :

`1/(1/(1+sqrt(2))+2)+1`

After simplification with `normal` :

`sqrt(2)`

Input :

`dfc2f([1,2,3])`

Output :

`10/7`

Input :

`normal(dfc2f([3,3,6,[3,6]]))`

Output :

`sqrt(11)`

Input :

`dfc2f([1,2,3,4,5,6,7])`

Output :

`9976/6961`

Input to verify :
`1+1/(2+1/(3+1/(4+1/(5+1/(6+1/7)))))`
Output :
`9976/6961`
Input :

`dfc2f([1,2,3,4,5,43/7])`

Output :

`9976/6961`

Input to verify :
`1+1/(2+1/(3+1/(4+1/(5+7/43))))`
Output :
`9976/6961`