| 1 | | As to a unification, the coefficients could be viewed as a sequence generated by a rational ordinary generating function p(x)/q(x) (C-finite sequence, see #15714) where: |
| 2 | | * q(x)=1 for rational contfracs (=finite sequence) |
| 3 | | * q(x)=1-x^d^ with d the contfrac period for quad. irrationals (=infinite sequence) |
| 4 | | * other p/q, e.g. (2+x+2x^2^-3x^3^-x^4^+x^6^)/(1-2x^3^+x^6^) for e. Of course, absent a theory these must be guessed but that code exists already. |
| 5 | | * would make e+sqrt(2) exact |
| 6 | | |
| 7 | | Arithmetic with p/q is obvious, only back-conversion to non-rational looks impossible at the moment to me. |
