Changes between Version 2 and Version 3 of Ticket #14567, comment 34


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Timestamp:
03/03/14 21:45:43 (6 years ago)
Author:
rws
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  • Ticket #14567, comment 34

    v2 v3  
    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.