Bill Allombert on Fri, 05 Aug 2005 14:28:15 +0200

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contfrac for power series

Hello PARI-dev,

I would like to extend contfrac (and bestappr and algdep) to
handle approximation of rational and algebraic functions
by power series.

However there is a semantic mismatch:

Theses functions handle rational functions according to the
topology defined by the degree (X^-n go to 0), while we can
only handle power series according to the valuation (X^n go to
0). This means we have to do subst(truncate(S),x,1/x) to convert
meaningfully power series to rational functions.

For example the meaningful result for 
contfrac(1/x+2*x+O(x^2)) should be [1/x,1/(2*x)]
but contfrac returns [2*x,x] because it truncate the