15698: Allow construction of power series from fractions

delegating conversion type check to numerator/denominator construction
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do not abbreviate 3.99999... to 3.99 with # abs tol 1e-2
Trac #15799: floating point tolerance in gsl fft doctest

The difference between 4.0=3.9999... and 3.99 is 1e-2, so if you doctest
that with # abs tol 1e-2 then you are numerically unstable.
{{{
sage -t --long src/sage/gsl/fft.pyx
**********************************************************************
File "src/sage/gsl/fft.pyx", line 61, in
sage.gsl.fft.FastFourierTransform
Failed example:
    a                       #abs tol 1e-2
Expected:
    [(36.0, 0.0), (-4.00, 9.65), (-4.0, 4.0), (-3.99, 1.65), (-4.0,
0.0), (-4.0, -1.65), (-4.0, -4.0), (-3.99, -9.65)]
Got:
    [(36.0, 0.0), (-4.0, 9.65685424949238), (-4.000000000000001,
3.9999999999999996), (-4.000000000000001, 1.6568542494923795), (-4.0,
0.0), (-3.9999999999999996, -1.6568542494923801), (-3.9999999999999996,
-3.9999999999999996), (-3.9999999999999982, -9.65685424949238)]
Tolerance exceeded in 1 of 16
    -3.99 vs -4.000000000000001
}}}

URL: http://trac.sagemath.org/15799
Reported by: vbraun
Ticket author(s): Volker Braun
Reviewer(s): Marc Mezzarobba
Trac #15698: conversion from polynomial fraction to its power series expansion

Original description was:

The following behaviour is not implemented, example:
{{{
  sage: R.<t> = QQ[]; A=1/(1-t)
  sage: A.expand(5)
  1+t+t^2+t^3+t^4+t^5+O(t^6)
  sage: A+O(t^6)
  1+t+t^2+t^3+t^4+t^5+O(t^6)
}}}
Add a parameter to specify the respective series variable (for
derivation) then multivariate polynomial fractions can be handled.
Result type being a power series. The pari function Ser() implements the
same behaviour. Note: I would like to implement this.

URL: http://trac.sagemath.org/15698
Reported by: rws
Ticket author(s): Ralf Stephan
Reviewer(s): Marc Mezzarobba