Lazy laurent series

[klee]

Introduce lazy laurent series to Sage.

A lazy laurent series computes coefficients only when demanded or needed. In a sense, lazy laurent series are laurent series of infinite precision.

A generating function example from the code:

Generating functions are laurent series over the integer ring::

    sage: from sage.rings.lazy_laurent_series_ring import LazyLaurentSeriesRing
    sage: L = LazyLaurentSeriesRing(ZZ, 'z')

This defines the generating function of Fibonacci sequence::

    sage: def coeff(s, i):
    ....:     if i in [0, 1]:
    ....:         return 1
    ....:     else:
    ....:         return s.coefficient(i - 1) + s.coefficient(i - 2)
    ....:
    sage: f = L.series(coeff, valuation=0); f
    1 + z + 2*z^2 + 3*z^3 + 5*z^4 + 8*z^5 + 13*z^6 + ...

The 100th element of Fibonacci sequence can be obtained from the generating
function::

    sage: f.coefficient(100)
    573147844013817084101 

Lazy laurent series is of course useful for other things. This will be used to implement infinite precision laurent series expansion of algebraic functions in function fields, as a sequel to #27418.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​5d24a34

Introduce lazy laurent series

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​ace4282

pyflakes fixes

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​389798e

Add series method

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​43ba785

Small fixes on docstrings