Module laurent_series_ring_element

File: sage/rings/laurent_series_ring_element.pyx (starting at line 1)

Laurent Series

EXAMPLES:

    sage: R.<t> = LaurentSeriesRing(GF(7), 't'); R
    Laurent Series Ring in t over Finite Field of size 7
    sage: f = 1/(1-t+O(t^10)); f
    1 + t + t^2 + t^3 + t^4 + t^5 + t^6 + t^7 + t^8 + t^9 + O(t^10)

Laurent series are immutable:
    sage: f[2]
    1
    sage: f[2] = 5
    Traceback (most recent call last):
    ...
    IndexError: Laurent series are immutable    

We compute with a Laurent series over the complex mpfr numbers. 
    sage: K.<q> = Frac(CC[['q']])
    sage: K
    Laurent Series Ring in q over Complex Field with 53 bits of precision
    sage: q
    1.00000000000000*q

Saving and loading.
    sage: loads(q.dumps()) == q
    True
    sage: loads(K.dumps()) == K
    True

IMPLEMENTATION: Laurent series in SAGE are represented internally as a
    power of the variable times the unit part (which need not be a
    unit -- it's a polynomial with nonzero constant term).  The zero
    Laurent series has unit part 0.


AUTHORS:
    -- William Stein: original version
    -- David Joyner: added examples 2006-01-22
    -- Robert Bradshaw: optimizations, shifting 2007-04
    -- Robert Bradshaw: SageX version