LaurentSeriesRing(base_ring,
name=['4ti2-20061025', 'R-2.6.0', 'atlas-3.7.37', 'atlas-3.8.1', 'a...,
names=['4ti2-20061025', 'R-2.6.0', 'atlas-3.7.37', 'atlas-3.8.1', 'a...,
sparse=False)
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EXAMPLES:
sage: R = LaurentSeriesRing(QQ, 'x'); R
Laurent Series Ring in x over Rational Field
sage: x = R.0
sage: g = 1 - x + x^2 - x^4 +O(x^8); g
1 - x + x^2 - x^4 + O(x^8)
sage: g = 10*x^(-3) + 2006 - 19*x + x^2 - x^4 +O(x^8); g
10*x^-3 + 2006 - 19*x + x^2 - x^4 + O(x^8)
You can also use more mathematical notation when the base is a field:
sage: Frac(QQ[['x']])
Laurent Series Ring in x over Rational Field
sage: Frac(GF(5)['y'])
Fraction Field of Univariate Polynomial Ring in y over Finite Field of size 5
Here the fraction field is not just the Laurent series ring, so you can't
use the \code{Frac} notation to make the Laurent series ring.
sage: Frac(ZZ[['t']])
Fraction Field of Power Series Ring in t over Integer Ring
Laurent series rings are determined by their variable and the base ring,
and are globally unique.
sage: K = Qp(5, prec = 5)
sage: L = Qp(5, prec = 200)
sage: R.<x> = LaurentSeriesRing(K)
sage: S.<y> = LaurentSeriesRing(L)
sage: R is S
False
sage: T.<y> = LaurentSeriesRing(Qp(5,prec=200))
sage: S is T
True
sage: W.<y> = LaurentSeriesRing(Qp(5,prec=199))
sage: W is T
False
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