Module: sage.rings.laurent_series_ring
Module-level Functions
base_ring, [name=None]) |
sage: R = LaurentSeriesRing(Q, '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(Q[['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 Frac
notation to make the Laurent series ring.
sage: Frac(Z[['t']]) Fraction Field of Power Series Ring in t over Integer Ring
x) |
Class: LaurentSeriesRing_domain
self, base_ring, [name=None]) |
Functions: fraction_field
Class: LaurentSeriesRing_field
self, base_ring, [name=None]) |
Class: LaurentSeriesRing_generic
sage: K, q = LaurentSeriesRing(C, 'q').objgen(); K Laurent Series Ring in q over Complex Field with 53 bits of precision sage: loads(K.dumps()) == K True
self, base_ring, [name=None]) |
Functions: base_ring,
characteristic,
default_prec,
gen,
ngens,
power_series_ring,
set_default_prec
self) |
sage: R = LaurentSeriesRing(QQ, "x") sage: R.base_ring() Rational Field sage: S = LaurentSeriesRing(GF(17)['x'], 'y') sage: S Laurent Series Ring in y over Univariate Polynomial Ring in x over Finite Field of size 17 sage: S.base_ring() Univariate Polynomial Ring in x over Finite Field of size 17
self) |
If this is the Laurent series ring
, return the power
series ring
.
sage: R = LaurentSeriesRing(QQ, "x") sage: R.power_series_ring() Power Series Ring in x over Rational Field
Special Functions: __call__,
__cmp__,
__reduce__,
__repr__,
_is_valid_homomorphism_