parent, f, [n=0]) |
Create the Laurent series
. The default is n=0.
INPUT: parent -- a Laurent series ring f -- a power series (or something can be coerced to one) n -- integer (default 0) OUTPUT: a Laurent series
...
add_bigoh,
copy,
degree,
derivative,
integral,
is_zero,
power_series,
prec,
unit_part,
valuation,
variable
Further documentation:
) |
The derivative of this Laurent series.
) |
The integral of this Laurent series with 0 constant term.
The integral may or may not be defined if the base ring is not a field.
sage: t = LaurentSeriesRing(IntegerRing(), 't').gen() sage: f = 2*t**-3 + 3*t**2 + O(t**4) sage: f.integral() -t^-2 + t^3 + O(t^5)
sage: f = t**3 sage: f.integral() Traceback (most recent call last): ... ArithmeticError: Coefficients of integral of t^3 cannot be coerced into the base ring
The integral of 1/t is
, which is not given by a Laurent series:
sage: t = LaurentSeriesRing(RationalField(), 't').gen() sage: f = -1/t**3 - 31/t + O(t**3) sage: f.integral() Traceback (most recent call last): ... ArithmeticError: The integral of -t^-3 - 31*t^-1 + O(t^3) is not a Laurent series, since t^-1 has nonzero coefficient -31.
) |
This function returns the n so that the Laurent series is
of the form (stuff) +
. It doesn't matter how many
negative powers appear in the expansion. In particular,
prec could be negative.
Instances of class LaurentSeries also have the following special methods:
__add__,
__call__,
__cmp__,
__div__,
__getitem__,
__mul__,
__neg__,
__pow__,
__repr__,
__setitem__,
__sub__,
_latex_,
_LaurentSeries__normalize
Further documentation:
) |
A Laurent series is a pair (u(t), n), where either u=0 (to
some precision) or u is a unit. This pair corresponds to
.
See About this document... for information on suggesting changes.