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
...
derivative,
integral,
prec
These methods are defined as follows:
) |
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()).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()).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.
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