15.1 Univariate Power Series Rings

Module: sage.rings.power_series_ring

sage: R.<t> = PowerSeriesRing(RationalField())
sage: R.random_element(6)
-t - t^2 - t^3 - t^4 + O(t^6)

sage: S = R([1, 3, 5, 7], 10); S
1 + 3*t + 5*t^2 + 7*t^3 + O(t^10)

sage: S.truncate(3)
5*t^2 + 3*t + 1

Author Log:

Module-level Functions

PowerSeriesRing( base_ring, [name=20], [default_prec=None])

is_PowerSeriesRing( x)

Class: PowerSeriesRing_domain

class PowerSeriesRing_domain
PowerSeriesRing_domain( self, base_ring, [name=20], [default_prec=None])

Class: PowerSeriesRing_generic

class PowerSeriesRing_generic
PowerSeriesRing_generic( self, base_ring, [name=20], [default_prec=None])

Functions: assign_names,$  $ base_ring,$  $ characteristic,$  $ gen,$  $ is_atomic_repr,$  $ is_field,$  $ is_finite,$  $ laurent_series_ring,$  $ ngens,$  $ random_element

laurent_series_ring( self)

If this is the power series ring R[[t]], return the Laurent series ring R((t)).

random_element( self, prec, [bound=0])

Return a random power series.

INPUT:
    prec -- an int
    bound -- an int (default: 0, which tries to spread choice across ring,
if implemented)

OUTPUT:
    Polynomial -- A polynomial such that the coefficient of x^i,
    for i up to degree, are coercisions to the base ring of
    random integers between -bound and bound.

Special Functions: __call__,$  $ __cmp__,$  $ __contains__,$  $ __repr__,$  $ _is_valid_homomorphism_,$  $ _latex_,$  $ _poly_ring

Class: PowerSeriesRing_over_field

class PowerSeriesRing_over_field
PowerSeriesRing_over_field( self, base_ring, [name=20], [default_prec=None])

Functions: fraction_field

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