4.10.2.2 PowerSeries_generic_dense Objects

class PowerSeries_generic_dense
PowerSeries_generic_dense( parent, [f=False], [prec=True], [check=Infinity], [is_gen=0])

Instances of class PowerSeries_generic_dense have the following methods (in addition to inherited methods and special methods):

integral,$  $ reversion

These methods are defined as follows:

integral( )

The integral of this power series with 0 constant term.

reversion( )

Return the reversion of f, i.e., the series g such that g(f(x)) = x.

sage: x = PowerSeriesRing(RationalField()).gen()
sage: f = 2*x + 3*x^2 - x^4 + O(x^5)
sage: g = f.reversion()
sage: g
1/2*t - 3/8*t^2 + 9/16*t^3 - 131/128*t^4 + O(t^5)
sage: f(g)
t + O(t^5)
sage: g(f)
t + O(t^5)

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