Some code for Lagrange inversion has been posted on the "generic power
series reversion" trac ticket: http://trac.sagemath.org/sage_trac/ticket/7644
The code doesn't quite run, since it references some other function
(ps_coefficient); here's an updated version which uses only built-in
functions:
def ps_inverse_Lagrange(f):
if f.valuation() != 1:
raise ValueError, "series must have valuation one for
reversion"
if f.prec() is infinity:
raise ValueError, "series must have finite precision for
reversion"
t = parent(f).gen()
h = t/f
k = 1
g = 0
for i in range(1, f.prec()):
k *= h
g += (1/i)*k.padded_list(i)[i - 1]*t^i
g += O(t^f.prec())
return g
On Dec 9, 3:20 pm, William Stein <wst...@gmail.com> wrote:
> On Wed, Dec 9, 2009 at 10:50 AM, Matt Bainbridge
>
> <bainbridge.m...@gmail.com> wrote:
> > Its easy enough to code this in sage. This seems to work over any
> > field:
>
> Thanks. This is now http://trac.sagemath.org/sage_trac/ticket/7644
>
>
>
>
>
> > def ps_inverse(f):
> > if f.prec() is infinity:
> > raise ValueError, "series must have finite precision for
> > reversion"
> > if f.valuation() != 1:
> > raise ValueError, "series must have valuation one for
> > reversion"
> > t = parent(f).gen()
> > a = 1/f.coefficients()[0]
> > g = a*t
> > for i in range(2, f.prec()):
> > g -= ps_coefficient((f + O(t^(i+1)))(g),i)*a*t^i
> > g += O(t^f.prec())
> > return g
>
> > def ps_coefficient(f,i):
> > if i >= f.prec():
> > raise ValueError, "that coefficient is undefined"
> > else:
> > return f.padded_list(f.prec())[i]
>
> > --
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>
> --
> William Stein
> Associate Professor of Mathematics
> University of Washingtonhttp://wstein.org
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