Its easy enough to code this in sage. This seems to work over any
field:
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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