DeRhamComputation/auxilliaries/reverse.sage

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2022-11-18 15:00:34 +01:00
# Given power_series, find its reverse (g with g \circ power_series = id) with given precision
def new_reverse(power_series, prec = 10):
F = power_series.parent().base()
Rt.<t> = LaurentSeriesRing(F, default_prec=prec)
RtQ = FractionField(Rt)
power_series = RtQ(power_series)
a = power_series.list()[0]
g = 1/a*t
n = 2
while(n <= prec):
aux = power_series(t = g) - t
if aux.valuation() > n:
b = 0
else:
b = aux.list()[0]
g = g - b/a*t^n
n += 1
return g