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