#7644: generic power series reversion
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Reporter: was | Owner: AlexGhitza
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.3
Component: algebra | Keywords:
Work_issues: | Author:
Upstream: N/A | Reviewer:
Merged: |
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Comment(by fwclarke):
Lagrange inversion is significantly faster. With
{{{
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)*ps_coefficient(k, i - 1)*t^i
g += O(t^f.prec())
return g
}}}
I found
{{{
sage: R.<x> = QQ[[]]
sage: f = exp(x) - 1
sage: timeit('ps_inverse(f)')
5 loops, best of 3: 552 ms per loop
sage: timeit('ps_inverse_Lagrange(f)')
5 loops, best of 3: 74 ms per loop
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7644#comment:2>
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