#8283: A better Carmichael lambda function
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Reporter: wdj | Owner: mvngu
Type: defect | Status: new
Priority: minor | Milestone:
Component: cryptography | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Reported by ylchapuy:
Here is another implementation:
{{{
def carmichael_lambda(n):
n = Integer(n)
if n < 1:
raise ValueError("Input n must be a positive integer.")
F = n.factor()
L = []
# first get rid of the even part
if n & 1 == 0:
e = F[0][1]
F = F[1:]
if e < 3:
e = e-1
else:
e = e-2
L.append(1<<e)
# then other prime factors
L += [ p**(k-1)*(p-1) for p,k in F]
# finish the job
return lcm(L)
}}}
This is a bit faster than the current implementation and, if you replace
lcm with sage.rings.integer.LCM_list, it is even faster.
A bug with the current function is that the output is not always an
integer: e.g., carmichael_lambda(16) is of type
sage.rings.rational.Rational .
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8283>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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