#7931: Improved nth root for finite fields and integer_mods
-------------------------------+--------------------------------------------
Reporter: roed | Owner: roed
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-4.6
Component: algebra | Keywords: finite fields, nth root
Author: David Roe | Upstream: N/A
Reviewer: Paul Zimmermann | Merged:
Work_issues: |
-------------------------------+--------------------------------------------
Changes (by zimmerma):
* status: needs_review => needs_work
Comment:
sorry, another problem:
{{{
sage: n=13777831336991389951
sage: b=3798677550250515336
sage: e=10608321776141318019
sage: K = Integers(n)
sage: b=K(b)
sage: b.nth_root(e)
---------------------------------------------------------------------------
ZeroDivisionError Traceback (most recent call
last)
}}}
The documentation does not say when {{{ZeroDivisionError}}} can be
obtained.
This was found with the following program:
{{{
while True:
n = randint(0,2^64)
K = Integers(n)
b = K.random_element()
e = randint(0,2^64)
print n, b, e, a
sys.stdout.flush()
try:
a = b.nth_root(e)
if a^e <> b:
print n, b, e, a
raise NotImplementedError
except ValueError:
n = 0
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7931#comment:28>
Sage <http://www.sagemath.org>
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