"divides" in ring of integers

John Bamberg
1 ●1 ●1

5251 ●3 ●44 ●116

It seems the method for "divides" is inherited to a ring_of_integers, but has undesirable behaviour:

f = CyclotomicField(3)
r = f.ring_of_integers()
gens = r.gens()
x = 1 + gens[1]
r(x).divides(r(gens[1]))

returns "True". Have I overlooked something here?

1 Answer

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Luca
890 ●6 ●21

With your input,

( r(gens[1]) / r(x) ).is_integral()

returns True. So, no, I see no problem here. However

sage: f = CyclotomicField(3)
sage: r.<z> = f.ring_of_integers()
sage: r(2).divides(z)
True
sage: (z/2).is_integral()
False

which is fishy.

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Asked: 2014-07-20 11:57:57 +0100

Seen: 412 times

Last updated: Jul 20 '14