Zero does not belong to zero ideal of a number field

[sagetrac-olitb]

The following is mathematically wrong:

sage: 0 in CyclotomicField(3).ideal(0)
False

It comes from the function contains(self, x) in the class NumberFieldIdeal (file sage/rings/number_field/number_field_ideal.py), which tries to compute the coordinates of the element in a basis (over ZZ) of the ideal. The function coordinates(self, x) fails for the zero ideal, raising a TypeError (in fact when _contains_ is called directly, a TypeError is raised).
A workaround is to replace

def _contains_(self, x):
    return self.coordinates(self.number_field()(x)).denominator() == 1

with

def _contains_(self, x):
    return x==0 or self.coordinates(self.number_field()(x)).denominator() == 1

but I am not sure if it is the "right" way to do it.
Is it desirable to have the _contains_ function in sage/rings/ideal.py catch the TypeError (silently)?

Apply attachment: 14366_metrod3.patch​

Component: number fields

Keywords: sd51

Author: Michiel Kosters

Reviewer: David Loeffler

Merged: sage-5.12.beta3

Issue created by migration from https://trac.sagemath.org/ticket/14366

[rharron]

comment:1

It seems to me that there is generic code in sage/rings/ideal.py for __contains__ and this code shouldn't be touched. Basically, what it does is punts to the specific case's implementation of _contains_. I think the bug you point out means that for number field ideals, _contains_ is buggy. So, the type of fix you suggest I think makes sense. Though, rather than x == 0, it should probably be x == self.number_field().zero(), otherwise anything that is 0 will evaluate as True.

(I do wonder why the code for __contains__ in sage/rings/ideal.py doesn't just return True for the zero element).

[sagetrac-mkosters]

Attachment: trac_14366.patch.gz

[sagetrac-mkosters]

comment:4

Now with a commit message.

[saraedum]

comment:6

I just bumped into this bug myself. Wouldn't it make more sense to make coordinates() return an empty tuple instead? I believe this makes sense since 0 is in the zero-dimensional vector space.

[saraedum]

Changed keywords from none to sd51