#5306: [with patch, needs work] More number field ideal utilities
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Reporter: cremona | Owner: was
Type: enhancement | Status: new
Priority: major | Milestone: sage-3.4.2
Component: number theory | Keywords:
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Comment(by davidloeffler):
The patch applies cleanly to 3.4.1.rc1, and all tests in
sage/rings/number_field pass. However, there is a trivial little problem:
the documentation won't build -- Sphinx crashes on trying to read
number_field_ideal.py. The obvious suspect is the accented character in
Maite Aranes' name in the docstring for invertible_residues_mod_units. It
processes fine with the accent removed.
Also: a pedantic docstring issue -- for invertible_residues_mod_units, the
docstring says: "Returns an iterator through a list of invertible residues
modulo the integral ideal self and the list of units u." Firstly, I don't
think that's very clear -- there's a confusion between residue classes and
representatives for them. Secondly, does the list of units need to be a
subgroup? I suggest: "Returns an iterator through a set of representatives
for the units modulo the integral ideal self and the subgroup generated by
the list of units u".
Similarly I'm not very happy with the docstring for "reduce": from what it
says, one might expect to get back an element of some quotient ring
structure. It should probably say something closer to what the Pari
documentation says, i.e. something like "Given an element `f` of the
ambient number field, find an element `g` such that `f - g` belongs to the
(integral) ideal self, and `g` is small." I think that's a better
explanation of what it's actually doing, particularly since it isn't
generally the case that I.reduce(x) is one of the representatives returned
by I.residues() (if x is non-integral but coprime to I). It might even be
worth adding the remark that reduced representatives aren't necessarily
unique into the docstring.
These are only very small glitches, though; with these fixed I'd be happy
to give a positive review.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5306#comment:2>
Sage <http://sagemath.org/>
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