#5306: [with new patch, needs review again] More number field ideal utilities
---------------------------+------------------------------------------------
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):
At risk of being really ridiculously pedantic: there's a typo in the new
docstring for invertible_residues_mod_units (and invertible_residues):
"represnting".
Also, as for our terminological confusion, I think that the whole thing
can be explained more clearly by *not* distinguishing between "units" and
"invertible residues". You're clearly thinking of taking the quotient of a
local unit group by the image of a subgroup of the global units; but the
function as coded here works perfectly well for finding any quotient of
the form (O_K / I)^* / U where U is an arbitrary subgroup of (O_K / I)^*.
E.g.
{{{
sage: K.<a> = NumberField(x - 1)
sage: I = K.ideal(5)
sage: list(I.invertible_residues_mod_units([4]))
[1, 2]
}}}
The fact that 4 isn't a unit in K is no problem. And this makes it easier
to avoid getting tied up in terminological knots: we can now just drop all
mention of "units", and call it "invertible_residues_mod", with the
docstring
"Returns an iterator through a set of representatives for the group of
invertible residues modulo this ideal, modulo the subgroup generated by
the elements in the list u."
I think I've tortured you (and Maite) enough now: I'll write a patch
myself for this change, and if you agree it's OK we'll call it a +ve
review.
(I'll also fix a micro-bug: the invertible_residues function ignores its
second argument -- it always calls invertible_residues_mod_units with
reduce = True.)
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5306#comment:7>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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