#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 cremona):
On invertible_residues_mod_units() it is not easy to explain what this is:
Let R be the ring of integers and I the ideal (self). When there are no
units given we iterate through {{{(R/I)^*}}}. When there are units which
generate some subgroup U of the unit group {{{R^*}}} (which in our
applications will always be all of {{{R^*}}}) we want to iterate through
elements of R representing the elements of {{{(R/I)^*/U_I}}}, where U_I is
the image of U in {{{(R/I)^*}}}.
Believe me, we need this for enumeration of cusps over number fields for
the subgroup Gamma_0(n) where n is an ideal in GL(2,R)!. Now I need to
find a way of writing that succinctly in a docstring. [The special case
where U is [] will be of most use to most people, so we could provide a
clear indication of how to use that.]
On reduce: I'll need to check whether the element being reduced also
needs to be integral (I suspect so) and adapt the docstring if so.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5306#comment:5>
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