#9332: S_class_group() should return a group
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Reporter: stankewicz | Owner:
davidloeffler
Type: enhancement | Status:
needs_work
Priority: major | Milestone:
Component: number fields | Keywords:
Author: Jim Stankewicz, Erin Beyerstedt, Anna Haensch | Upstream:
N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by davidloeffler):
The AttributeError comes up because attributes whose names start with an
underscore are private, and ones with two underscores are "very private"
-- so private that they aren't even accessible to subclasses. So when code
in {{{FractionalIdealClass}}} sets {{{__ideal}}}, code in the subclass
{{{SFractionalIdealClass}}}. In fact it is still accessible but under a
mangled name: see [http://docs.python.org/tutorial/classes.html#private-
variables].
But there is another, deeper, bug which will be uncovered when you fix
this. After my changes at #9244, a {{{FractionalIdealClass}}} stores both
a representing ideal of that class, accessed via {{{self.ideal()}}}, and
an expression for self in terms of the generators of its parent class
group, accessed via {{{self.list()}}}. The way you've set this up,
elements of an S-class group use the same data structure, but the data
which {{{list()}}} uses is set completely wrongly: it's set to the
exponents of the given ideal in terms of the generators of the class
group, but it should be in terms of the generators of the **S-class
group**. What you need to do is to store somewhere the expressions for the
generators of the S-class group in terms of the generators of the class
group (i.e. the matrix of the quotient map) and then multiply the output
of {{{_ideal_class_log}}} by this.
This is the sort of stuff that #6449 was intended to solve: quotients of
abelian groups should be automatically handled by general code, rather
than having to do it by hand in every specific example.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9332#comment:9>
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