#15348: "R.<a> =" syntactic sugar incorrect for EquationOrder
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Reporter: emassop | Owner:
Type: defect | Status: needs_review
Priority: major | Milestone: sage-7.0
Component: number fields | Resolution:
Keywords: | Merged in:
Authors: Jeroen Demeyer | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/jdemeyer/ticket/15348 | 496f5ac31807f7613aaddbef6dd8119e33ca4366
Dependencies: | Stopgaps:
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Comment (by emassop):
Replying to [comment:33 jdemeyer]:
> I now changed `_defining_generators()` to use the number field gens
instead. This fixes the case of relative extensions.
Disregarding the change to `gen_dict()`, this makes sense to me. I would
on first sight argue that `defining_generators` should not be defined for
an order that has not been defined by generators, but since this is a
private method used only by `R.<...>` (disregarding `gen_dict`), which
moreover throws an exception if the elements are not in the order, I think
it's fine here.
Taking `gen_dict()` back into the picture, I'm not so happy with its
elements not necessarily generating the order anymore (as a module, or as
a ring), as there is nothing in the name `gen_dict` that suggests this
would not be the case. For instance
{{{
K.<a> = QuadraticField(-163)
R = K.ring_of_integers()
dict_gens_values = [R(x) for x in K.gens()]
S = K.order(dict_gens_values)
print S.index_in(R)
}}}
prints 2 instead of the expected 1.
Tangentially, `NumberField.ring_of_integers` should pass its arguments to
`self.maximal_order`, in the same way that `NumberField.OK` does. (For the
deprecation policy, this is probably not currently feasible, but we can
deprecate non-empty arguments.) As a side-effect, this prohibits the
syntax `R.<w> = K.ring_of_integers()`, in the same that `R.<w> =
K.order(...)` is prohibited (which made one of my earlier points moot).
This also makes the following impossible, where `w` does not become the
expected generator:
{{{
K.<a> = QuadraticField(-163)
R.<w> = K.ring_of_integers()
w = a # Since I'm not running the version with the patch.
print K.order(w).index_in(R) # R.<w> suggests this prints 1, but it
actually prints 2.
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/15348#comment:34>
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