#15348: "R.<a> =" syntactic sugar incorrect for EquationOrder and ZZ.extension
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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 | e857c9a484132348092e21cd1de0711686b8b7f0
Dependencies: | Stopgaps:
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Comment (by emassop):
Replying to [comment:20 jdemeyer]:
> Replying to [comment:19 emassop]:
> > Perhaps there could be `defining_generators.set(...)` that would
> > * populate the cache if it has no value,
> > * do nothing if the cache and the argument agree,
> > * populate the cache with an invalid value when the argument and the
cache disagree.
> > The invalid value would make a call to `defining_generators` raise an
exception.
> I see no reason for this additional layer of complexity. I don't know of
any cached function in Sage which does this and I don't see why
`defining_generators` would need it.
It seems weird if the return value of `.defining_generators` changes
during an object's life. If the value gets set only once during an
object's life-time (and survives pickling), then not having this
additional complexity is okay. The proposal above is merely to enforce
that the value does not get changed accidentally.
> > Finally, does it make sense to define `defining_generators` in
`category_object.pyx` as simply `gens()`, and put the override to
`ring_generators` in `class Order`?
> I don't really see why. Currently, `Order` is the only class with
`ring_generators` but if a new class comes around implementing
`ring_generators`, I guess (but this is really guessing) that it would
make sense to use it as defining generators.
So all other rings with generators use `gens()` for their ring generators?
Why is `Order` different, especially given that there also is `basis()`?
For instance
{{{
R.<i> = ZZ.extension(x^2+1)
S.<x> = QQ[]
A.<a> = QQ.extension(x^2-3)
B.<b> = ZZ.extension(x^2-3)
C.<c> = R.extension(x^2-3)
D.<d> = S.extension(x^2-3)
print A.gens(), B.gens(), C.gens(), D.gens()
}}}
prints `(a,) [1, b] (c,) (d,)` with B.gens() being the odd one out.
--
Ticket URL: <http://trac.sagemath.org/ticket/15348#comment:22>
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