#14990: Implement algebraic closures of finite fields
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Reporter: pbruin | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.2
Component: algebra | Resolution:
Keywords: finite field | Merged in:
algebraic closure | Reviewers:
Authors: Peter Bruin | Work issues:
Report Upstream: N/A | Commit:
Branch: u/pbruin/14990 | f9162dbae92551a67aea7a489d96591141fdebc8
Dependencies: #14958, #13214 | Stopgaps:
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Comment (by pbruin):
Hi Vincent,
> 2) It makes sense to have something more flexible like
> {{{
> sage: AC = AlgebraicClosureFiniteField_pseudo_conway
> sage: AC(GF(3), lattice=my_pc_lattice)
> }}}
> where "my_pc_lattice" is an instance of a subclass or
`PseudoConwayLattice` or something with the same specifications (i.e. at
least a method `polynomial`). That way we can already have two
implementations of the algebraic closure (calling `PseudoConwayLattice`
with the option `use_database=True` or `use_database=False`).
This is implemented in one of the two new commits; one can now pass a
`lattice` argument, and the `use_database` flag is now accepted here as
well.
> 3) In the example above, there is some redundancy as the pseudo-Conway
lattice already knows the finite field... so it would be nice if the
pseudo-Conway lattice implements a method `base_ring` that returns the
finite field it is based on.
It already has a public attribute `p` for the characteristic; since the
PCL is not really meant to be used directly anyway, I think it is
redundant to also add a `base_ring()` method.
> 4) It would also make sense in `PseudoConwayLattice` to have a method
`associated_finite_field_algebraic_closure` (with a better name if
possible).
I agree with Jean-Pierre here; this doesn't seem to be useful. To
compare, we don't have (and don't need) a method
`associated_finite_field()` for polynomials over '''F''',,''p'',, either.
--
Ticket URL: <http://trac.sagemath.org/ticket/14990#comment:71>
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