#13214: Finite field homomorphisms and Frobenius endomorphisms
-------------------------------------+-------------------------------------
Reporter: caruso | Owner: AlexGhitza
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.11
Component: finite rings | Resolution:
Keywords: frobenius finite | Merged in:
fields sd51 | Reviewers: Paul Zimmermann,
Authors: Xavier Caruso, | Peter Bruin
Peter Bruin | Work issues:
Report Upstream: N/A | Commit:
Branch: | Stopgaps:
Dependencies: #8335 |
-------------------------------------+-------------------------------------
Changes (by {'newvalue': u'Xavier Caruso, Peter Bruin', 'oldvalue': u'Xavier
Caruso'}):
* author: Xavier Caruso => Xavier Caruso, Peter Bruin
* cc: JCooley, dfesti (added)
* component: basic arithmetic => finite rings
* dependencies: #13184 => #8335
* reviewer: Paul Zimmermann => Paul Zimmermann, Peter Bruin
Old description:
> Here is a patch implementing:
>
> 1. Frobenius endomorphisms over finite fields (generic implementation,
> plus special implementations for prime finite fields and givaro finite
> fields)
> 1. embeddings between finite fields (with again a special implementation
> for givaro finite fields)
> 1. hashing and rich comparisons for general morphisms
>
> ----
> Apply: [attachment:trac_13214_hom_finite_field.patch]
New description:
Here is a patch implementing:
1. Frobenius endomorphisms over finite fields (generic implementation,
plus special implementations for prime finite fields and givaro finite
fields)
1. embeddings between finite fields (with again a special implementation
for givaro finite fields)
1. hashing and rich comparisons for general morphisms
----
Apply: [attachment:trac_13214_hom_finite_field.patch],
[attachment:trac_13214-reviewer.patch]
--
Comment:
In principle I am giving this a positive review, but since the reviewer
patch I just uploaded contains some non-trivial changes, I think it is
best if someone else reviews those changes first.
Summary of changes in [attachment:trac_13214-reviewer.patch]:
- Do not add `inverse()` method to `Section`; it is currently not used and
does not seem to be the best name, since its return value (the original
map) is only a one-sided inverse.
- Add method `gens()` to `CombinatorialFreeModule` to fix a doctest
failure in `modules_with_basis.py`. I guess this is the same failure
discussed in comment:14 above.
- Rename `[Section]FiniteFieldEmbedding_*` to
`[Section]FiniteFieldHomomorphism_*`; even though finite field
homomorphisms are automatically injective, I think "homomorphism" fits
better with existing code. Furthermore, to me "embedding" makes it sound
too much like finite field homomorphisms are canonical.
- Derive `FiniteFieldHomomorphism_generic` from `RingHomomorphism_im_gens`
as suggested above.
- Replace the existing `FiniteFieldHomomorphism_im_gens` by the new
`FiniteFieldHomomorphism_generic`.
- Better integration of the new code into the existing finite field code.
- Remove the `_repr_()` method of `FiniteFieldHomomorphism_generic`, so
that the output is the same as for the old
`FiniteFieldHomomorphism_im_gens`.
- Do not automatically generate a section for every finite field
homomorphism.
- Numerous whitespace edits and some other typographical changes.
--
Ticket URL: <http://trac.sagemath.org/ticket/13214#comment:34>
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