Finite field lattices via Conway polynomials

[roed314]

Implements coercion within lattices of finite fields lying above the same prime when implemented with Conway polynomials.

sage: k = GF(9, conway=True, prefix='z')
sage: l = GF(27, conway=True, prefix='z')
sage: x = k.gen() + l.gen(); x
z6^5 + 2*z6^4 + 2*z6^3 + z6^2 + 2*z6 + 1
sage: x.parent()
Finite Field in z6 of size 3^6

When using the conway and prefix parameters, one does not need to specify an explicit variable name; if no variable name is given, it is constructed from the prefix and the degree (as in the above code snippet).

In the future, the functionality of this ticket will be incorporated into that for algebraic closures of finite fields. It will then be possible to construct compatible systems of finite fields outside the range of the Conway polynomial database using the pseudo-Conway polynomials from #14958: polynomials that satisfy all of the algebraic constraints on Conway polynomials without the lexicographic constraint that imposes uniqueness.

Apply:

• attachment: trac_8335-finite_field_coerce-5.11.b3-14888.patch
• attachment: trac_8335-no_pseudo.patch

Depends on #14958
Depends on #12142

CC: @defeo @rbeezer @sagetrac-hds @simon-king-jena @zimmermann6 @xcaruso @pjbruin @sagetrac-mraum @fredstro @sagetrac-JCooley @loefflerd @sagetrac-dfesti

Component: algebra

Keywords: days49 sd51

Author: David Roe, Jean-Pierre Flori, Peter Bruin

Reviewer: Jean-Pierre Flori, Luca De Feo

Merged: sage-5.13.beta1

Issue created by migration from https://trac.sagemath.org/ticket/8335

[roed314]

comment:2

Part of a series:

8218 -> 8332 -> 7880 -> 7883 -> 8333 -> 8334 -> 8335

I tried to make each of these mostly self contained, with doctests passing after every ticket, but I didn't entirely succeed. If you're reviewing one of these tickets, applying later tickets will hopefully fix doctest failures that you're seeing.

[roed314]

Includes everything in 8218, 8332, 7880, 7883, 8333, 8334 and 8335 except the 8218 bundle, which you must apply first.

[roed314]

comment:4

Attachment: finite_field_coerce_ALL.patch.gz

For convenience, I added a giant patch which includes all the changes except the bundle at 8218 (which we want to leave as a bundle in order to preserve file history).

[loefflerd]

comment:6

This doesn't apply cleanly: the patch 8335_pseudo_conway.patch seems to conflict with something. FWIW, I am using 4.4.alpha0 with qseries

trac_8446.patch
trac_8446_microfix.patch
trac_8722.patch
7883_ideals.patch
8333_parent_init.patch
8333_finite_fields_to_new_coercion.patch
7585_9_1_frac_and_coerce_updates.patch
8334_residue_fields-rebased_for_8446.patch
7585_12_1_fixes.patch
8335_pseudo_conway.patch

[roed314]

Attachment: 8335_pseudo_conway.patch.gz

Apply first

[roed314]

comment:8

To work against 4.7, apply 8335_pseudo_conway.patch then 8335_finite_field_coerce_vs_47.patch.

[roed314]

Apply second

[roed314]

Attachment: 8335_finite_field_coerce.patch.gz

Against 4.7 for patchbot

[roed314]

comment:9

Attachment: 8335_finite_field_coerce_vs_47.patch.gz

To work against 4.7, apply 8335_pseudo_conway.patch then 8335_finite_field_coerce_vs_47.patch.

[roed314]

comment:10

Apply 8335_pseudo_conway.patch, 8335_finite_field_coerce_vs_47.patch

[defeo]

comment:11

I still get the following failures on 4.7.1.alpha4 with 8335_pseudo_conway.patch and 8335_finite_field_coerce_vs_47.patch applied:

	sage -t -long devel/sage/sage/matrix/matrix2.pyx # 2 doctests failed
	sage -t -long devel/sage/sage/rings/finite_rings/constructor.py # 1 doctests failed

[defeo]

comment:12

I also get 7 warnings when building the docs. These all seem to be missing blank lines and unmatched backquoutes in sage/rings/finite_rings/constructor.py

[jpflori]

Attachment: trac_8335-pseudo_conway-5.7.b3.patch.gz

Patch for PCP; rebased on top of 5.7.beta3.

[jpflori]

Attachment: trac_8335-finite_field_coerce-5.7.b3.patch.gz

Patch for coercion; rebased on top of 5.7.beta3.

[pjbruin]

Changed work issues from store ref to PCL in finite field (or implement another way of weak caching) to none

[pjbruin]

comment:113

For patchbot:

apply trac_8335-finite_field_coerce-5.11.b3-14888.patch​, trac_8335-no_pseudo.patch​ 

Note: attachment: trac_8335-rebase_14958.patch​ is not needed if we go for this approach.

[jpflori]

comment:114

Looks ok.
Still depending on #14958 as functions related to (non-pseudo) Conway polys were moved around there.

[jdemeyer]

Merged: sage-5.13.beta1