Implement pseudo-Conway polynomials

[pjbruin]

This patch implements pseudo-Conway polynomials, which are used to enable coercion between finite fields. This has been split off from #8335, and is a dependency of that ticket.

Apply: attachment: trac_14958-pseudo_conway_simplified.patch

Depends on #14833
Depends on #14957

CC: @roed314 @jpflori @sagetrac-mraum @fredstro @sagetrac-JCooley @loefflerd @sagetrac-dfesti

Component: finite rings

Keywords: Conway polynomial sd51

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

Reviewer: Jean-Pierre Flori, Peter Bruin

Merged: sage-5.13.beta0

Issue created by migration from https://trac.sagemath.org/ticket/14958

[pjbruin]

Changed dependencies from #14957 to #14833, #14957

[pjbruin]

comment:2

CC-ing the authors of #8335 and Sage Days 51 participants on this split-off ticket.

[pjbruin]

Description changed:

--- 
+++ 
@@ -2,3 +2,4 @@
 
 The attached patch passes most doctests, but not all, and has to be cleaned up a bit.
 
+Some of the changes from trac_8335-fixes-5.11.b3.patch will have to be applied here, several of them probably by hand.

[pjbruin]

Description changed:

--- 
+++ 
@@ -1,5 +1,2 @@
-This patch implements pseudo-Conway polynomials, which will be used later to enable coercion between finite fields.  This has been split off from #8335, and will be a dependency of that ticket.
+This patch implements pseudo-Conway polynomials, which will be used later to enable coercion between finite fields.  This has been split off from #8335, and is a dependency of that ticket.
 
-The attached patch passes most doctests, but not all, and has to be cleaned up a bit.
-
-Some of the changes from trac_8335-fixes-5.11.b3.patch will have to be applied here, several of them probably by hand.

[pjbruin]

comment:6

I rebased and updated the code written by David Roe and Jean-Pierre Flori.

One important question before me or someone else reviews this: why does this patch introduce objects that are called pseudo-Conway polynomial trees? This strongly suggests that the system of compatible finite fields that it represents forms a tree, which is definitely NOT the case. This is the whole reason why all of this work needs to be done to get such a system of finite fields!

[pjbruin]

comment:7

The last patch still needed some cleaning up; here is a new one.