Added some functionality to ideals

[robertwb]

Added some functionality to ideals (is_maximal works more often now, and there's a new ideal class for univariate polynomial rings). Changed the logic on what class is chosen for ideals so that it's easier to override with ideal_class. Number of generators?

Prerequisite for #8333, #8334, #8335, #9887.

CC: @roed314

Component: commutative algebra

Keywords: ideals

Author: David Roe

Reviewer: Robert Bradshaw, David Loeffler

Merged: sage-4.6.alpha2

Issue created by migration from https://trac.sagemath.org/ticket/7883

[robertwb]

Description changed:

--- 
+++ 
@@ -1,2 +1 @@
-Added some functionality to ideals (is_maximal works more often now, and there's a new ideal class for univariate polynomial rings).  Changed the logic on what class is chosen for ideals so that it's easier to override with _ideal_class_.
-
+Added some functionality to ideals (is_maximal works more often now, and there's a new ideal class for univariate polynomial rings).  Changed the logic on what class is chosen for ideals so that it's easier to override with _ideal_class_. Number of generators? 

[robertwb]

comment:1

Attachment: 7585_7_ideal.patch.gz

There's a lot of useful looking code in here, but it's unclear what exactly it does or it's intended to fix. Some more explanations would be nice, and the new behavior should be doctested. Especially for most of the changes in sage/rings/ideal.py

What is the parameter in _ideal_class_ supposed to mean? (Then why is it 0 by default?)

Depends on #7881?

[roed314]

Attachment: 7883_ideals.patch.gz

Rebased against 4.3.3; may need 8218, 8332, 7880, but probably not.

[roed314]

comment:2

I haven't made the changes Robert suggested, but I wanted to get an updated patch up since other finite field functionality depends on this.

[roed314]

comment:3

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.

[loefflerd]

comment:4

Tried this under 4.3.4.rc0 with 8218, 8332, 7880 applied. It applies fine but seven doctests fail. Moreover, I second Robert's criticism: it's not clear what all this new code is actually for. (The fact that other finite-field stuff depends on this doesn't change that.) Can we have a new patch with some more docstrings etc?

[roed314]

Attachment: 7883_fixes.patch.gz

Addresses referee comments

[roed314]

comment:5

Apply:

7883_ideals.patch
7883_fixes.patch

Probably will not pass doctests unless you also apply the patches on #8333 and #8334.