Add the categories of magmas and additive magmas

[nthiery]

This patch adds the categories Magmas() and AdditiveMagmas()
(sets with a plain binary operation * or +).

It factors out some of the code previously in Semigroups / CommutativeAdditiveSemigroups.

This is used by the updated #7555 to make it more general.

Depends trivially on #7880.

CC: @sagetrac-sage-combinat @roed314

Component: categories

Keywords: magma

Author: Nicolas M. Thiéry

Reviewer: Robert Beezer, Florent Hivert

Merged: sage-4.4.alpha0

Issue created by migration from https://trac.sagemath.org/ticket/8579

[nthiery]

Changed keywords from none to magma

[nthiery]

Description changed:

--- 
+++ 
@@ -3,4 +3,4 @@
 
 It factors out some of the code previously in Semigroups / CommutativeAdditiveSemigroups.
 
-
+This is used by the updated #7555 to make it more general.

[rbeezer]

comment:2

Hi Nicolas,

I get about 10 "hunk failures" trying to apply this to a stock 4.3.4.

I noticed a "-git" in the diff commands in the patch, which I don't see in the patches I usually make. Is it it me, or does this patch need some attention?

Rob

[nthiery]

Description changed:

--- 
+++ 
@@ -4,3 +4,5 @@
 It factors out some of the code previously in Semigroups / CommutativeAdditiveSemigroups.
 
 This is used by the updated #7555 to make it more general.
+
+Depends trivially on #7880.

[rbeezer]

comment:4

Thanks, Nicolas, I'll test tonight with #7880.

[nthiery]

Attachment: trac_8579-category-magmas-nt.patch.gz

This updated patch fixes the copyright headers

[rbeezer]

comment:5

This passes all tests on 4.3.4.final and docs build without any problems. It also works well when the fairly extensive #7555 is applied on top of it. So there should be no surprises for the interested reviewer.

I can't say at the moment that I know enough about implementing categories to verify its completeness, so right now it either (a) needs a quick review from a knowledgeable category specialist, or (b) I need to get more education on categories so #7555 can go in.

Rob

[williamstein]

comment:6

Finally, Magma gets included in Sage!!

[hivert]

comment:7

Hi Rob,

Replying to @rbeezer:

This passes all tests on 4.3.4.final and docs build without any problems. It also works well when the fairly extensive #7555 is applied on top of it. So there should be no surprises for the interested reviewer.

Thanks for checking this.

I can't say at the moment that I know enough about implementing categories to verify its completeness, so right now it either (a) needs a quick review from a knowledgeable category specialist, or (b) I need to get more education on categories so #7555 can go in.

From the category implementation point of view, everything looks fine upto the
following small problem which can be left for a future patch: the
SubQuotient code in Semigroups() is sufficiently general to work
in magmas (computing product by lifting/retracting). It should be moved in
Magmas().

Otherwise, I'm okay to give a positive review. I'll ask Nicolas directly.

Florent