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.

[rbeezer]

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

[rbeezer]

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

[nthiery]

This updated patch fixes the copyright headers

[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.

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

[was]

Finally, Magma gets included in Sage!!

[hivert]

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

[nthiery]

Replying to hivert:

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().

Ah, right, I forgot to mention that. I decided to implement this moving in the upcoming functorial construction patch instead, in order to avoid potential conflicts between the two patches.

[hivert]

Replying to nthiery:

Ah, right, I forgot to mention that. I decided to implement this moving in the upcoming functorial construction patch instead, in order to avoid potential conflicts between the two patches.

Then It's ok ! positive review.

[rbeezer]

Replying to hivert:

Then It's ok ! positive review.

Florent,

Thanks for finishing this one off!

Rob

[jhpalmieri]

Merged "trac_8579-category-magmas-nt.patch" in 4.4.alpha0