#16718: Create a category for Cartesian products of groups
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Reporter: tscrim | Owner: tscrim
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.3
Component: group theory | Resolution:
Keywords: cartesian | Merged in:
product, generators, categories | Reviewers:
Authors: Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | 6664adb7da87177ef6ae877c10dcf0a49fece50e
public/groups/cartesian_product_category-16718| Stopgaps:
Dependencies: |
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Comment (by tscrim):
Replying to [comment:5 ncohen]:
> The code that only exists in your head again ....
There's thousands of lines by hundreds of people. `:p`
> > Plus `group_generators` currently does not call `monoid_generators`
and not all groups have a `monoid_generators` method.
>
> Why don't all groups have a `monoid_generators` method ? They are
monoids, aren't they ?
Yes, but as I stated above, there are often more generators as a monoid
than as a group. For example, take `ZZ` under addition, there is 1
generator as a group (`+1`) but 2 generators as a monoid (`+/-1`). However
for C,,n,, (cyclic group), the generators as a group and as a monoid are
the same. I guess we could define the monoid generators as the group
generators and their inverses as a general method for general groups and
for finite groups, the generators as a group also generate as a monoid.
This is now #16725.
As for why this is not there for many groups is that they were implemented
before monoids were considered in Sage (I believe).
--
Ticket URL: <http://trac.sagemath.org/ticket/16718#comment:6>
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