#18002: Submonoids and subsemigroup defined by generators
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Reporter: virmaux | Owner:
Type: enhancement | Status: closed
Priority: major | Milestone: sage-6.6
Component: combinatorics | Resolution: fixed
Keywords: monoids, days64 | Merged in:
Authors: Nicolas M. Thiéry, Aladin | Reviewers: Anne
Virmaux | Schilling
Report Upstream: N/A | Work issues:
Branch: | Commit:
a8306e4da2265d06e6fc20ca3f16989632132fee | Stopgaps:
Dependencies: #17160 |
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Comment (by vdelecroix):
Replying to [comment:60 nthiery]:
> Replying to [comment:58 vdelecroix]:
> > The example in the description is precisely an example where we want
to override the method `.submonoid()` since everything can be computed
using `gcd`!
>
> We are looking for a multiplicative monoid here, not additive. So I
don't see from the top of my head how to do it with `gcd`.
Indeed, `gcd` is not enough.
> And I certainly agree that there must be some better way than brute
force in such a specific situation. I was just looking for a simple
example where one can easily check things by hand.
In the case of `Z/nZ` we know the multiplicative structure! That is indeed
a great advantage. I would decompose `Z/nZ = Prod_i (Z/(p_i)^k_i Z`. Then
determine the order of the generators in each projection and the
(multiplicative) subgroup they generate. And finally glue back.
But I am pretty sure that this was not the situation you had in mind with
Aladin when you wrote this ticket ;-)
Vincent
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Ticket URL: <http://trac.sagemath.org/ticket/18002#comment:61>
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