On Tuesday, July 25, 2017 at 5:53:37 AM UTC-7, springfield .gion wrote:
>
> Hi, I need to create and manipulate the additive semigroups generated by
> integers (such as those generated by tuples of coprime integers), but I am
> struggling with the syntax; is there an easy way to create something along
> the line of:
>
> S = ZZ.Semigroup([2,3])
> S = {0,2,3,4,....}
>
> Thanks in advance
>
You can try this:
S = NN.subsemigroup([2,3]) # or ZZ.subsemigroup([2,3])
although (a) it is not clear to me that this the right thing (it looks like
the multiplicative subsemigroup, not the additive one) and (b) I can't do
anything sensible with it.
So I tried to use multiplicative semigroups instead. If A is the
multiplicative semigroup consisting of powers of 2, then we could ask for
the multiplicative subsemigroup generated by 2**2 and 2**3, which should be
analogous to what you want. Unfortunately, it is broken:
sage: A = NN.subsemigroup([2])
sage: S = A.subsemigroup([2**2, 2**3])
Listing some elements and their base 2 logs is promising:
sage: list(S.some_elements()) # output omitted since it is a little
lengthy
sage: [log_b(ZZ(_),2) for _ in list(S.some_elements())] # output
omitted
but this is surprising:
sage: S.cardinality()
11441
I certainly didn't know that this semigroup was finite, let alone precisely
what its cardinality is.
--
John
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