[sage-support] Re: numerical semigroup in sagemath

[John H Palmieri]

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

-- 
You received this message because you are subscribed to the Google Groups 
"sage-support" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to sage-support+unsubscr...@googlegroups.com.
To post to this group, send email to sage-support@googlegroups.com.
Visit this group at https://groups.google.com/group/sage-support.
For more options, visit https://groups.google.com/d/optout.

[sage-support] Re: numerical semigroup in sagemath

[Kwankyu]

There is a nice GAP package for numerical semigroups. You can use that via 
sage interface once you install it into the GAP under Sage (which could be 
tricky). Check

https://www.gap-system.org/Packages/numericalsgps.html 

-- 
You received this message because you are subscribed to the Google Groups 
"sage-support" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to sage-support+unsubscr...@googlegroups.com.
To post to this group, send email to sage-support@googlegroups.com.
Visit this group at https://groups.google.com/group/sage-support.
For more options, visit https://groups.google.com/d/optout.

[sage-support] Re: numerical semigroup in sagemath

[Simon King]

Hi!

On 2017-07-25, 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,}

I would expect the syntax
  S = NN*[2,3]
(which is meant to create the set of NN-linear combinations of the given
generators 2, 3, and is analogous on how one can create an ideal in 
some ring R), but it seems to be not implemented.

Best regards,
Simon

-- 
You received this message because you are subscribed to the Google Groups 
"sage-support" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to sage-support+unsubscr...@googlegroups.com.
To post to this group, send email to sage-support@googlegroups.com.
Visit this group at https://groups.google.com/group/sage-support.
For more options, visit https://groups.google.com/d/optout.