ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 09 Mar 2021 22:03:57 +0100Create quotient group of units of mod nhttps://ask.sagemath.org/question/55868/create-quotient-group-of-units-of-mod-n/ I would like to work with the group $\mathbb{Z}_m^* / \langle p \rangle$. Do you know how I can create it?
For example:
p = 2
m = 17^2
Zm = ZZ.quotient(m) # ring of integers mod m
Zms = Zm.unit_group() # cyclic group (Z/mZ)^* generated by 3
Zms.quotient(p)
But the last line raises a `NotImplementedError`.Wed, 24 Feb 2021 09:28:08 +0100https://ask.sagemath.org/question/55868/create-quotient-group-of-units-of-mod-n/Comment by John Palmieri for <p>I would like to work with the group $\mathbb{Z}_m^* / \langle p \rangle$. Do you know how I can create it?</p>
<p>For example:</p>
<pre><code>p = 2
m = 17^2
Zm = ZZ.quotient(m) # ring of integers mod m
Zms = Zm.unit_group() # cyclic group (Z/mZ)^* generated by 3
Zms.quotient(p)
</code></pre>
<p>But the last line raises a <code>NotImplementedError</code>.</p>
https://ask.sagemath.org/question/55868/create-quotient-group-of-units-of-mod-n/?comment=56088#post-id-56088Quotients of additive cyclic groups are implemented, though: `C272 = groups.misc.AdditiveCyclic(272)` and then `C272.quotient(...)` works.Tue, 09 Mar 2021 22:03:57 +0100https://ask.sagemath.org/question/55868/create-quotient-group-of-units-of-mod-n/?comment=56088#post-id-56088Comment by Hilder Vitor Lima Pereira for <p>I would like to work with the group $\mathbb{Z}_m^* / \langle p \rangle$. Do you know how I can create it?</p>
<p>For example:</p>
<pre><code>p = 2
m = 17^2
Zm = ZZ.quotient(m) # ring of integers mod m
Zms = Zm.unit_group() # cyclic group (Z/mZ)^* generated by 3
Zms.quotient(p)
</code></pre>
<p>But the last line raises a <code>NotImplementedError</code>.</p>
https://ask.sagemath.org/question/55868/create-quotient-group-of-units-of-mod-n/?comment=56074#post-id-56074Hi @JohnPalmieri. Yes, so even if I map p to an element of Zms, the command Zms.quotient will not work...Tue, 09 Mar 2021 17:32:25 +0100https://ask.sagemath.org/question/55868/create-quotient-group-of-units-of-mod-n/?comment=56074#post-id-56074Comment by John Palmieri for <p>I would like to work with the group $\mathbb{Z}_m^* / \langle p \rangle$. Do you know how I can create it?</p>
<p>For example:</p>
<pre><code>p = 2
m = 17^2
Zm = ZZ.quotient(m) # ring of integers mod m
Zms = Zm.unit_group() # cyclic group (Z/mZ)^* generated by 3
Zms.quotient(p)
</code></pre>
<p>But the last line raises a <code>NotImplementedError</code>.</p>
https://ask.sagemath.org/question/55868/create-quotient-group-of-units-of-mod-n/?comment=55997#post-id-55997There are a few issues. One is that quotients of arbitrary groups, even of arbitrary abelian groups, are not implemented. The second is that `Zms` doesn't remember that it is the group of units in `Zm` — it is just an abstract multiplicative abelian group, cyclic of order 272 — so `p` is not an element in it.Tue, 02 Mar 2021 20:46:26 +0100https://ask.sagemath.org/question/55868/create-quotient-group-of-units-of-mod-n/?comment=55997#post-id-55997