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, 02 Oct 2018 11:13:48 +0200How to create a morphism between a permutation groups and a matrix groups by explicitley giving the map?https://ask.sagemath.org/question/43809/how-to-create-a-morphism-between-a-permutation-groups-and-a-matrix-groups-by-explicitley-giving-the-map/I looking to define a homomorphism between a permutation group to another permutation group by defining the map explicitly. Same between matrix groups? Can some body help? For example
The following codes gives an error
sage: G = SymmetricGroup(5)
sage: r = G('(1,3,5,2,4)')
sage: s = G('(2,5),(3,4)')
sage: H = G.subgroup([r,s])
sage: D = DihedralGroup(5)
sage: (a,b)= D.gens()
phi = PermutationGroupMorphism(H,D, [a,b])
phi(x)Tue, 02 Oct 2018 02:20:02 +0200https://ask.sagemath.org/question/43809/how-to-create-a-morphism-between-a-permutation-groups-and-a-matrix-groups-by-explicitley-giving-the-map/Answer by tmonteil for <p>I looking to define a homomorphism between a permutation group to another permutation group by defining the map explicitly. Same between matrix groups? Can some body help? For example
The following codes gives an error</p>
<pre><code>sage: G = SymmetricGroup(5)
sage: r = G('(1,3,5,2,4)')
sage: s = G('(2,5),(3,4)')
sage: H = G.subgroup([r,s])
sage: D = DihedralGroup(5)
sage: (a,b)= D.gens()
phi = PermutationGroupMorphism(H,D, [a,b])
phi(x)
</code></pre>
https://ask.sagemath.org/question/43809/how-to-create-a-morphism-between-a-permutation-groups-and-a-matrix-groups-by-explicitley-giving-the-map/?answer=43810#post-id-43810First, `phi(x)` does not makes much sense since `x` benongs to the symbolic ring, and has nothing to do with your group `H`.
However, i agree that the following seems and issue:
sage: phi(r)
RuntimeError: Gap produced error output
Error, usage: Image(<map>), Image(<map>,<elm>), Image(<map>,<coll>)
executing __SAGE_LAST__:="__SAGE_LAST__";;Image(\$sage11,\$sage9);;
And even:
sage: phi(H(r))
RuntimeError: Gap produced error output
Error, usage: Image(<map>), Image(<map>,<elm>), Image(<map>,<coll>)
executing __SAGE_LAST__:="__SAGE_LAST__";;Image(\$sage21,\$sage20);;
Thanks for reporting, someone should have a deeper look and see what does gap return to understand.
Tue, 02 Oct 2018 10:51:07 +0200https://ask.sagemath.org/question/43809/how-to-create-a-morphism-between-a-permutation-groups-and-a-matrix-groups-by-explicitley-giving-the-map/?answer=43810#post-id-43810Comment by ajit for <p>First, <code>phi(x)</code> does not makes much sense since <code>x</code> benongs to the symbolic ring, and has nothing to do with your group <code>H</code>.</p>
<p>However, i agree that the following seems and issue:</p>
<pre><code>sage: phi(r)
RuntimeError: Gap produced error output
Error, usage: Image(<map>), Image(<map>,<elm>), Image(<map>,<coll>)
executing __SAGE_LAST__:="__SAGE_LAST__";;Image(\$sage11,\$sage9);;
</code></pre>
<p>And even:</p>
<pre><code>sage: phi(H(r))
RuntimeError: Gap produced error output
Error, usage: Image(<map>), Image(<map>,<elm>), Image(<map>,<coll>)
executing __SAGE_LAST__:="__SAGE_LAST__";;Image(\$sage21,\$sage20);;
</code></pre>
<p>Thanks for reporting, someone should have a deeper look and see what does gap return to understand.</p>
https://ask.sagemath.org/question/43809/how-to-create-a-morphism-between-a-permutation-groups-and-a-matrix-groups-by-explicitley-giving-the-map/?comment=43811#post-id-43811Thanks, I shall wait for someone to resolve this issue!Tue, 02 Oct 2018 11:13:48 +0200https://ask.sagemath.org/question/43809/how-to-create-a-morphism-between-a-permutation-groups-and-a-matrix-groups-by-explicitley-giving-the-map/?comment=43811#post-id-43811