ASKSAGE: Sage Q&A Forum - Latest question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 25 Jul 2017 10:22:22 -0500Check if a finitely generated matrix group is finite (works with QQ and not with CC)https://ask.sagemath.org/question/38403/check-if-a-finitely-generated-matrix-group-is-finite-works-with-qq-and-not-with-cc/Dear all, I am a newbie in sage. I would like to check if a finitely generated matrix group is finite. Before to proceed with the calculation on my actual problem (where matrices have complex entries), I have tried a very simple example. Consider the group generated by the matrices [1,0,0,1] and [0,1,1,0], this group is clearly finite. Can somebody explain me why the following code works:
sage: MS = MatrixSpace(QQ, 2, 2)
sage: G = MatrixGroup([MS([1,0,0,1]),MS([0,1,1,0])])
sage: G.is_finite()
True
but if I change the field QQ -> RR (or CC), an error is generated:
sage: MS = MatrixSpace(RR, 2, 2)
sage: G = MatrixGroup([MS([1,0,0,1]),MS([0,1,1,0])])
sage: G.is_finite()
---------------------------------------------------------------------------
NotImplementedError Traceback (most recent call last)
<ipython-input-215-0022a668c150> in <module>()
----> 1 G.is_finite()
/Applications/SageMath-7.6.app/Contents/Resources/sage/src/sage/groups/group.pyx in sage.groups.group.Group.is_finite (/Applications/SageMath-7.6.app/Contents/Resources/sage/src/build/cythonized/sage/groups/group.c:2696)()
179 NotImplementedError
180 """
--> 181 return self.order() != infinity
182
183 def is_multiplicative(self):
/Applications/SageMath-7.6.app/Contents/Resources/sage/src/sage/groups/group.pyx in sage.groups.group.Group.order (/Applications/SageMath-7.6.app/Contents/Resources/sage/src/build/cythonized/sage/groups/group.c:2623)()
164 NotImplementedError
165 """
--> 166 raise NotImplementedError
167
168 def is_finite(self):
NotImplementedError:
Is there any way to force the second piece of code to work with matrices with entries in CC?
Thank you in advance.frenkyoTue, 25 Jul 2017 10:22:22 -0500https://ask.sagemath.org/question/38403/Sage, small group libraryhttps://ask.sagemath.org/question/23168/sage-small-group-library/Is there anyway to call the GAP small group library in the Sage? ahannahanWed, 02 Jul 2014 12:45:34 -0500https://ask.sagemath.org/question/23168/Problem with GeneralDihedralGroup constructorhttps://ask.sagemath.org/question/10476/problem-with-generaldihedralgroup-constructor/While exploring cayley graphs of generalized dihedral groups I get a wrong result if I use `GeneralDihedralGroup([n])` to create a simple dihedral group for some values on `n`, 6 and 10 for instance. Sage responds that it is isomorphic to `DihedralGroup(n)`, but the cayley graphs and group generators are not the same. Is it me or the system?
For example:
sage: gd=GeneralDihedralGroup([10])
sage: CGD10=Graph(gd.cayley_graph())
sage: CGD10.diameter()
4
sage: CGD10.degree()
[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]
sage: dih10=DihedralGroup(10)
sage: sage: Cdih10=Graph(dih10.cayley_graph())
sage: Cdih10.diameter()
6
sage: Cdih10.degree()
[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]
sage: gd.is_isomorphic(DihedralGroup(10))
True
sage: dih10.gens()
[(1,2,3,4,5,6,7,8,9,10), (1,10)(2,9)(3,8)(4,7)(5,6)]
sage: gd.gens()
[(4,7)(5,6), (3,4,5,6,7), (1,2)]`QuestorsTue, 27 Aug 2013 08:57:13 -0500https://ask.sagemath.org/question/10476/