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2017-07-25 19:02:45 +0200 received badge  Student (source)
2017-07-25 17:49:53 +0200 asked a question 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.