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) in () ----> 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.