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Matrix groups

I'm using Sage Cell Server and I have trouble with the Matrix group command. More precisely I have invertible matrices defined over Z, but their inverses have coefficients in Q, and Sage doesn't want to create the group. Here is my code and the error message :

B = Matrix([[1,0,0],[1,-1,1],[0,0,2]])
MatrixGroup([B])


Error message :

ValueError Traceback (most recent call last) <ipython-input-1-5e10d3c2096b> in <module>() 30 31 B = Matrix([[Integer(1),Integer(0),Integer(0)],[Integer(1),-Integer(1),Integer(1)],[Integer(0),Integer(0),Integer(2)]]) ---> 32 Invariant_group([B])

<ipython-input-1-5e10d3c2096b> in __init__(self, G) 2 def __init__(self,G): 3 # data : G est une liste de matrices inversibles engendrant un groupe fini. ----> 4 self.Groupe = MatrixGroup(G) 5 assert self.Groupe.is_finite() 6 self.Group_order = self.Groupe.order()

/home/sc_serv/sage/local/lib/python2.7/site-packages/sage/misc/lazy_import.pyx in sage.misc.lazy_import.LazyImport.__call__ (build/cythonized/sage/misc/lazy_import.c:3690)() 352 True 353 """ --> 354 return self.get_object()(args, *kwds) 355 356 def __repr__(self):

/home/sc_serv/sage/local/lib/python2.7/site-packages/sage/groups/matrix_gps/finitely_generated.pyc in MatrixGroup(gens, *kwds) 292 gens = normalize_square_matrices(gens) 293 if check and any(not g.is_invertible() for g in gens): --> 294 raise ValueError('each generator must be an invertible matrix') 295 MS = gens.universe() 296 base_ring = MS.base_ring()

ValueError: each generator must be an invertible matrix

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Notice the difference

sage: B = Matrix(ZZ, [[1,0,0],[1,-1,1],[0,0,2]])
sage: MatrixGroup([B])
Traceback (most recent call last):
...
ValueError: each generator must be an invertible matrix


versus

sage: B = Matrix(QQ, [[1,0,0],[1,-1,1],[0,0,2]])
sage: MatrixGroup([B])
Matrix group over Rational Field with 1 generators (
[ 1  0  0]
[ 1 -1  1]
[ 0  0  2]
)
`
more

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Asked: 2019-08-08 14:42:31 +0200

Seen: 35 times

Last updated: Aug 09 '19