Checking if the given matrices will generate a finite Group

edit

Hello,

I am a newcomer to the SageMath. Basically, I have 100 matrices which have 4x4 dimensions in python. I want to check if this 100 matrices can generate an infinite group or not. P.S These matrices produced as SU(2) matrices and then were converted 4x4 matrices.

According to the document of sagemath, I tried to write a code but I am constantly having error:

from sage.all import *
for i in su4_np:
      sage_matrix = np.matrix((i),complex)
      sage_matrix = matrix(sage_matrix)
      matrix_su4_np.append(sage_matrix)
#F = GL(4, 5) 
F = SL(4,5) #CC ,CyclotomicField(10)

gens = matrix_su4_np #this is the matrix which contains all 100 matrices
G = MatrixGroup(F,4,gens)   
#G.order
MatrixGroup(F,4,gens).is_finite()

This is the error:

> --------------------------------------------------------------------------- MemoryError                           
> Traceback (most recent call last)
> <ipython-input-218-8f1964d06d6d> in
> <module>
>       4 
>       5 gens = matrix_su4_np
> ----> 6 G = MatrixGroup(F,4,gens)
>       7 MatrixGroup(F,4,gens).is_finite()
> 
> /usr/lib/python3/dist-packages/sage/misc/lazy_import.pyx
> in
> sage.misc.lazy_import.LazyImport.__call__
> (build/cythonized/sage/misc/lazy_import.c:3686)()
>     351             True
>     352         """
> --> 353         return self.get_object()(*args, **kwds)
>     354 
>     355     def __repr__(self):
> 
> /usr/lib/python3/dist-packages/sage/groups/matrix_gps/finitely_generated.py
> in MatrixGroup(*gens, **kwds)
>     290     if len(gens) == 0:
>     291         raise ValueError('need at least one generator')
> --> 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')
> 
> /usr/lib/python3/dist-packages/sage/groups/matrix_gps/finitely_generated.py
> in normalize_square_matrices(matrices)
>     120             continue
>     121         try:
> --> 122             m = list(m)
>     123         except TypeError:
>     124             gens.append(m)

MemoryError: 
> Blockquote

I am guessing the error comes because of the F = SL(4,5) line. However, I do not know what to put instead of that line. Do we have a function which can check if we have finite group or not just from matrices? How to solve this error? I tried quite a lot combination to solve this problem but I always got an error