ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 19 Aug 2020 08:26:15 +0200Quotient group for matrix groups?https://ask.sagemath.org/question/53099/quotient-group-for-matrix-groups/Is there a way to create a quotient group for groups in the class MatrixGroup? The following use of .quotient(H) gives a NotImplementedError.
p=3
F=FiniteField(p)
t1=matrix(F,3,[1,0,1,0,1,0,0,0,1])
t2=matrix(F,3,[1,0,0,0,1,1,0,0,1])
t3=matrix(F,3,[1,0,0,0,1,0,0,1,1])
G=MatrixGroup([t1,t2,t3])
opts=[]
for a in G:
h=a*t1*a^-1
if h not in opts:
opts.append(h)
H=G.subgroup(opts)
print(H.order())
Q=G.quotient(H)
ndhanson3Wed, 19 Aug 2020 08:26:15 +0200https://ask.sagemath.org/question/53099/What is the most useful basefield for finite matrix groups?https://ask.sagemath.org/question/51559/what-is-the-most-useful-basefield-for-finite-matrix-groups/Hi everyone,
I am trying to write a notebook that does some elementary computations in a finite matrix group like conjugacy classes and character tables. It is meant to be used in cases where the group is realized explicitly as some subgroup of GL(3,R) or GL(2,R). My problem now is that if I want to implement rotations like
rotations=[]
for t in [1/3,2/3]:
rotations.append(matrix([[cos(2*pi*t),-sin(2*pi*t)],[sin(2*pi*t),cos(2*pi*t)]]))
the base ring will be the symbolic ring SR because there is a sqrt(2) in some denominators. If I then try to compute the characters via
gens=rotations
G2=MatrixGroup(gens)
G2.character_table()
I will get an error message. My assumption is that because of the base ring SR, Sage doesn't realize that this is in fact a finite group. What would a suitable base field be to make this computation possible?
Thanks in advance.Robin_FTue, 26 May 2020 17:23:17 +0200https://ask.sagemath.org/question/51559/Matrix groupshttps://ask.sagemath.org/question/47437/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`
invertiblematrixThu, 08 Aug 2019 14:42:31 +0200https://ask.sagemath.org/question/47437/Matrix Group over Symbolic Ringhttps://ask.sagemath.org/question/40976/matrix-group-over-symbolic-ring/I have problem on generate matrix group over symbolic ring.
First, I define
eta=I;
eta2=(1+I)*sqrt(2)/2;
Then, define a generator matrix
T=matrix(SR,4,[eta**(i*j)*eta2/2 for i in range(4) for j in range(4)]);
I try to make a matrix group by
G=MatrixGroup(T);
What I get is only very long computation that does not give any result.
Can somebody help me? Thank you very much.
I have checked the order of T, I got 8 since T**8=I where I is identity matrix. dimahphoneMon, 05 Feb 2018 05:31:14 +0100https://ask.sagemath.org/question/40976/It takes so long to generate dictionary of GL elements.https://ask.sagemath.org/question/40987/it-takes-so-long-to-generate-dictionary-of-gl-elements/The following command
GL4dicthash={hash(g):None for g in GL(4,2)}
takes 9 seconds to execute. On the other hand
GL4dict={g:None for g in GL(4,2)}
takes minutes and does not seem to terminate.
If I understand python dictionary correctly, they should take about the same time. So what happened?
Symbol 1Tue, 06 Feb 2018 02:03:25 +0100https://ask.sagemath.org/question/40987/