def normalize_square_matrices(matrices):
"""
Find a common space for all matrices.
OUTPUT:
A list of matrices, all elements of the same matrix space.
EXAMPLES::
sage: from sage.groups.matrix_gps.finitely_generated import normalize_square_matrices
sage: m1 = [[1,2],[3,4]]
sage: m2 = [2, 3, 4, 5]
sage: m3 = matrix(QQ, [[1/2,1/3],[1/4,1/5]])
sage: m4 = MatrixGroup(m3).gen(0)
sage: normalize_square_matrices([m1, m2, m3, m4])
[
[1 2] [2 3] [1/2 1/3] [1/2 1/3]
[3 4], [4 5], [1/4 1/5], [1/4 1/5]
]
"""
deg = []
gens = []
for m in matrices:
if is_MatrixGroupElement(m):
deg.append(m.parent().degree())
gens.append(m.matrix())
continue
if is_Matrix(m):
if not m.is_square():
raise TypeError('matrix must be square')
deg.append(m.ncols())
gens.append(m)
continue
try:
m = list(m)
except TypeError:
gens.append(m)
continue
if isinstance(m[0], (list, tuple)):
m = map(list, m)
degree = ZZ(len(m))
else:
degree, rem = ZZ(len(m)).sqrtrem()
if rem != 0:
raise ValueError(
'list of plain numbers must have square integer length')
deg.append(degree)
gens.append(matrix(degree, degree, m))
deg = set(deg)
if len(set(deg)) != 1:
raise ValueError('not all matrices have the same size')
gens = Sequence(gens, immutable=True)
MS = gens.universe()
if not is_MatrixSpace(MS):
raise TypeError('all generators must be matrices')
if MS.nrows() != MS.ncols():
raise ValueError('matrices must be square')
return gens
def normalize_square_matrices(matrices):
"""
Find a common space for all matrices.
OUTPUT:
A list of matrices, all elements of the same matrix space.
EXAMPLES::
sage: from sage.groups.matrix_gps.finitely_generated import normalize_square_matrices
sage: m1 = [[1,2],[3,4]]
sage: m2 = [2, 3, 4, 5]
sage: m3 = matrix(QQ, [[1/2,1/3],[1/4,1/5]])
sage: m4 = MatrixGroup(m3).gen(0)
sage: normalize_square_matrices([m1, m2, m3, m4])
[
[1 2] [2 3] [1/2 1/3] [1/2 1/3]
[3 4], [4 5], [1/4 1/5], [1/4 1/5]
]
"""
deg = []
gens = []
for m in matrices:
if is_MatrixGroupElement(m):
deg.append(m.parent().degree())
gens.append(m.matrix())
continue
if is_Matrix(m):
if not m.is_square():
raise TypeError('matrix must be square')
deg.append(m.ncols())
gens.append(m)
continue
try:
m = list(m)
except TypeError:
gens.append(m)
continue
if isinstance(m[0], (list, tuple)):
m = map(list, m)
degree = ZZ(len(m))
else:
degree, rem = ZZ(len(m)).sqrtrem()
if rem!=0:
raise ValueError('list of plain numbers must have square integer length')
deg.append(degree)
gens.append(matrix(degree, degree, m))
deg = set(deg)
if len(set(deg)) != 1:
raise ValueError('not all matrices have the same size')
gens = Sequence(gens, immutable=True)
MS = gens.universe()
if not is_MatrixSpace(MS):
raise TypeError('all generators must be matrices')
if MS.nrows() != MS.ncols():
raise ValueError('matrices must be square')
return gens
def __init__(self, gensG, category = None):
v = Sequence(gensG, immutable=True)
M = v.universe()
if not is_MatrixSpace(M):
raise TypeError, "universe of sequence (=%s) of generators must be a matrix space"%M
if M.nrows() != M.ncols():
raise ValueError, "matrices must be square."
for x in v:
if not x.is_invertible():
raise ValueError, "each generator must be an invertible matrix but one is not:\n%s"%x
self._gensG = v
MatrixGroup_gap.__init__(self, M.nrows(), M.base_ring(), category = category)
def __init__(self, gensG, category=None):
v = Sequence(gensG, immutable=True)
M = v.universe()
if not is_MatrixSpace(M):
raise TypeError, "universe of sequence (=%s) of generators must be a matrix space" % M
if M.nrows() != M.ncols():
raise ValueError, "matrices must be square."
for x in v:
if not x.is_invertible():
raise ValueError, "each generator must be an invertible matrix but one is not:\n%s" % x
self._gensG = v
MatrixGroup_gap.__init__(self,
M.nrows(),
M.base_ring(),
category=category)
