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 = [list(_) for _ in 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 = [list(_) for _ in 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 is_matrix_space(self):
"""
Return whether the free module is a matrix space.
OUTPUT:
Boolean. Whether the :meth:`free_module` factor in the tensor
product is a matrix space.
EXAMPLES::
sage: mip = MixedIntegerLinearProgram()
sage: LF = mip.linear_functions_parent()
sage: LF.tensor(RDF^2).is_matrix_space()
False
sage: LF.tensor(RDF^(2,2)).is_matrix_space()
True
"""
from sage.matrix.matrix_space import is_MatrixSpace
return is_MatrixSpace(self.free_module())
