def __init__(self, degree, base_ring, generator_matrices, category=None):
"""
Matrix group generated by a finite number of matrices.
EXAMPLES::
sage: m1 = matrix(SR, [[1,2],[3,4]])
sage: m2 = matrix(SR, [[1,3],[-1,0]])
sage: G = MatrixGroup(m1, m2)
sage: TestSuite(G).run()
sage: type(G)
<class 'sage.groups.matrix_gps.finitely_generated.FinitelyGeneratedMatrixGroup_generic_with_category'>
sage: from sage.groups.matrix_gps.finitely_generated import \
....: FinitelyGeneratedMatrixGroup_generic
sage: G = FinitelyGeneratedMatrixGroup_generic(2, QQ, [matrix(QQ,[[1,2],[3,4]])])
sage: G.gens()
(
[1 2]
[3 4]
)
"""
self._gens_matrix = generator_matrices
MatrixGroup_generic.__init__(self,
degree,
base_ring,
category=category)
def __init__(self, degree, base_ring, special, sage_name, latex_string):
"""
Base class for "named" matrix groups
INPUT:
- ``degree`` -- integer. The degree (number of rows/columns of matrices).
- ``base_ring`` -- ring. The base ring of the matrices.
- ``special`` -- boolean. Whether the matrix group is special,
that is, elements have determinant one.
- ``latex_string`` -- string. The latex representation.
EXAMPLES::
sage: G = GL(2, QQ)
sage: from sage.groups.matrix_gps.named_group import NamedMatrixGroup_generic
sage: isinstance(G, NamedMatrixGroup_generic)
True
"""
MatrixGroup_generic.__init__(self, degree, base_ring)
self._special = special
self._name_string = sage_name
self._latex_string = latex_string
def __init__(self, degree, base_ring, special, sage_name, latex_string):
"""
Base class for "named" matrix groups
INPUT:
- ``degree`` -- integer. The degree (number of rows/columns of matrices).
- ``base_ring`` -- ring. The base ring of the matrices.
- ``special`` -- boolean. Whether the matrix group is special,
that is, elements have determinant one.
- ``latex_string`` -- string. The latex representation.
EXAMPLES::
sage: G = GL(2, QQ)
sage: from sage.groups.matrix_gps.named_group import NamedMatrixGroup_generic
sage: isinstance(G, NamedMatrixGroup_generic)
True
"""
MatrixGroup_generic.__init__(self, degree, base_ring)
self._special = special
self._name_string = sage_name
self._latex_string = latex_string
def __init__(self,
degree,
base_ring,
special,
sage_name,
latex_string,
category=None,
invariant_form=None):
"""
Base class for "named" matrix groups
INPUT:
- ``degree`` -- integer; the degree (number of rows/columns of
matrices)
- ``base_ring`` -- ring; the base ring of the matrices
- ``special`` -- boolean; whether the matrix group is special,
that is, elements have determinant one
- ``sage_name`` -- string; the name of the group
- ``latex_string`` -- string; the latex representation
- ``category`` -- (optional) a subcategory of
:class:`sage.categories.groups.Groups` passed to
the constructor of
:class:`sage.groups.matrix_gps.matrix_group.MatrixGroup_generic`
- ``invariant_form`` -- (optional) square-matrix of the given
degree over the given base_ring describing a bilinear form
to be kept invariant by the group
EXAMPLES::
sage: G = GL(2, QQ)
sage: from sage.groups.matrix_gps.named_group import NamedMatrixGroup_generic
sage: isinstance(G, NamedMatrixGroup_generic)
True
.. SEEALSO::
See the examples for :func:`GU`, :func:`SU`, :func:`Sp`, etc.
as well.
"""
MatrixGroup_generic.__init__(self,
degree,
base_ring,
category=category)
self._special = special
self._name_string = sage_name
self._latex_string = latex_string
self._invariant_form = invariant_form
def __init__(self, degree, base_ring, special, sage_name, latex_string,
category=None, invariant_form=None):
"""
Base class for "named" matrix groups
INPUT:
- ``degree`` -- integer; the degree (number of rows/columns of
matrices)
- ``base_ring`` -- ring; the base ring of the matrices
- ``special`` -- boolean; whether the matrix group is special,
that is, elements have determinant one
- ``sage_name`` -- string; the name of the group
- ``latex_string`` -- string; the latex representation
- ``category`` -- (optional) a subcategory of
:class:`sage.categories.groups.Groups` passed to
the constructor of
:class:`sage.groups.matrix_gps.matrix_group.MatrixGroup_generic`
- ``invariant_form`` -- (optional) square-matrix of the given
degree over the given base_ring describing a bilinear form
to be kept invariant by the group
EXAMPLES::
sage: G = GL(2, QQ)
sage: from sage.groups.matrix_gps.named_group import NamedMatrixGroup_generic
sage: isinstance(G, NamedMatrixGroup_generic)
True
.. SEEALSO::
See the examples for :func:`GU`, :func:`SU`, :func:`Sp`, etc.
as well.
"""
MatrixGroup_generic.__init__(self, degree, base_ring, category=category)
self._special = special
self._name_string = sage_name
self._latex_string = latex_string
self._invariant_form = invariant_form
def __init__(self, degree, base_ring, generator_matrices, category=None):
"""
Matrix group generated by a finite number of matrices.
EXAMPLES::
sage: m1 = matrix(SR, [[1,2],[3,4]])
sage: m2 = matrix(SR, [[1,3],[-1,0]])
sage: G = MatrixGroup(m1, m2)
sage: TestSuite(G).run()
sage: type(G)
<class 'sage.groups.matrix_gps.finitely_generated.FinitelyGeneratedMatrixGroup_generic_with_category'>
sage: from sage.groups.matrix_gps.finitely_generated import \
....: FinitelyGeneratedMatrixGroup_generic
sage: G = FinitelyGeneratedMatrixGroup_generic(2, QQ, [matrix(QQ,[[1,2],[3,4]])])
sage: G.gens()
(
[1 2]
[3 4]
)
"""
self._gens_matrix = generator_matrices
MatrixGroup_generic.__init__(self, degree, base_ring, category=category)
def __richcmp__(self, other, op):
"""
Override comparison.
We need to override the comparison since the named groups
derive from
:class:`~sage.structure.unique_representation.UniqueRepresentation`,
which compare by identity.
EXAMPLES::
sage: G = GL(2,3)
sage: G == MatrixGroup(G.gens())
True
sage: G = groups.matrix.GL(4,2)
sage: H = MatrixGroup(G.gens())
sage: G == H
True
sage: G != H
False
"""
return MatrixGroup_generic.__richcmp__(self, other, op)
