def __init__(self, parent, A):
"""
INPUT:
- ``parent`` - a homspace
- ``A`` - matrix
EXAMPLES::
sage: from sage.modules.matrix_morphism import MatrixMorphism
sage: T = End(ZZ^3)
sage: M = MatrixSpace(ZZ,3)
sage: I = M.identity_matrix()
sage: A = MatrixMorphism(T, I)
sage: loads(A.dumps()) == A
True
"""
if not matrix.is_Matrix(A):
A = matrix.MatrixSpace(parent.category().base_ring(),
parent.domain().rank(),
parent.codomain().rank())(A)
R = A.base_ring()
if A.nrows() != parent.domain().rank():
raise ArithmeticError, "number of rows of matrix (=%s) must equal rank of domain (=%s)" % (
A.nrows(), parent.domain().rank())
if A.ncols() != parent.codomain().rank():
raise ArithmeticError, "number of columns of matrix (=%s) must equal rank of codomain (=%s)" % (
A.ncols(), parent.codomain().rank())
self._matrix = A
MatrixMorphism_abstract.__init__(self, parent)
def _matrix_space(self):
"""
Return underlying matrix space that contains the matrices that define
the homomorphisms in this free module homspace.
OUTPUT:
- matrix space
EXAMPLES::
sage: H = Hom(QQ^3, QQ^2)
sage: H._matrix_space()
Full MatrixSpace of 3 by 2 dense matrices over Rational Field
"""
try:
return self.__matrix_space
except AttributeError:
R = self.domain().base_ring()
M = matrix.MatrixSpace(R, self.domain().rank(), self.codomain().rank())
self.__matrix_space = M
return M
# Distributed under the terms of the GNU General Public License (GPL)
#
# The full text of the GPL is available at:
#
# http://www.gnu.org/licenses/
#
################################################################################
from sage.structure.element import MultiplicativeGroupElement
from sage.rings.all import ZZ
import sage.matrix.all as matrix
from sage.matrix.matrix_integer_2x2 import Matrix_integer_2x2 as mi2x2
from all import is_ArithmeticSubgroup
M2Z = matrix.MatrixSpace(ZZ, 2)
class ArithmeticSubgroupElement(MultiplicativeGroupElement):
r"""
An element of the group `{\rm SL}_2(\ZZ)`, i.e. a 2x2 integer matrix of
determinant 1.
"""
def __init__(self, parent, x, check=True):
"""
Create an element of an arithmetic subgroup.
INPUT:
- parent - an arithmetic subgroup