def __call__(self, f, check=True, unitary=True):
"""
Construct a homomorphism.
.. TODO::
Implement taking generator images and converting them to a matrix.
EXAMPLES::
sage: A = FiniteDimensionalAlgebra(QQ, [Matrix([1])])
sage: B = FiniteDimensionalAlgebra(QQ, [Matrix([[1, 0], [0, 1]]), Matrix([[0, 1], [0, 0]])])
sage: H = Hom(A, B)
sage: H(Matrix([[1, 0]]))
Morphism from Finite-dimensional algebra of degree 1 over Rational Field to
Finite-dimensional algebra of degree 2 over Rational Field given by matrix
[1 0]
"""
if isinstance(f, FiniteDimensionalAlgebraMorphism):
if f.parent() is self:
return f
if f.parent() == self:
return FiniteDimensionalAlgebraMorphism(self, f._matrix, check, unitary)
elif is_Matrix(f):
return FiniteDimensionalAlgebraMorphism(self, f, check, unitary)
try:
from sage.matrix.constructor import Matrix
return FiniteDimensionalAlgebraMorphism(self, Matrix(f), check, unitary)
except Exception:
return RingHomset_generic.__call__(self, f, check)
def __call__(self, f, check=True, unitary=True):
"""
Construct a homomorphism.
.. TODO::
Implement taking generator images and converting them to a matrix.
EXAMPLES::
sage: A = FiniteDimensionalAlgebra(QQ, [Matrix([1])])
sage: B = FiniteDimensionalAlgebra(QQ, [Matrix([[1, 0], [0, 1]]), Matrix([[0, 1], [0, 0]])])
sage: H = Hom(A, B)
sage: H(Matrix([[1, 0]]))
Morphism from Finite-dimensional algebra of degree 1 over Rational Field to
Finite-dimensional algebra of degree 2 over Rational Field given by matrix
[1 0]
"""
if isinstance(f, FiniteDimensionalAlgebraMorphism):
if f.parent() is self:
return f
if f.parent() == self:
return FiniteDimensionalAlgebraMorphism(
self, f._matrix, check, unitary)
elif is_Matrix(f):
return FiniteDimensionalAlgebraMorphism(self, f, check, unitary)
try:
from sage.matrix.constructor import Matrix
return FiniteDimensionalAlgebraMorphism(self, Matrix(f), check,
unitary)
except Exception:
return RingHomset_generic.__call__(self, f, check)
def __init__(self, R, S, category=None):
"""
TESTS:
Check that :trac:`23647` is fixed::
sage: K.<a, b> = NumberField([x^2 - 2, x^2 - 3])
sage: e, u, v, w = End(K)
sage: e.abs_hom().parent().category()
Category of homsets of number fields
sage: (v*v).abs_hom().parent().category()
Category of homsets of number fields
"""
if category is None:
from sage.categories.all import Fields, NumberFields
if S in NumberFields:
category = NumberFields()
elif S in Fields:
category = Fields()
RingHomset_generic.__init__(self, R, S, category)
def __init__(self, R, S, category=None):
"""
TESTS:
Check that :trac:`23647` is fixed::
sage: K.<a, b> = NumberField([x^2 - 2, x^2 - 3])
sage: e, u, v, w = End(K)
sage: e.abs_hom().parent().category()
Category of homsets of number fields
sage: (v*v).abs_hom().parent().category()
Category of homsets of number fields
"""
if category is None:
from sage.categories.all import Fields, NumberFields
if S in NumberFields:
category = NumberFields()
elif S in Fields:
category = Fields()
RingHomset_generic.__init__(self, R, S, category)