Bases: sage.rings.homset.RingHomset_generic
Set of morphisms between two finite-dimensional algebras.
Construct the zero morphism of self.
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.zero()
Morphism from Finite-dimensional algebra of degree 1 over Rational Field to
Finite-dimensional algebra of degree 2 over Rational Field given by matrix
[0 0]
Bases: sage.rings.morphism.RingHomomorphism_im_gens
Create a morphism between two finite-dimensional algebras.
INPUT:
The algebras A and B must be defined over the same base field.
EXAMPLES:
sage: from sage.algebras.finite_dimensional_algebras.finite_dimensional_algebra_morphism import FiniteDimensionalAlgebraMorphism
sage: A = FiniteDimensionalAlgebra(QQ, [Matrix([[1, 0], [0, 1]]), Matrix([[0, 1], [0, 0]])])
sage: B = FiniteDimensionalAlgebra(QQ, [Matrix([1])])
sage: H = Hom(A, B)
sage: f = H(Matrix([[1], [0]]))
sage: f.domain() is A
True
sage: f.codomain() is B
True
sage: f(A.basis()[0])
e
sage: f(A.basis()[1])
0
Todo
An example illustrating unitary flag.
Return the inverse image of I under self.
INPUT:
OUTPUT:
– FiniteDimensionalAlgebraIdeal, the inverse image of under self.
EXAMPLE:
sage: A = FiniteDimensionalAlgebra(QQ, [Matrix([[1, 0], [0, 1]]), Matrix([[0, 1], [0, 0]])])
sage: I = A.maximal_ideal()
sage: q = A.quotient_map(I)
sage: B = q.codomain()
sage: q.inverse_image(B.zero_ideal()) == I
True
Return the matrix of self.
EXAMPLES:
sage: A = FiniteDimensionalAlgebra(QQ, [Matrix([[1, 0], [0, 1]]), Matrix([[0, 1], [0, 0]])])
sage: B = FiniteDimensionalAlgebra(QQ, [Matrix([1])])
sage: M = Matrix([[1], [0]])
sage: H = Hom(A, B)
sage: f = H(M)
sage: f.matrix() == M
True