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# Morphisms of Hecke modules

AUTHORS:

- William Stein

class `sage.modular.hecke.morphism.``HeckeModuleMorphism`

  Bases: `sage.categories.morphism.Morphism`

  Abstract base class for morphisms of Hecke modules.

class `sage.modular.hecke.morphism.``HeckeModuleMorphism_matrix`(parent, A, name='')

  Bases: `sage.modules.matrix_morphism.MatrixMorphism`, `sage.modular.hecke.morphism.HeckeModuleMorphism`

  Morphisms of Hecke modules when the morphism is given by a matrix.

  Note that care is needed when composing morphisms, because morphisms in Sage act on the left, but their matrices act on the right (!). So if F: A -> B and G : B -> C are morphisms, the composition A -> C is G*F, but its matrix is F.matrix() * G.matrix().

  EXAMPLE:

      sage: A = ModularForms(1, 4)
      sage: B = ModularForms(1, 16)
      sage: C = ModularForms(1, 28)
      sage: F = A.Hom(B)(matrix(QQ,1,2,srange(1, 3)))
      sage: G = B.Hom(C)(matrix(QQ,2,3,srange(1, 7)))
      sage: G * F
      Hecke module morphism defined by the matrix
      [ 9 12 15]
      Domain: Modular Forms space of dimension 1 for Modular Group SL(2,Z) ...
      Codomain: Modular Forms space of dimension 3 for Modular Group SL(2,Z) ...
      sage: F * G
      Traceback (most recent call last):
      ...
      TypeError: Incompatible composition of morphisms: domain of left morphism must be codomain of right.

  `name`(new=None)

    Return the name of this operator, or set it to a new name.

    EXAMPLES:

        sage: M = ModularSymbols(6)
        sage: t = M.Hom(M)(matrix(QQ,3,3,srange(9)), name="spam"); t
        Hecke module morphism spam defined by ...
        sage: t.name()
        'spam'
        sage: t.name("eggs"); t
        Hecke module morphism eggs defined by ...

`sage.modular.hecke.morphism.``is_HeckeModuleMorphism`(x)

  Return True if x is of type HeckeModuleMorphism.

  EXAMPLES:

      sage: sage.modular.hecke.morphism.is_HeckeModuleMorphism(ModularSymbols(6).hecke_operator(7).hecke_module_morphism())
      True

`sage.modular.hecke.morphism.``is_HeckeModuleMorphism_matrix`(x)

  EXAMPLES:

      sage: sage.modular.hecke.morphism.is_HeckeModuleMorphism_matrix(ModularSymbols(6).hecke_operator(7).matrix_form().hecke_module_morphism())
      True

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