Morphisms of Hecke modules

AUTHORS:

  • William Stein
class sage.modular.hecke.morphism.HeckeModuleMorphism

Abstract base class for morphisms of Hecke modules.

__weakref__
list of weak references to the object (if defined)
class sage.modular.hecke.morphism.HeckeModuleMorphism_matrix(parent, A, name='')

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
...
TypeError: Incompatible composition of morphisms: domain of left morphism must be codomain of right.
__init__(parent, A, name='')

INPUT:

  • parent - ModularSymbolsHomspace
  • A - Matrix
  • name - str (defaults to ‘’) name of the morphism (used for printing)

EXAMPLE:

sage: M = ModularSymbols(6)
sage: t = M.Hom(M)(matrix(QQ,3,3,srange(9)), name="spam"); t
Hecke module morphism spam defined by the matrix
[0 1 2]
[3 4 5]
[6 7 8]
Domain: Modular Symbols space of dimension 3 for Gamma_0(6) of weight ...
Codomain: Modular Symbols space of dimension 3 for Gamma_0(6) of weight ...
sage: t == loads(dumps(t))
True
_repr_()

String representation of self.

EXAMPLES:

sage: M = ModularSymbols(6)
sage: t = M.Hom(M)(matrix(QQ,3,3,srange(9))); t._repr_()
'Hecke module morphism defined by the matrix\n[0 1 2]\n[3 4 5]\n[6 7 8]\nDomain: Modular Symbols space of dimension 3 for Gamma_0(6) of weight ...\nCodomain: Modular Symbols space of dimension 3 for Gamma_0(6) of weight ...'
sage: t.name('spam'); t._repr_()
'Hecke module morphism spam defined by the matrix\n[0 1 2]\n[3 4 5]\n[6 7 8]\nDomain: Modular Symbols space of dimension 3 for Gamma_0(6) of weight ...\nCodomain: Modular Symbols space of dimension 3 for Gamma_0(6) of weight ...'
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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