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# Degeneracy maps

class `sage.modular.hecke.degenmap.``DegeneracyMap`(matrix, domain, codomain, t)

  Bases: `sage.modular.hecke.morphism.HeckeModuleMorphism_matrix`

  A degeneracy map between Hecke modules of different levels.

  EXAMPLES: We construct a number of degeneracy maps:

      sage: M = ModularSymbols(33)
      sage: d = M.degeneracy_map(11)
      sage: d
      Hecke module morphism degeneracy map corresponding to f(q) |--> f(q) defined by the matrix
      [ 1  0  0]
      [ 0  0  1]
      [ 0  0 -1]
      [ 0  1 -1]
      [ 0  0  1]
      [ 0 -1  1]
      [-1  0  0]
      [-1  0  0]
      [-1  0  0]
      Domain: Modular Symbols space of dimension 9 for Gamma_0(33) of weight ...
      Codomain: Modular Symbols space of dimension 3 for Gamma_0(11) of weight ...
      sage: d.t()
      1
      sage: d = M.degeneracy_map(11,3)
      sage: d.t()
      3

  The parameter d must be a divisor of the quotient of the two levels:

      sage: d = M.degeneracy_map(11,2)
      Traceback (most recent call last):
      ...
      ValueError: The level of self (=33) must be a divisor or multiple of level (=11), and t (=2) must be a divisor of the quotient.

  Degeneracy maps can also go from lower level to higher level:

      sage: M.degeneracy_map(66,2)
      Hecke module morphism degeneracy map corresponding to f(q) |--> f(q^2) defined by the matrix
      [ 2  0  0  0  0  0  1  0  0  0  1 -1  0  0  0 -1  1  0  0  0  0  0  0  0 -1]
      [ 0  0  1 -1  0 -1  1  0 -1  2  0  0  0 -1  0  0 -1  1  2 -2  0  0  0 -1  1]
      [ 0  0  1  0  0  0  0  0  1  0  0  0  1  0  0  0 -1  1  0  0 -1  1  0  0  0]
      [ 0  0  0  0  0  0  0  0  0  2 -1  0  0  1  0  0 -1  1  0  0  1  0 -1 -1  1]
      [ 0 -1  0  0  1  0  0  0  0  0  0  1  0  0  1  1 -1  0  0 -1  0  0  0  0  0]
      [ 0  0  0  0  0  0  0  1 -1  0  0  2 -1  0  0  1  0  0  0 -1  0 -1  1 -1  1]
      [ 0  0  0  0  1 -1  0  1 -1  0  0  0  0  0 -1  2  0  0  0  0  1  0  1  0  0]
      [ 0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0  1  1  0  0]
      [ 0  0  0  0  0  0  0  0  0  0 -1  0  0  0  0  0  0  0  0  1  1  1  0  0  0]
      Domain: Modular Symbols space of dimension 9 for Gamma_0(33) of weight ...
      Codomain: Modular Symbols space of dimension 25 for Gamma_0(66) of weight ...

  `t`()

    Return the divisor of the quotient of the two levels associated to the degeneracy map.

    EXAMPLES:

        sage: M = ModularSymbols(33)
        sage: d = M.degeneracy_map(11,3)
        sage: d.t()
        3
        sage: d = M.degeneracy_map(11,1)
        sage: d.t()
        1

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