### Navigation

- index
- modules |
- next |
- previous |
- Modular Symbols »

# A single element of an ambient space of modular symbols

class `sage.modular.modsym.element.``ModularSymbolsElement`(parent, x, check=True)

  Bases: `sage.modular.hecke.element.HeckeModuleElement`

  An element of a space of modular symbols.

  TESTS:

      sage: x = ModularSymbols(3, 12).cuspidal_submodule().gen(0)
      sage: x == loads(dumps(x))
      True

  `list`()

    Return a list of the coordinates of self in terms of a basis for the ambient space.

    EXAMPLE:

        sage: ModularSymbols(37, 2).0.list()
        [1, 0, 0, 0, 0]

  `manin_symbol_rep`()

    Returns a representation of self as a formal sum of Manin symbols.

    EXAMPLE:

        sage: x = ModularSymbols(37, 4).0
        sage: x.manin_symbol_rep()
        [X^2,(0,1)]

    The result is cached:

        sage: x.manin_symbol_rep() is x.manin_symbol_rep()
        True

  `modular_symbol_rep`()

    Returns a representation of self as a formal sum of modular symbols.

    EXAMPLE:

        sage: x = ModularSymbols(37, 4).0
        sage: x.modular_symbol_rep()
        X^2*{0, Infinity}

    The result is cached:

        sage: x.modular_symbol_rep() is x.modular_symbol_rep()
        True

`sage.modular.modsym.element.``is_ModularSymbolsElement`(x)

  Return True if x is an element of a modular symbols space.

  EXAMPLES:

      sage: sage.modular.modsym.element.is_ModularSymbolsElement(ModularSymbols(11, 2).0)
      True
      sage: sage.modular.modsym.element.is_ModularSymbolsElement(13)
      False

`sage.modular.modsym.element.``set_modsym_print_mode`(mode='manin')

  Set the mode for printing of elements of modular symbols spaces.

  INPUT:

  - `mode` - a string. The possibilities are as follows:
  - `'manin'` - (the default) formal sums of Manin symbols [P(X,Y),(u,v)]
  - `'modular'` - formal sums of Modular symbols P(X,Y)*alpha,beta, where alpha and beta are cusps
  - `'vector'` - as vectors on the basis for the ambient space

  OUTPUT: none

  EXAMPLE:

      sage: M = ModularSymbols(13, 8)
      sage: x = M.0 + M.1 + M.14
      sage: set_modsym_print_mode('manin'); x
      [X^5*Y,(1,11)] + [X^5*Y,(1,12)] + [X^6,(1,11)]
      sage: set_modsym_print_mode('modular'); x
      1610510*X^6*{-1/11, 0} - 248832*X^6*{-1/12, 0} + 893101*X^5*Y*{-1/11, 0} - 103680*X^5*Y*{-1/12, 0} + 206305*X^4*Y^2*{-1/11, 0} - 17280*X^4*Y^2*{-1/12, 0} + 25410*X^3*Y^3*{-1/11, 0} - 1440*X^3*Y^3*{-1/12, 0} + 1760*X^2*Y^4*{-1/11, 0} - 60*X^2*Y^4*{-1/12, 0} + 65*X*Y^5*{-1/11, 0} - X*Y^5*{-1/12, 0} + Y^6*{-1/11, 0}
      sage: set_modsym_print_mode('vector'); x
      (1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0)
      sage: set_modsym_print_mode()

### Navigation

- index
- modules |
- next |
- previous |
- Modular Symbols »