Package sage :: Package modular :: Module congroup_element :: Class CongruenceSubgroupElement

Class CongruenceSubgroupElement

                      object --+                
                               |                
structure.sage_object.SageObject --+            
                                   |            
           structure.element.Element --+        
                                       |        
         structure.element.MonoidElement --+    
                                           |    
structure.element.MultiplicativeGroupElement --+
                                               |
                                              CongruenceSubgroupElement

Instance Methods

[hide private]

__init__(self, parent, x, check=True)
x.__init__(...) initializes x; see x.__class__.__doc__ for signature

source code

__repr__(self)
File: sage/structure/sage_object.pyx (starting at line 86)

source code

_mul_(self, right)
File: sage/structure/element.pyx (starting at line 1113)

source code

__invert__(self)
File: sage/structure/element.pyx (starting at line 1227)

source code

matrix(self)

source code

determinant(self)

source code

det(self)

source code

a(self)

source code

b(self)

source code

c(self)

source code

d(self)

source code

acton(self, z)
Return the result of the action of self on z as a fractional linear transformation.

source code

Inherited from structure.element.MultiplicativeGroupElement: __div__, __new__, __rdiv__, _add_, _div_, order

Inherited from structure.element.MonoidElement: __mul__, __nonzero__, __pow__, __rmul__, __rpow__, multiplicative_order

Inherited from structure.element.Element: __cmp__, __eq__, __ge__, __gt__, __hash__, __le__, __lt__, __ne__, __reduce__, __rxor__, __xor__, _cmp_, _im_gens_, _repr_, _richcmp_, base_base_extend, base_base_extend_canonical_sym, base_extend, base_extend_canonical, base_extend_canonical_sym, base_extend_recursive, base_ring, category, is_zero, n, parent, subs, substitute

Inherited from structure.element.Element (private): _coeff_repr, _is_atomic, _latex_coeff_repr, _make_new_with_parent_c, _set_parent

Inherited from structure.sage_object.SageObject: _axiom_, _axiom_init_, _gap_, _gap_init_, _gp_, _gp_init_, _interface_, _interface_init_, _interface_is_cached_, _kash_, _kash_init_, _macaulay2_, _macaulay2_init_, _magma_, _magma_init_, _maple_, _maple_init_, _mathematica_, _mathematica_init_, _maxima_, _maxima_init_, _octave_, _octave_init_, _pari_, _pari_init_, _r_init_, _sage_, _singular_, _singular_init_, db, dump, dumps, plot, rename, reset_name, save, version

Inherited from object: __delattr__, __getattribute__, __reduce_ex__, __setattr__, __str__

Properties

[hide private]

Inherited from object: __class__

Method Details

[hide private]

init(self, parent, x, check=True)
(Constructor)

source code

x.__init__(...) initializes x; see x.__class__.__doc__ for signature

Overrides: structure.element.Element.__init__: (inherited documentation)

repr(self)
(Representation operator)

source code

File: sage/structure/sage_object.pyx (starting at line 86)

Overrides: structure.sage_object.SageObject.__repr__: (inherited documentation)

_mul_(self, right)

source code

File: sage/structure/element.pyx (starting at line 1113)

Overrides: structure.element.MonoidElement._mul_: (inherited documentation)

invert(self)

source code

File: sage/structure/element.pyx (starting at line 1227)

Overrides: structure.element.MultiplicativeGroupElement.__invert__: (inherited documentation)

acton(self, z)

source code


Return the result of the action of self on z as a fractional linear
transformation.

EXAMPLES:
    sage: G = Gamma0(15)
    sage: g = G([1, 2, 15, 31])

An example of g acting on a symbolic variable:
    sage: z = var('z')
    sage: g.acton(z)
    (z + 2)/(15*z + 31)

An example involving the Gaussian numbers:
    sage: K.<i> = NumberField(x^2 + 1)
    sage: g.acton(i)
    1/1186*i + 77/1186

An example with complex numbers:
    sage: C.<i> = ComplexField()
    sage: g.acton(i)
    0.0649241146711636 + 0.000843170320404721*I

Class CongruenceSubgroupElement

__init__(self, parent, x, check=True) (Constructor)

__repr__(self) (Representation operator)

_mul_(self, right)

__invert__(self)

acton(self, z)

init(self, parent, x, check=True)
(Constructor)

repr(self)
(Representation operator)

invert(self)