Package sage :: Package algebras :: Module quaternion_order :: Class QuaternionOrder_generic

Class QuaternionOrder_generic

                      object --+                            
                               |                            
structure.sage_object.SageObject --+                        
                                   |                        
             structure.parent.Parent --+                    
                                       |                    
    structure.parent_base.ParentWithBase --+                
                                           |                
        structure.parent_gens.ParentWithGens --+            
                                               |            
                                 rings.ring.Ring --+        
                                                   |        
                                  rings.ring.Algebra --+    
                                                       |    
                      algebra_order.AlgebraOrder_generic --+
                                                           |
                                                          QuaternionOrder_generic


An order in a quaternion algebra.

Instance Methods

[hide private]

__init__(self, H, R, gens, basis=['4ti2-20061025', 'R-2.6.0', 'atlas-3.7.37', 'atlas-3.8.1', 'a...)
An order in a quaternion algebra. source code

__call__(self, x, check=True)
File: sage/rings/ring.pyx (starting at line 37) Coerce x into the ring.

source code

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

source code

discriminant(self)

source code

gram_matrix(self)

source code

inner_product_matrix(self)

source code

random_element(self)
File: sage/rings/ring.pyx (starting at line 642) Return a random integer coerced into this ring, where the integer is chosen uniformly from the interval [-bound,bound].

source code

Inherited from algebra_order.AlgebraOrder_generic: __contains__, algebra_basis_elements, ambient_algebra, base_ring, basis, embedding_matrix, gen, gens, inverse_embedding_matrix, module, ngens, rank

Inherited from rings.ring.Algebra: __new__, characteristic

Inherited from rings.ring.Ring: __getitem__, __hash__, __iter__, __len__, __mul__, __rmul__, __rxor__, __xor__, _ideal_class_, base_extend, category, ideal, is_atomic_repr, is_commutative, is_exact, is_field, is_finite, is_integral_domain, is_noetherian, is_prime_field, is_ring, is_subring, one_element, order, principal_ideal, unit_ideal, zero_element, zero_ideal, zeta, zeta_order

Inherited from rings.ring.Ring (private): _r_action

Inherited from structure.parent_gens.ParentWithGens: __getslice__, __getstate__, __setstate__, _is_valid_homomorphism_, gens_dict, hom, inject_variables, injvar, latex_name, latex_variable_names, list, objgen, objgens, variable_name, variable_names

Inherited from structure.parent_gens.ParentWithGens (private): _assign_names, _first_ngens

Inherited from structure.parent_base.ParentWithBase: Hom, base, base_extend_canonical, base_extend_canonical_sym, base_extend_recursive

Inherited from structure.parent.Parent: _coerce_, coerce_map_from, coerce_map_from_impl, construction, get_action, get_action_impl, has_coerce_map_from, has_coerce_map_from_impl, init_coerce

Inherited from structure.parent.Parent (private): _an_element, _an_element_impl, _coerce_impl, _coerce_self, _coerce_try

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__, __reduce_ex__, __setattr__, __str__

Properties

[hide private]

Inherited from rings.ring.Ring (private): _one_element, _unit_ideal, _zero_element, _zero_ideal

Inherited from structure.parent_gens.ParentWithGens (private): _gens, _gens_dict, _latex_names, _list, _names

Inherited from structure.parent.Parent (private): _has_coerce_map_from

Inherited from object: __class__

Method Details

[hide private]

init(self, H, R, gens, basis=`['4ti2-20061025',` `'R-2.6.0',` `'atlas-3.7.37',` `'atlas-3.8.1',` `'a...`)
(Constructor)

source code


An order in a quaternion algebra.

Overrides: algebra_order.AlgebraOrder_generic.__init__

call(self, x, check=True)
(Call operator)

source code

File: sage/rings/ring.pyx (starting at line 37)

Coerce x into the ring.

Overrides: algebra_order.AlgebraOrder_generic.__call__

repr(self)
(Representation operator)

source code

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

Overrides: algebra_order.AlgebraOrder_generic.__repr__

random_element(self)

source code

File: sage/rings/ring.pyx (starting at line 642)

Return a random integer coerced into this ring, where the
integer is chosen uniformly from the interval [-bound,bound].

INPUT:
    bound -- integer (default: 2)
    
ALGORITHM:
     -- uses Python's randint.

TESTS:
The following example returns a NotImplementedError since the generic
ring class \code(__call__) function ruturns a NotImplementedError.
Note that \code(sage.rings.ring.Ring.random_element) performs a
call in the generic ring class by a random integer.
    sage: R = sage.rings.ring.Ring(ZZ); R
    <type 'sage.rings.ring.Ring'>
    sage: R.random_element()
    Traceback (most recent call last):
    ...
    NotImplementedError

Overrides: rings.ring.Ring.random_element: (inherited documentation)

Class QuaternionOrder_generic

__init__(self, H, R, gens, basis=['4ti2-20061025', 'R-2.6.0', 'atlas-3.7.37', 'atlas-3.8.1', 'a...) (Constructor)

__call__(self, x, check=True) (Call operator)

__repr__(self) (Representation operator)

random_element(self)

init(self, H, R, gens, basis=`['4ti2-20061025',` `'R-2.6.0',` `'atlas-3.7.37',` `'atlas-3.8.1',` `'a...`)
(Constructor)

call(self, x, check=True)
(Call operator)

repr(self)
(Representation operator)