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Package sage :: Package modules :: Module free_module :: Class FreeModule_ambient_field
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Class FreeModule_ambient_field

source code

                             object --+                                    
                                      |                                    
       structure.sage_object.SageObject --+                                
                                          |                                
                    structure.parent.Parent --+                            
                                              |                            
           structure.parent_base.ParentWithBase --+                        
                                                  |                        
               structure.parent_gens.ParentWithGens --+                    
                                                      |                    
    structure.parent_gens.ParentWithAdditiveAbelianGens --+                
                                                          |                
                                              module.Module --+            
                                                              |            
                                             FreeModule_generic --+        
                                                                  |        
                                             FreeModule_generic_pid --+    
                                                                      |    
                                               FreeModule_generic_field --+
                                                                          |
                             object --+                                   |
                                      |                                   |
       structure.sage_object.SageObject --+                               |
                                          |                               |
                    structure.parent.Parent --+                           |
                                              |                           |
           structure.parent_base.ParentWithBase --+                       |
                                                  |                       |
               structure.parent_gens.ParentWithGens --+                   |
                                                      |                   |
    structure.parent_gens.ParentWithAdditiveAbelianGens --+               |
                                                          |               |
                                              module.Module --+           |
                                                              |           |
                                             FreeModule_generic --+       |
                                                                  |       |
                                             FreeModule_generic_pid --+   |
                                                                      |   |
                         object --+                                   |   |
                                  |                                   |   |
   structure.sage_object.SageObject --+                               |   |
                                      |                               |   |
                structure.parent.Parent --+                           |   |
                                          |                           |   |
       structure.parent_base.ParentWithBase --+                       |   |
                                              |                       |   |
           structure.parent_gens.ParentWithGens --+                   |   |
                                                  |                   |   |
structure.parent_gens.ParentWithAdditiveAbelianGens --+               |   |
                                                      |               |   |
                                          module.Module --+           |   |
                                                          |           |   |
                                         FreeModule_generic --+       |   |
                                                              |       |   |
                                             FreeModule_ambient --+   |   |
                                                                  |   |   |
                                          FreeModule_ambient_domain --+   |
                                                                      |   |
                                                 FreeModule_ambient_pid --+
                                                                          |
                                                                         FreeModule_ambient_field
Known Subclasses:
quotient_module.FreeModule_ambient_field_quotient, ComplexDoubleVectorSpace_class, RealDoubleVectorSpace_class
Instance Methods [hide private]
 
__init__(self, base_field, dimension, sparse=False, inner_product_matrix=['4ti2-20061025', 'R-2.6.0', 'atlas-3.7.37', 'atlas-3.8.1', 'a...) source code
 
_repr_(self) source code
 
ambient_vector_space(self)
Returns the ambient vector space.		 source code
 
base_field(self)
Returns the base field of this vector space.		 source code
 
__call__(self, e, coerce=True, copy=True, check=True)
EXAMPLE:...		 source code

Inherited from FreeModule_generic_field: __add__, __div__, category, echelonized_basis_matrix, intersection, is_subspace, quotient, quotient_abstract, scale, span, span_of_basis, subspace, subspace_with_basis, vector_space, zero_submodule, zero_subspace

Inherited from FreeModule_generic_pid: __radd__, basis_matrix, denominator, index_in, index_in_saturation, is_submodule, saturation, submodule, submodule_with_basis, vector_space_span, vector_space_span_of_basis

Inherited from FreeModule_ambient_domain: coordinate_vector

Inherited from FreeModule_ambient: __cmp__, __hash__, _latex_, ambient_module, basis, change_ring, echelon_coordinate_vector, echelon_coordinates, echelonized_basis, is_ambient, linear_combination_of_basis

Inherited from FreeModule_ambient (private): _dense_module, _sparse_module

Inherited from FreeModule_generic: __contains__, __iter__, __len__, _magma_init_, base_extend, construction, coordinate_module, coordinates, degree, dense_module, dimension, direct_sum, discriminant, element_class, free_module, gen, gram_matrix, has_user_basis, inner_product_matrix, is_dense, is_finite, is_full, is_sparse, matrix, ngens, nonembedded_free_module, random_element, rank, sparse_module, uses_ambient_inner_product, zero_vector

Inherited from FreeModule_generic (private): _an_element_impl, _coerce_impl, _has_coerce_map_from_space, _inner_product_is_dot_product

Inherited from module.Module: __new__, endomorphism_ring, is_atomic_repr

Inherited from structure.parent_gens.ParentWithAdditiveAbelianGens: generator_orders

Inherited from structure.parent_gens.ParentWithGens: __getitem__, __getslice__, __getstate__, __setstate__, _is_valid_homomorphism_, gens, 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, base_ring

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

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

Inherited from structure.sage_object.SageObject: __repr__, _axiom_, _axiom_init_, _gap_, _gap_init_, _gp_, _gp_init_, _interface_, _interface_init_, _interface_is_cached_, _kash_, _kash_init_, _macaulay2_, _macaulay2_init_, _magma_, _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 structure.parent_gens.ParentWithAdditiveAbelianGens (private): _generator_orders

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, base_field, dimension, sparse=False, inner_product_matrix=['4ti2-20061025', 'R-2.6.0', 'atlas-3.7.37', 'atlas-3.8.1', 'a...)
(Constructor)

source code 
Overrides: FreeModule_generic_field.__init__

_repr_(self)

source code 
Overrides: FreeModule_ambient_pid._repr_

ambient_vector_space(self)

source code  

Returns the ambient vector space.

EXAMPLES:
    sage: M = QQ^3
    sage: M.ambient_vector_space()
    Vector space of dimension 3 over Rational Field
Overrides: FreeModule_ambient_domain.ambient_vector_space

base_field(self)

source code  

Returns the base field of this vector space. 

EXAMPLES:
    sage: M = QQ^3
    sage: M.base_field()
    Rational Field
Overrides: FreeModule_generic_pid.base_field

__call__(self, e, coerce=True, copy=True, check=True)
(Call operator)

source code  


EXAMPLE:
    sage: k.<a> = GF(3^4)
    sage: VS = k.vector_space()
    sage: VS(a)
    (0, 1, 0, 0)
Overrides: FreeModule_generic.__call__

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