Package sage :: Package algebras :: Module algebra_order :: Class AlgebraOrder_generic
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Class AlgebraOrder_generic

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


An order in an algebra.



Instance Methods [hide private]
 
__init__(self, A, R, gens=[], basis=['4ti2-20061025', 'R-2.6.0', 'atlas-3.7.37', 'atlas-3.8.1', 'a..., rank=0)
x.__init__(...) initializes x; see x.__class__.__doc__ for signature
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__repr__(self)
File: sage/structure/sage_object.pyx (starting at line 86)
source code
 
__call__(self, x, check=True)
File: sage/rings/ring.pyx (starting at line 37) Coerce x into the ring.
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__contains__(self, x)
y in x
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ambient_algebra(self)
Return the ambient algebra of this algebra order
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base_ring(self)
Return the base ring of this algebra order
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__compute_order_basis(self)
Compute a basis as an order.
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basis(self)
Return the basis of this algebra order
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algebra_basis_elements(self)
Return the basis of this algebra order as a tuple
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embedding_matrix(self)
Return the $n\times n$ matrix whose rows are the vectors expressing the basis elements of this algebra order in terms of the ambient algebra's basis.
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inverse_embedding_matrix(self)
Return the inverse of the $n\times n$ matrix whose rows are the vectors expressing the basis elements of this algebra order in terms of the ambient algebra's basis.
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module(self)
Convert this algebra order into a module over the base ring.
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gen(self, i)
Return the i'th generator of this algebra order
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gens(self)
Return the generators of this algebra order as a tuple
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ngens(self)
Return the number of generators of this algebra order
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rank(self)
Return the rank of this algebra order
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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, random_element, 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_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.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 structure.parent.Parent (private): _has_coerce_map_from

Inherited from object: __class__

Method Details [hide private]

__init__(self, A, R, gens=[], basis=['4ti2-20061025', 'R-2.6.0', 'atlas-3.7.37', 'atlas-3.8.1', 'a..., rank=0)
(Constructor)

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

Overrides: rings.ring.Algebra.__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)

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

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

Coerce x into the ring.

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

__contains__(self, x)
(In operator)

source code 
y in x

Overrides: structure.parent.Parent.__contains__
(inherited documentation)

base_ring(self)

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Return the base ring of this algebra order

Overrides: structure.parent_base.ParentWithBase.base_ring

gen(self, i)

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Return the i'th generator of this algebra order

Overrides: structure.parent_gens.ParentWithGens.gen

gens(self)

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Return the generators of this algebra order as a tuple

Overrides: structure.parent_gens.ParentWithGens.gens

ngens(self)

source code 

Return the number of generators of this algebra order

Overrides: structure.parent_gens.ParentWithGens.ngens