Package sage :: Package algebras :: Module free_algebra_quotient_element :: Class FreeAlgebraQuotientElement

Class FreeAlgebraQuotientElement

                      object --+                    
                               |                    
structure.sage_object.SageObject --+                
                                   |                
           structure.element.Element --+            
                                       |            
         structure.element.ModuleElement --+        
                                           |        
               structure.element.RingElement --+    
                                               |    
                structure.element.AlgebraElement --+
                                                   |
                                                  FreeAlgebraQuotientElement

Known Subclasses:: quaternion_algebra_element.QuaternionAlgebraElement

Instance Methods

[hide private]

__init__(self, A, x)
Create the element x of the FreeAlgebraQuotient A.

source code

_repr_(self)
File: sage/structure/element.pyx (starting at line 291)

source code

_latex_(self)

source code

vector(self)

source code

__cmp__(self, right)
cmp(x,y)

source code

__neg__(self)
File: sage/structure/element.pyx (starting at line 845) Top-level negation operator for ModuleElements.

source code

_add_(self, y)
File: sage/structure/element.pyx (starting at line 746) Python classes should override this function to implement addition.

source code

_sub_(self, y)
File: sage/structure/element.pyx (starting at line 816) Python classes should override this function to implement subtraction.

source code

_mul_(self, y)
File: sage/structure/element.pyx (starting at line 1395) Python classes should override this function to implement multiplication.

source code

_rmul_(self, c)
File: sage/structure/element.pyx (starting at line 997)

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_lmul_(self, c)
File: sage/structure/element.pyx (starting at line 1023)

source code

Inherited from structure.element.AlgebraElement: __new__

Inherited from structure.element.RingElement: __div__, __idiv__, __imul__, __invert__, __mul__, __pos__, __pow__, __rdiv__, __rmul__, __rpow__, __rtruediv__, __truediv__, _div_, _idiv_, _imul_, abs, additive_order, is_nilpotent, is_one, is_unit, multiplicative_order, order

Inherited from structure.element.ModuleElement: __add__, __iadd__, __isub__, __radd__, __rsub__, __sub__, _iadd_, _ilmul_, _isub_, _neg_

Inherited from structure.element.ModuleElement (private): _lmul_nonscalar, _rmul_nonscalar

Inherited from structure.element.Element: __eq__, __ge__, __gt__, __hash__, __le__, __lt__, __ne__, __nonzero__, __reduce__, __rxor__, __xor__, _cmp_, _im_gens_, _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: __repr__, _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, A, x)
(Constructor)

source code


Create the element x of the FreeAlgebraQuotient A.

Overrides: structure.element.Element.__init__

_repr_(self)

source code

File: sage/structure/element.pyx (starting at line 291)

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

cmp(self, right)
(Comparison operator)

source code

cmp(x,y)

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

neg(self)

source code

File: sage/structure/element.pyx (starting at line 845)

Top-level negation operator for ModuleElements.
See extensive documentation at the top of element.pyx.

Overrides: structure.element.ModuleElement.__neg__: (inherited documentation)

_add_(self, y)

source code

File: sage/structure/element.pyx (starting at line 746)

Python classes should override this function to implement addition.

See extensive documentation at the top of element.pyx.

Overrides: structure.element.ModuleElement._add_: (inherited documentation)

_sub_(self, y)

source code

File: sage/structure/element.pyx (starting at line 816)

Python classes should override this function to implement subtraction.

See extensive documentation at the top of element.pyx.

Overrides: structure.element.ModuleElement._sub_: (inherited documentation)

_mul_(self, y)

source code

File: sage/structure/element.pyx (starting at line 1395)

Python classes should override this function to implement multiplication.
See extensive documentation at the top of element.pyx.

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

_rmul_(self, c)

source code

File: sage/structure/element.pyx (starting at line 997)

Overrides: structure.element.ModuleElement._rmul_: (inherited documentation)

_lmul_(self, c)

source code

File: sage/structure/element.pyx (starting at line 1023)

Overrides: structure.element.ModuleElement._lmul_: (inherited documentation)

Class FreeAlgebraQuotientElement

__init__(self, A, x) (Constructor)

_repr_(self)

__cmp__(self, right) (Comparison operator)

__neg__(self)

_add_(self, y)

_sub_(self, y)

_mul_(self, y)

_rmul_(self, c)

_lmul_(self, c)

init(self, A, x)
(Constructor)

cmp(self, right)
(Comparison operator)

neg(self)