Package sage :: Package algebras :: Module quaternion_algebra_element :: Class QuaternionAlgebraElement_fast

Class QuaternionAlgebraElement_fast

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

Instance Methods

[hide private]

__init__(self, H, x)
Create the element x of the quaternion algebra H.

source code

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

source code

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

source code

_neg_(self, other)
File: sage/structure/element.pyx (starting at line 879) Python classes should override this function to implement negation.

source code

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

source code

conjugate(self)
Return the conjugate of this element.

source code

Inherited from QuaternionAlgebraElement: __cmp__, _backslash_, _div_, additive_order, characteristic_polynomial, charpoly, is_pure, is_scalar, is_unit, minimal_polynomial, minpoly, pure_part, reduced_norm, reduced_trace, scalar_part

Inherited from free_algebra_quotient_element.FreeAlgebraQuotientElement: __neg__, _latex_, _lmul_, _repr_, _rmul_, vector

Inherited from structure.element.AlgebraElement: __new__

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

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

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, H, x)
(Constructor)

source code


Create the element x of the quaternion algebra H.

Overrides: QuaternionAlgebraElement.__init__: (inherited documentation)

_add_(self, other)

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: free_algebra_quotient_element.FreeAlgebraQuotientElement._add_

_sub_(self, other)

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: free_algebra_quotient_element.FreeAlgebraQuotientElement._sub_

_neg_(self, other)

source code

File: sage/structure/element.pyx (starting at line 879)

Python classes should override this function to implement negation.

See extensive documentation at the top of element.pyx.

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

_mul_(self, other)

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: free_algebra_quotient_element.FreeAlgebraQuotientElement._mul_

conjugate(self)

source code


Return the conjugate of this element.

EXAMPLES:
    sage: A.<i,j,k>=QuaternionAlgebra(QQ,-5,-2)
    sage: x=3*i-j+2
    sage: x.conjugate()
    2 - 3*i + j

Overrides: QuaternionAlgebraElement.conjugate: (inherited documentation)

Class QuaternionAlgebraElement_fast

__init__(self, H, x) (Constructor)

_add_(self, other)

_sub_(self, other)

_neg_(self, other)

_mul_(self, other)

conjugate(self)

init(self, H, x)
(Constructor)