Package sage :: Package monoids :: Module free_monoid_element :: Class FreeMonoidElement

Class FreeMonoidElement

                      object --+            
                               |            
structure.sage_object.SageObject --+        
                                   |        
           structure.element.Element --+    
                                       |    
         structure.element.MonoidElement --+
                                           |
                                          FreeMonoidElement

Known Subclasses:: string_monoid_element.StringMonoidElement


Element of a free monoid.

EXAMPLES:
        sage: a = FreeMonoid(5, 'a').gens()
        sage: x = a[0]*a[1]*a[4]**3
        sage: x**3
        a0*a1*a4^3*a0*a1*a4^3*a0*a1*a4^3
        sage: x**0
        1
        sage: x**(-1)
        Traceback (most recent call last):
        ...
        TypeError: bad operand type for unary ~: 'FreeMonoidElement'

Instance Methods

[hide private]

__init__(self, F, x, check=True)
Create the element $x$ of the FreeMonoid $F$.

source code

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

source code

_latex_(self)
Return latex representation of self.

source code

__call__(self, *x, **kwds)
EXAMPLES: sage: M.<x,y,z>=FreeMonoid(3) sage: (x*y).subs(x=1,y=2,z=14) 2 sage: (x*y).subs({x:z,y:z}) z^2 sage: M1=MatrixSpace(ZZ,1,2) sage: M2=MatrixSpace(ZZ,2,1) sage: (x*y).subs({x:M1([1,2]),y:M2([3,4])}) [11] AUTHOR: -- Joel B.

source code

__mul__(self, y)
Multiply 2 free monoid elements.

source code

__len__(self)
Return the number of products that occur in this monoid element.

source code

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

source code

Inherited from structure.element.MonoidElement: __new__, __nonzero__, __pow__, __rmul__, __rpow__, _mul_, multiplicative_order, order

Inherited from structure.element.Element: __eq__, __ge__, __gt__, __hash__, __le__, __lt__, __ne__, __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, F, x, check=True)
(Constructor)

source code


Create the element $x$ of the FreeMonoid $F$.

This should typically be called by a FreeMonoid.

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)

_latex_(self)

source code


Return latex representation of self.

EXAMPLES:
    sage: F = FreeMonoid(3, 'a')
    sage: z = F([(0,5),(1,2),(0,10),(0,2),(1,2)])
    sage: z._latex_()
    'a_{0}^{5}a_{1}^{2}a_{0}^{12}a_{1}^{2}'
    sage: F, (alpha,beta,gamma) = FreeMonoid(3, 'alpha,beta,gamma').objgens()
    sage: latex(alpha*beta*gamma)
    \alpha\beta\gamma

call(self, *x, **kwds)
(Call operator)

source code


EXAMPLES:
    sage: M.<x,y,z>=FreeMonoid(3)
    sage: (x*y).subs(x=1,y=2,z=14)
    2
    sage: (x*y).subs({x:z,y:z})
    z^2
    sage: M1=MatrixSpace(ZZ,1,2)
    sage: M2=MatrixSpace(ZZ,2,1)
    sage: (x*y).subs({x:M1([1,2]),y:M2([3,4])})
    [11]

AUTHOR:
    -- Joel B. Mohler (2007.10.27)

mul(self, y)

source code


Multiply 2 free monoid elements.

EXAMPLES:
    sage: a = FreeMonoid(5, 'a').gens()
    sage: x = a[0] * a[1] * a[4]**3
    sage: y = a[4] * a[0] * a[1]
    sage: x*y
    a0*a1*a4^4*a0*a1

Overrides: structure.element.MonoidElement.__mul__

len(self)
(Length operator)

source code


Return the number of products that occur in this monoid element.
For example, the length of the identity is 0, and the length
of the monoid $x_0^2x_1$ is three.

EXAMPLES:
    sage: F = FreeMonoid(3, 'a')
    sage: z = F(1)
    sage: len(z)
    0
    sage: a = F.gens()
    sage: len(a[0]**2 * a[1])
    3

cmp(self, y)
(Comparison operator)

source code

cmp(x,y)

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

Class FreeMonoidElement

__init__(self, F, x, check=True) (Constructor)

_repr_(self)

_latex_(self)

__call__(self, *x, **kwds) (Call operator)

__mul__(self, y)

__len__(self) (Length operator)

__cmp__(self, y) (Comparison operator)

init(self, F, x, check=True)
(Constructor)

call(self, *x, **kwds)
(Call operator)

mul(self, y)

len(self)
(Length operator)

cmp(self, y)
(Comparison operator)