21.2 Monoid Elements

Module: sage.monoids.free_monoid_element

Monoid Elements

Author: David Kohel (kohel@maths.usyd.edu.au), 2005/09/29

Elements of free monoids are represented internally as lists of pairs of integers.

Module-level Functions

is_FreeMonoidElement( x)

Class: FreeMonoidElement

class FreeMonoidElement
Element of a free monoid.

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'
FreeMonoidElement( self, F, x, [check=True])

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

This should typically be called by a FreeMonoid.

Special Functions: __call__,$ \,$ __cmp__,$ \,$ __init__,$ \,$ __len__,$ \,$ __mul__,$ \,$ _latex_,$ \,$ _repr_

__call__( self)

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)

__len__( self)

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.

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

__mul__( self, y)

Multiply 2 free monoid elements.

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

_latex_( self)

Return latex representation of self.

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

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