AUTHORS:
Elements of free monoids are represented internally as lists of pairs of integers.
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)
...
TypeError: bad operand type for unary ~: 'FreeMonoidElement'
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]
AUTHORS:
Create the element of the FreeMonoid
.
This should typically be called by a FreeMonoid.
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 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
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
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