F, x, [check=True]) |
Create the element
of the FreeMonoid
.
This should typically be called by a FreeMonoid.
Instances of class FreeMonoidElement also have the following special methods:
__cmp__,
__len__,
__mul__,
__pow__,
__repr__,
_latex_
Further documentation:
) |
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.
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
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 a_0*a_1*a_4^4*a_0*a_1
n) |
Return the
-th power of this monoid element.
sage: a = FreeMonoid(5, 'a').gens() sage: x = a[0]*a[1]*a[4]**3 sage: x**3 a_0*a_1*a_4^3*a_0*a_1*a_4^3*a_0*a_1*a_4^3 sage: x**0 1
Note that raising to a negative power is not a constructor for an element of the corresponding free group (yet).
sage: x**(-1) Traceback (most recent call last): ... IndexError: Argument n (= -1) must be non-negative.
) |
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}'
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