Module: sage.monoids.free_monoid_element
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
x) |
Class: FreeMonoidElement
self, F, x, [check=True]) |
Create the element
of the FreeMonoid
.
This should typically be called by a FreeMonoid.
Special Functions: __cmp__,
__len__,
__mul__,
__pow__,
__repr__,
_latex_
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
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
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
self, 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 a0*a1*a4^3*a0*a1*a4^3*a0*a1*a4^3 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.
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_() 'a0^{5}a1^{2}a0^{12}a1^{2}'
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