
[index] Algebra::PermutationGroup / Algebra::Permutation

Algebra::PermutationGroup

This is the class of permutations. The elements are assumed to be the instances
of Permutation.

File Name:

 ¡¦ permutation-group.rb

SuperClass:

 ¡¦ Group

Class Methods:

::new(u, [g0, [g1, ...]])
    Returns the group with unit u, whcih consists of g0, g1, ....
   
::unit_group(d)
    Return the unit group of degree d.
   
::unity(n)
    Retunrs the unity of degree n.
   
::perm(a)
    Returns the permuation represented by the array a.
   
::symmetric(n)
    Returns the simmetric group of degree n
   
::alternate(n)
    Returns the alternative group of dgree n.
   

Algebra::Permutation

File Name:

 ¡¦ permutation-group.rb

SuperClass:

 ¡¦ Object

Included Module:

 ¡¦ Enumerable
 ¡¦ Powers

Class Methods:

::new(x)
    Returns the permutaiont represented by the array x.
   
::[[n0, [n1, [n2, ..., ]]]]
    Returns the permutation [n0, n1, n2, ..., ].
   
    Example:
    a = Permutation[1, 2, 0]
    p a**2 #=> [2, 0, 1]
    p a**3 #=> [0, 1, 2]
   
::unity(d)
    Returns the unity of degree d.
   
::cyclic2perm(c, n)
    Returns the Permutation represented by c : the array of arrays of cyclic
    permutations, where n is the degree. This method is the inverse of
    decompose_cyclic.
   
    Example:
    Permutation.cyclic2perm([[1,6,5,4], [2,3]], 7) #=> [0, 6, 3, 2, 1, 4, 5]
    Permutation[0, 6, 3, 2, 1, 4, 5].decompose_cyclic #=> [[1,6,5,4], [2,3]]
   

Methods:

unity
    Returns the unity.
   
perm
    Returns the array which represents self
   
degree
    Returns the degree
   
size
    Alias of degree.
   
each
    Iterates for each entry.
   
eql?(other)
    Returns true if self is equal to other.
   
==
    Alias of eql?.
   
hash
    Returns the hash number.
   
[i]
    Returns the number to which i is transferrd.
   
call
    Alias of [].
   
index(i)
    Returns the number from which i is transferred.
   
right_act(other)
    Returns the value multiplied by other from right. It follows (g.right_act
    (h))[x] == h[g[x]].
   
*
    Alias of right_act
   
left_act(other)
    Returns the value multiplied by other from left. It follows (g.left_act(h))
    [x] == g[h[x]].
   
inverse
    Returns the inverse element.
   
inv
    Alias of inverse.
   
sign
    Returns the sign of self.
   
conjugate(g)
    Returns the conjugate by g: g * self * g.inv.
   
decompose_cyclic
    Returns the array of arrays of cyclic permutations. This is the inverse of
    ::cyclic2perm(c, n).
   
to_map
    Returns the Map object of self.
   
decompose_transposition
    Decompose into the array of the transpositions.
   

