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

Algebra::PermutationGroup

ִΥ饹ǤǤȤ Permutation Υ󥹥󥹤ꤵƤȤ


ե̾:

  permutation-group.rb

ѡ饹:

  Group

饹᥽å:

::new(u, [g0, [g1, ...]])
    u ñ̸Ȥg0, g1, ... ǹ뷲֤ޤ
   
::unit_group(d)
     d ñ̷֤ޤ
   
::unity(n)
     n ñ̸֤ޤ
   
::perm(a)
     a ɽִ֤ޤ
   
::symmetric(n)
    n оη֤ޤ
   
::alternate(n)
    n θ已֤ޤ
   

Algebra::Permutation

ִɽ륯饹Ǥ

ե̾:

  permutation-group.rb

ѡ饹:

  Object

󥯥롼ɤƤ⥸塼:

  Enumerable
  Powers

饹᥽å:

::new(x)
    x Ȥɽִޤ
   
::[[n0, [n1, [n2, ..., ]]]]
    [n0, n1, n2, ..., ] Ȥִޤ
    a = Permutation[1, 2, 0]
    p a**2 #=> [2, 0, 1]
    p a**3 #=> [0, 1, 2]
   
::unity(d)
    d ñ̸֤ޤ
   
::cyclic2perm(c, n)
    c Ȥִɽ󤫤顢Permutation ֥Ȥޤ
    n ϼǤ decompose_cyclic εդǤ
   
    :
    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]]
   

᥽å:

unity
    ñ̸֤ޤ
   
perm
    ɽ֤ޤ
   
degree
    ֤ޤ
   
size
    degree ΥꥢǤ
   
each
    ִγƸˤĤƷ֤ޤ
   
eql?(other)
    other Ȥ֤ޤ
   
==
    eql? ΥꥢǤ
   
hash
    ϥå֤ͤޤ
   
[i]
    i ִ֤ޤ
   
call
    [] ΥꥢǤ
   
index(i)
    i ִ֤ޤ
   
right_act(other)
    other 򱦤餫ޤʤ (g.right_act(h))[x] == h[g[x]] Ω
    
   
*
    right_act ΥꥢǤ
   
left_act(other)
    other 򺸤餫餫ޤʤ (g.left_act(h))[x] == g[h[x]] Ω
    ޤ
   
inverse
    ո֤ޤ
   
inv
    inverse ΥꥢǤ
   
sign
    ֤ޤ
   
conjugate(g)
    g ˤ붦 g * self * g.inv ֤ޤ
   
decompose_cyclic
    ˤɽ֤ޤ ::cyclic2perm(c, n) εդǤ
   
to_map
    Map ֥Ȳޤ
   
decompose_transposition
    ߴʬ򤷤Τ֤ޤ
   

