Module permgroup_element

File: sage/groups/perm_gps/permgroup_element.pyx (starting at line 1)

Permutation group elements

AUTHORS:
    - David Joyner (2006-02)
    - David Joyner (2006-03), word problem method and reorganization
    - Robert Bradshaw (2007-11), convert to Cython

EXAMPLES:
The Rubik's cube group:
    sage: f= [(17,19,24,22),(18,21,23,20),(6,25,43,16),(7,28,42,13),(8,30,41,11)]
    sage: b=[(33,35,40,38),(34,37,39,36),( 3, 9,46,32),( 2,12,47,29),( 1,14,48,27)]
    sage: l=[( 9,11,16,14),(10,13,15,12),( 1,17,41,40),( 4,20,44,37),( 6,22,46,35)]
    sage: r=[(25,27,32,30),(26,29,31,28),( 3,38,43,19),( 5,36,45,21),( 8,33,48,24)]
    sage: u=[( 1, 3, 8, 6),( 2, 5, 7, 4),( 9,33,25,17),(10,34,26,18),(11,35,27,19)]
    sage: d=[(41,43,48,46),(42,45,47,44),(14,22,30,38),(15,23,31,39),(16,24,32,40)]
    sage: cube = PermutationGroup([f,b,l,r,u,d])
    sage: F=cube.gens()[0]
    sage: B=cube.gens()[1]
    sage: L=cube.gens()[2]
    sage: R=cube.gens()[3]
    sage: U=cube.gens()[4]
    sage: D=cube.gens()[5]
    sage: cube.order()
    43252003274489856000
    sage: F.order()
    4
    
The interested user may wish to explore the following commands:
move = cube.random_element() and time word_problem([F,B,L,R,U,D], move, False).
This typically takes about 5 minutes (on a 2 Ghz machine) and outputs 
a word ('solving' the cube in the position move) with about 60 terms 
or so.

OTHER EXAMPLES:
We create element of a permutation group of large degree.
    sage: G = SymmetricGroup(30)
    sage: s = G(srange(30,0,-1)); s
    (1,30)(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)