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Modes Help # Data Control Program $x$ Plots Calculus Linear Graphs Number Theory Rings
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    $
    %sage
    # Data Calculus Rings
    82
     
    1
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    ## RUN the thing!!
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    print "Rubik cube \n \n"
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    S48=SymmetricGroup(48)
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    R=S48("(25,27,32,30)(26,29,31,28)(3,38,43,19)(5,36,45,21)(8,33,48,24)")
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    L=S48("(9,11,16,14)(10,13,15,12)(1,17,41,40)(4,20,44,37)(6,22,46,35)")
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    U=S48("(1,3,8,6)(2,5,7,4)(9,33,25,17)(10,34,26,18)(11,35,27,19)")
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    D=S48("(41,43,48,46)(42,45,47,44)(14,22,30,38)(15,23,31,39)(16,24,32,40)")
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    F=S48("(17,19,24,22)(18,21,23,20)(6,25,43,16)(7,28,42,13)(8,30,41,11)")
    13
    B=S48("(33,35,40,38)(34,37,39,36)(3,9,46,32)(2,12,47,29)(1,14,48,27)")
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    RC3=S48.subgroup([R,L,U,D,F,B]) # define Rubik’s cube group to be RC3
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    RC3.order()
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    S48("(7,18)") in RC3
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    S48("(7,18)(5,26)") in RC3
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    RC3.is_subgroup(S48)
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    rubik = CubeGroup()
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    print "rubik diagram \n"
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    rubik.display2d("")
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    rubik.order()  # same as RC3
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    R=rubik.R()
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    L=rubik.L()
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    U=rubik.U()
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    D=rubik.D()
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    F=rubik.F()
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    B=rubik.B()
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    show(R)
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    print "solve the 'word problem' \n"
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    state = rubik("(7,18)(5,26)")
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    rubik.solve(state) # calls the word solve algorithm
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    print "\n"
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    B^(-1)
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    F^2 * R^2 * B^(-1) * F^(-1) * D^(-1) * F * D * B * R^2 * F^(-1) * R^(-1) * F^(-1) * R
    42
    F^3
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    rubik.is_subgroup(S48)
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    state in S48
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    Permutation('(1,2,6,5)') in S48
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    show(Permutation('(1,2,6,5)'))
    12
    F=S48("(17,19,24,22)(18,21,23,20)(6,25,43,16)(7,28,42,13)(8,30,41,11)")