|\^/|     Maple 10 (SUN SPARC SOLARIS)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2005
 \  MAPLE  /  All rights reserved. Maple is a trademark of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
                         "jk: START of    0.mapleinit"


                                 [cos(x)    -sin(x)]
                          Rot := [                 ]
                                 [sin(x)    cos(x) ]


Rot := x -> rtable(1 .. 2, 1 .. 2,

    {(1, 1) = cos(x), (1, 2) = -sin(x), (2, 1) = sin(x), (2, 2) = cos(x)},

================================================================

> C := <<2,1>|<3,1>>; CInv := MI(C);
                                      [2    3]
                                 C  = [      ]
                                      [1    1]

                                      [-1     3]
                              CInv  = [        ]
                                      [ 1    -2]

> Rot(theta);
                          [cos(theta)    -sin(theta)]
                          [                         ]
                          [sin(theta)    cos(theta) ]


::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
> R := Rot(Pi/2);
                                     [0    -1]
                                R  = [       ]
                                     [1     0]

> WeirdR := CInv . R . C;
                                       [ 7    10]
                             WeirdR  = [        ]
                                       [-5    -7]

> WeirdRSqrd := WeirdR . WeirdR ;
                                         [-1     0]
                           WeirdRSqrd  = [        ]
                                         [ 0    -1]



::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
> Q := Rot(Pi/3);
                                  [           1/2]
                                  [          3   ]
                                  [1/2     - ----]
                                  [           2  ]
                             Q  = [              ]
                                  [ 1/2          ]
                                  [3             ]
                                  [----     1/2  ]
                                  [ 2            ]

> WeirdQ := CInv . Q . C ;
                             [         1/2                ]
                             [      7 3             1/2   ]
                             [1/2 + ------       5 3      ]
                             [        2                   ]
                   WeirdQ  = [                            ]
                             [       1/2               1/2]
                             [    5 3               7 3   ]
                             [  - ------      1/2 - ------]
                             [      2                 2   ]


> WeirdQSqrd := simplify(WeirdQ . WeirdQ) ;
                             [           1/2                  ]
                             [        7 3              1/2    ]
                             [- 1/2 + ------        5 3       ]
                             [          2                     ]
               WeirdQSqrd  = [                                ]
                             [        1/2                  1/2]
                             [     5 3                  7 3   ]
                             [   - ------       - 1/2 - ------]
                             [       2                    2   ]

> QSqrd := Q . Q ;
                                    [           1/2]
                                    [          3   ]
                                    [-1/2    - ----]
                                    [           2  ]
                           QSqrd  = [              ]
                                    [ 1/2          ]
                                    [3             ]
                                    [----     -1/2 ]
                                    [ 2            ]


> WeirdifyQSqrd := CInv . QSqrd . C ;
                               [           1/2                  ]
                               [        7 3              1/2    ]
                               [- 1/2 + ------        5 3       ]
                               [          2                     ]
              WeirdifyQSqrd  = [                                ]
                               [        1/2                  1/2]
                               [     5 3                  7 3   ]
                               [   - ------       - 1/2 - ------]
                               [       2                    2   ]


> simplify(WeirdifyQSqrd - WeirdQSqrd) ;
                                   [0    0]
                                   [      ]
                                   [0    0]

> WeirdQCubed := simplify(WeirdQ . WeirdQ . WeirdQ) ;
                                          [-1     0]
                           WeirdQCubed  = [        ]
                                          [ 0    -1]



::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
> P := CInv . Rot(t) . C ;
                      [cos(t) + 7 sin(t)        10 sin(t)    ]
                 P  = [                                      ]
                      [    -5 sin(t)        cos(t) - 7 sin(t)]





> PtoFourth :=  P^4 ;

PtoFourth =

    [   2            2 2
    [(%2  - 50 sin(t) )  + %4 %3 ,

       2            2                     2     2 ]
    (%2  - 50 sin(t) ) %4 + %4 (-50 sin(t)  + %1 )]


    [      2            2               2     2
    [%3 (%2  - 50 sin(t) ) + (-50 sin(t)  + %1 ) %3 ,

                       2     2 2]
    %4 %3 + (-50 sin(t)  + %1 ) ]


%1 := cos(t) - 7 sin(t)

%2 := cos(t) + 7 sin(t)

%3 := -5 %2 sin(t) - 5 sin(t) %1

%4 := 10 %2 sin(t) + 10 sin(t) %1




> PtoFourth  := simplify(PtoFourth) ;
PtoFourth =

  [         3                                     4           2                                    2       ]
  [56 cos(t)  sin(t) - 28 sin(t) cos(t) + 8 cos(t)  - 8 cos(t)  + 1 ,    40 sin(t) cos(t) (2 cos(t)  - 1)  ]
  [                                                                                                        ]
  [                           2                     3                                     4           2    ]
  [-20 sin(t) cos(t) (2 cos(t)  - 1) ,    -56 cos(t)  sin(t) + 28 sin(t) cos(t) + 8 cos(t)  - 8 cos(t)  + 1]




> NewPtoFourth := subs(t = Pi/4, PtoFourth); 
                                          [-1     0]
                          NewPtoFourth  = [        ]
                                          [ 0    -1]


%%%% End of "change-of-basis.txt"