|\^/|     Maple 11 (IBM INTEL LINUX)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007
 \  MAPLE  /  All rights reserved. Maple is a trademark of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
# equation on 3^(1/2)+5^(1/3)
#interface(prettyprint=0);
> with(LinearAlgebra):
> 
> x:=3^(1/2)+5^(1/3);
                                     1/2    (1/3)
                               x := 3    + 5

> x2:=expand(x^2);
                                     1/2  (1/3)    (2/3)
                        x2 := 3 + 2 3    5      + 5

> x3:=expand(x^3);
                           1/2      (1/3)      1/2  (2/3)
                  x3 := 3 3    + 9 5      + 3 3    5      + 5

> x4:=expand(x^4);
                         1/2  (1/3)       (2/3)       1/2      (1/3)
           x4 := 9 + 12 3    5      + 18 5      + 20 3    + 5 5

> x5:=expand(x^5);
           1/2       (1/3)       1/2  (2/3)             1/2  (1/3)      (2/3)
  x5 := 9 3    + 45 5      + 30 3    5      + 150 + 25 3    5      + 5 5

> x6:=expand(x^6);
               1/2  (1/3)        (2/3)        1/2        (1/3)       1/2  (2/3)
x6 := 52 + 54 3    5      + 135 5      + 300 3    + 225 5      + 30 3    5

> 
> M:=Matrix([
> [1,0,0,0,0,0],
> [0,1,1,0,0,0],
> [3,0,0,1,2,0],
> [5,3,9,0,0,3],
> [9,20,5,18,12,0],
> [150,9,45,5,25,30]]);
                         [  1     0     0     0     0     0]
                         [                                 ]
                         [  0     1     1     0     0     0]
                         [                                 ]
                         [  3     0     0     1     2     0]
                    M := [                                 ]
                         [  5     3     9     0     0     3]
                         [                                 ]
                         [  9    20     5    18    12     0]
                         [                                 ]
                         [150     9    45     5    25    30]

> 
> v:=Vector([52,300,225,135,54,30]);
                                        [ 52]
                                        [   ]
                                        [300]
                                        [   ]
                                        [225]
                                   v := [   ]
                                        [135]
                                        [   ]
                                        [ 54]
                                        [   ]
                                        [ 30]

> M1:=Transpose(MatrixInverse(M));
                    [     -455     455    769     -785     -1355]
                    [1    ----     ---    ---     ----     -----]
                    [     267      267    267     267       267 ]
                    [                                           ]
                    [      335     -68    -530     265     -131 ]
                    [0     ---     ---    ----     ---     ---- ]
                    [      267     267    267      267     267  ]
                    [                                           ]
                    [     -130     130    29       119     -260 ]
                    [0    ----     ---    ---      ---     ---- ]
                    [     267      267    267      267     267  ]
              M1 := [                                           ]
                    [      -80     80     100      -50      -71 ]
                    [0     ---     ---    ---      ---      --- ]
                    [      267     267    267      267      267 ]
                    [                                           ]
                    [              -5     16       -8       10  ]
                    [0    5/267    ---    ---      ---      --- ]
                    [              267    267      267      267 ]
                    [                                           ]
                    [              -8     -10               16  ]
                    [0    8/267    ---    ---     5/267     --- ]
                    [              267    267               267 ]

> MatrixVectorMultiply(M1,v);
                                     [  2]
                                     [   ]
                                     [ 90]
                                     [   ]
                                     [-27]
                                     [   ]
                                     [ 10]
                                     [   ]
                                     [  9]
                                     [   ]
                                     [  0]

> 
> p:=expand(x^6-9*x^4-10*x^3+27*x^2-90*x-2);
                                     p := 0

> x:='x';
                                     x := x

> factor(x^6-9*x^4-10*x^3+27*x^2-90*x-2);
                       6      4       3       2
                      x  - 9 x  - 10 x  + 27 x  - 90 x - 2

> 
> M:=Matrix([
> [0,1,1,0,0,0],
> [3,0,0,0,1,0],
> [0,0,0,1,1,0],
> [5,0,0,0,0,1],
> [0,0,3,0,0,1],
> [0,5,0,3,0,0]]);
                            [0    1    1    0    0    0]
                            [                          ]
                            [3    0    0    0    1    0]
                            [                          ]
                            [0    0    0    1    1    0]
                       M := [                          ]
                            [5    0    0    0    0    1]
                            [                          ]
                            [0    0    3    0    0    1]
                            [                          ]
                            [0    5    0    3    0    0]

> 
> p:=sort(CharacteristicPolynomial(M,z));
                         6      4       3       2
                   p := z  - 9 z  - 10 z  + 27 z  - 90 z - 2

> quit
bytes used=2410388, alloc=1834672, time=0.06