> with(linalg):
Warning, the protected names norm and trace have been redefined and
unprotected

> Fib := matrix(2,2,[0,1,1,1]);

                                  [0    1]
                           Fib := [      ]
                                  [1    1]

> for i from 1 to 7 do
> Fib := evalm(Fib^2); print(i,Fib); od;

                                  [1    1]
                           Fib := [      ]
                                  [1    2]


                                [1    1]
                             1, [      ]
                                [1    2]


                                  [2    3]
                           Fib := [      ]
                                  [3    5]


                                [2    3]
                             2, [      ]
                                [3    5]


                                 [13    21]
                          Fib := [        ]
                                 [21    34]


                               [13    21]
                            3, [        ]
                               [21    34]


                                [610     987]
                         Fib := [           ]
                                [987    1597]


                              [610     987]
                           4, [           ]
                              [987    1597]


                            [1346269    2178309]
                     Fib := [                  ]
                            [2178309    3524578]


                          [1346269    2178309]
                       5, [                  ]
                          [2178309    3524578]


                     [ 6557470319842    10610209857723]
              Fib := [                                ]
                     [10610209857723    17167680177565]


                   [ 6557470319842    10610209857723]
                6, [                                ]
                   [10610209857723    17167680177565]


  Fib :=

        [155576970220531065681649693 , 251728825683549488150424261]

        [251728825683549488150424261 , 407305795904080553832073954]


  7,

        [155576970220531065681649693 , 251728825683549488150424261]

        [251728825683549488150424261 , 407305795904080553832073954]

> evalm(Fib &* vector([0,1]));

      [251728825683549488150424261, 407305795904080553832073954]

> combinat[fibonacci](128);

                     251728825683549488150424261

> combinat[fibonacci](129);

                     407305795904080553832073954

> golden:=(1+sqrt(5))/2;

                     golden := 1/2 + 1/2 sqrt(5)

> f129:=golden^127;

                                               127
                    f129 := (1/2 + 1/2 sqrt(5))

> evalf(%,30);

                                                   27
                 .347880681146567910619198828846 10

> solve(x^2-x-1,x);

                 1/2 + 1/2 sqrt(5), 1/2 - 1/2 sqrt(5)

> combinat[fibonacci](129)/combinat[fibonacci](128);

                     407305795904080553832073954
                     ---------------------------
                     251728825683549488150424261

> evalf(%);

                             1.618033989

> evalf(golden);

                             1.618033989

> ?identity
> I4:=Matrix(4,4,shape=identity);

                             [1    0    0    0]
                             [                ]
                             [0    1    0    0]
                       I4 := [                ]
                             [0    0    1    0]
                             [                ]
                             [0    0    0    1]

> A := matrix(2,4);

                    A := array(1 .. 2, 1 .. 4, [])

> evalm(A &* I4);
> 

              [A[1, 1]    A[1, 2]    A[1, 3]    A[1, 4]]
              [                                        ]
              [A[2, 1]    A[2, 2]    A[2, 3]    A[2, 4]]

> F2 := matrix(2,2,[0,1,1,1]);

                                  [0    1]
                            F2 := [      ]
                                  [1    1]

> evalm(F2^(-1));

                              [-1    1]
                              [       ]
                              [ 1    0]

>