> with(LinearAlgebra):
> A := matrix(3,3): B := matrix(3,3): C := matrix(3,3):
> rnd := rand(0..10);

  rnd := proc()
local t;
global _seed;
    _seed := irem(427419669081*_seed, 999999999989);
    t := _seed;
    irem(t, 11)
end proc

> rnd();

                                  9

> for i from 1 to 3 do for j from 1 to 3 do
> A[i,j]:=rnd(); B[i,j]:=rnd(); C[i,j]:=rnd();
> od:od:
> print(A);

                           [10    10    5]
                           [             ]
                           [ 6     0    1]
                           [             ]
                           [10     8    9]

> print(B);

                            [8     0    6]
                            [            ]
                            [2    10    4]
                            [            ]
                            [2    10    4]

> print(C);

                            [8    7    6]
                            [           ]
                            [8    0    2]
                            [           ]
                            [6    1    8]

> AB := evalm(A &* B);

                            [110    150    120]
                            [                 ]
                      AB := [ 50     10     40]
                            [                 ]
                            [114    170    128]

> BC := evalm(B &* C);

                             [100    62    96]
                             [               ]
                       BC := [120    18    64]
                             [               ]
                             [120    18    64]

> evalm(AB &* C);

                        [2800    890    1920]
                        [                   ]
                        [ 720    390     640]
                        [                   ]
                        [3040    926    2048]

> evalm(A &* BC);

                        [2800    890    1920]
                        [                   ]
                        [ 720    390     640]
                        [                   ]
                        [3040    926    2048]

> with(combinat):
Warning, the protected name Chi has been redefined and unprotected

> for i from 0 to 10 do print(i,fibonacci(i)); od:

                                 0, 0


                                 1, 1


                                 2, 1


                                 3, 2


                                 4, 3


                                 5, 5


                                 6, 8


                                7, 13


                                8, 21


                                9, 34


                                10, 55

> for i from 0 to -10 by -1 do print(i, fibonacci(i)); od:

                                 0, 0


                                -1, 1


                                -2, -1


                                -3, 2


                                -4, -3


                                -5, 5


                                -6, -8


                                -7, 13


                               -8, -21


                                -9, 34


                               -10, -55

> Fibo:=Matrix(2,2,[[0,1],[1,1]]);

                                   [0    1]
                           Fibo := [      ]
                                   [1    1]

> f := <<0,1>>;

                                    [0]
                               f := [ ]
                                    [1]

> F10 := evalm(Fibo^10);

                                 [34    55]
                          F10 := [        ]
                                 [55    89]

> evalm(F10 &* f);

                                 [55]
                                 [  ]
                                 [89]

> FF := copy(Fibo);

                                  [0    1]
                            FF := [      ]
                                  [1    1]

> for i from 1 to 10 do
> FF := evalm(FF^2); od;

                                  [1    1]
                            FF := [      ]
                                  [1    2]


                                  [2    3]
                            FF := [      ]
                                  [3    5]


                                 [13    21]
                           FF := [        ]
                                 [21    34]


                               [610     987]
                         FF := [           ]
                               [987    1597]


                            [1346269    2178309]
                      FF := [                  ]
                            [2178309    3524578]


                     [ 6557470319842    10610209857723]
               FF := [                                ]
                     [10610209857723    17167680177565]


  FF :=

        [155576970220531065681649693 , 251728825683549488150424261]

        [251728825683549488150424261 , 407305795904080553832073954]


  FF :=

        [87571595343018854458033386304178158174356588264390370 ,

        141693817714056513234709965875411919657707794958199867]

        [141693817714056513234709965875411919657707794958199867 ,

        229265413057075367692743352179590077832064383222590237]


  FF :=

        [277459222893057168553384709160828150293488720296478308619\

        14852073402148308000613611082094085891168867554589 , 448938\
        4531330994297807729816066062664618188362388623979126969446\

        6661322268805744081870933775586567858979269]

        [448938453133099429780772981606606266461818836238862397912\

        69694466661322268805744081870933775586567858979269 , 726397\
        6760261565983341576907674344167553075565353407065318454654\

        0063470576806357692953027861477736726533858]


  FF :=

        [278529355069959292393881241266809350935330735212370380691\
        3182668987369503203465183625616759613324452749958549669966\
        8821911178954250152084554694037312726521582408256284848181\

        31485544230827304940519132195299466733282 , 450669963367781\
        9813104383235728886049367860596218604830803023149600030645\
        7087213962487926091410303962448732665803450112195302093674\
        2558101987106764609420026228520234665586889971108924677841\

        3354004103631553925405243]

        [450669963367781981310438323572888604936786059621860483080\
        3023149600030645708721396248792609141030396244873266580345\
        0112195302093674255810198710676460942002622852023466558688\

        99711089246778413354004103631553925405243 , 729199318437741\
        2737043195648396979558721167948342308637716205818587400148\
        9121865798744093687543548489948318162503118934106481047924\
        4078947534047137736685242052602797514068703119663347760571\

        8294523235826853392138525]

> evalm(FF &* f)[1,1];

  4506699633677819813104383235728886049367860596218604830803023149\
        6000306457087213962487926091410303962448732665803450112195\
        3020936742558101987106764609420026228520234665586889971108\
        9246778413354004103631553925405243

> fibonacci(2^10);

  4506699633677819813104383235728886049367860596218604830803023149\
        6000306457087213962487926091410303962448732665803450112195\
        3020936742558101987106764609420026228520234665586889971108\
        9246778413354004103631553925405243

> rts:=evalf(solve(x^2-x-1,x),30);

  rts := 1.61803398874989484820458683436,

        -.618033988749894848204586834360

> Phi:=rts[1];

                Phi := 1.61803398874989484820458683436

> evalf(Phi^(2^10)/sqrt(5),30);

                                                  214
                .450669963367781981310438321964 10

>