> with(linalg):
Warning, new definition for norm
Warning, new definition for trace
> A := matrix(3,7);

                    A := array(1 .. 3, 1 .. 7, [])

> B := matrix(7, 2);

                    B := array(1 .. 7, 1 .. 2, [])

> print(A);

        [A[1, 1] , A[1, 2] , A[1, 3] , A[1, 4] , A[1, 5] , A[1, 6] ,

        A[1, 7]]

        [A[2, 1] , A[2, 2] , A[2, 3] , A[2, 4] , A[2, 5] , A[2, 6] ,

        A[2, 7]]

        [A[3, 1] , A[3, 2] , A[3, 3] , A[3, 4] , A[3, 5] , A[3, 6] ,

        A[3, 7]]

> print(B);

                         [B[1, 1]    B[1, 2]]
                         [                  ]
                         [B[2, 1]    B[2, 2]]
                         [                  ]
                         [B[3, 1]    B[3, 2]]
                         [                  ]
                         [B[4, 1]    B[4, 2]]
                         [                  ]
                         [B[5, 1]    B[5, 2]]
                         [                  ]
                         [B[6, 1]    B[6, 2]]
                         [                  ]
                         [B[7, 1]    B[7, 2]]

> evalm(A &* B);

        [A[1, 1] B[1, 1] + A[1, 2] B[2, 1] + A[1, 3] B[3, 1]

         + A[1, 4] B[4, 1] + A[1, 5] B[5, 1] + A[1, 6] B[6, 1]

         + A[1, 7] B[7, 1] , A[1, 1] B[1, 2] + A[1, 2] B[2, 2]

         + A[1, 3] B[3, 2] + A[1, 4] B[4, 2] + A[1, 5] B[5, 2]

         + A[1, 6] B[6, 2] + A[1, 7] B[7, 2]]

        [A[2, 1] B[1, 1] + A[2, 2] B[2, 1] + A[2, 3] B[3, 1]

         + A[2, 4] B[4, 1] + A[2, 5] B[5, 1] + A[2, 6] B[6, 1]

         + A[2, 7] B[7, 1] , A[2, 1] B[1, 2] + A[2, 2] B[2, 2]

         + A[2, 3] B[3, 2] + A[2, 4] B[4, 2] + A[2, 5] B[5, 2]

         + A[2, 6] B[6, 2] + A[2, 7] B[7, 2]]

        [A[3, 1] B[1, 1] + A[3, 2] B[2, 1] + A[3, 3] B[3, 1]

         + A[3, 4] B[4, 1] + A[3, 5] B[5, 1] + A[3, 6] B[6, 1]

         + A[3, 7] B[7, 1] , A[3, 1] B[1, 2] + A[3, 2] B[2, 2]

         + A[3, 3] B[3, 2] + A[3, 4] B[4, 2] + A[3, 5] B[5, 2]

         + A[3, 6] B[6, 2] + A[3, 7] B[7, 2]]

> C := matrix(7,2);

                    C := array(1 .. 7, 1 .. 2, [])

> LS := evalm(A &* (B + C));

  LS :=

        [A[1, 1] (B[1, 1] + C[1, 1]) + A[1, 2] (B[2, 1] + C[2, 1])

         + A[1, 3] (B[3, 1] + C[3, 1]) + A[1, 4] (B[4, 1] + C[4, 1])

         + A[1, 5] (B[5, 1] + C[5, 1]) + A[1, 6] (B[6, 1] + C[6, 1])

         + A[1, 7] (B[7, 1] + C[7, 1]) , A[1, 1] (B[1, 2] + C[1, 2])

         + A[1, 2] (B[2, 2] + C[2, 2]) + A[1, 3] (B[3, 2] + C[3, 2])

         + A[1, 4] (B[4, 2] + C[4, 2]) + A[1, 5] (B[5, 2] + C[5, 2])

         + A[1, 6] (B[6, 2] + C[6, 2]) + A[1, 7] (B[7, 2] + C[7, 2])]

        [A[2, 1] (B[1, 1] + C[1, 1]) + A[2, 2] (B[2, 1] + C[2, 1])

         + A[2, 3] (B[3, 1] + C[3, 1]) + A[2, 4] (B[4, 1] + C[4, 1])

         + A[2, 5] (B[5, 1] + C[5, 1]) + A[2, 6] (B[6, 1] + C[6, 1])

         + A[2, 7] (B[7, 1] + C[7, 1]) , A[2, 1] (B[1, 2] + C[1, 2])

         + A[2, 2] (B[2, 2] + C[2, 2]) + A[2, 3] (B[3, 2] + C[3, 2])

         + A[2, 4] (B[4, 2] + C[4, 2]) + A[2, 5] (B[5, 2] + C[5, 2])

         + A[2, 6] (B[6, 2] + C[6, 2]) + A[2, 7] (B[7, 2] + C[7, 2])]

        [A[3, 1] (B[1, 1] + C[1, 1]) + A[3, 2] (B[2, 1] + C[2, 1])

         + A[3, 3] (B[3, 1] + C[3, 1]) + A[3, 4] (B[4, 1] + C[4, 1])

         + A[3, 5] (B[5, 1] + C[5, 1]) + A[3, 6] (B[6, 1] + C[6, 1])

         + A[3, 7] (B[7, 1] + C[7, 1]) , A[3, 1] (B[1, 2] + C[1, 2])

         + A[3, 2] (B[2, 2] + C[2, 2]) + A[3, 3] (B[3, 2] + C[3, 2])

         + A[3, 4] (B[4, 2] + C[4, 2]) + A[3, 5] (B[5, 2] + C[5, 2])

         + A[3, 6] (B[6, 2] + C[6, 2]) + A[3, 7] (B[7, 2] + C[7, 2])]

> RS := evalm( A &* B + A &* C);

  RS :=

        [A[1, 1] B[1, 1] + A[1, 2] B[2, 1] + A[1, 3] B[3, 1]

         + A[1, 4] B[4, 1] + A[1, 5] B[5, 1] + A[1, 6] B[6, 1]

         + A[1, 7] B[7, 1] + A[1, 1] C[1, 1] + A[1, 2] C[2, 1]

         + A[1, 3] C[3, 1] + A[1, 4] C[4, 1] + A[1, 5] C[5, 1]

         + A[1, 6] C[6, 1] + A[1, 7] C[7, 1] , A[1, 1] B[1, 2]

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

         + A[1, 5] B[5, 2] + A[1, 6] B[6, 2] + A[1, 7] B[7, 2]

         + A[1, 1] C[1, 2] + A[1, 2] C[2, 2] + A[1, 3] C[3, 2]

         + A[1, 4] C[4, 2] + A[1, 5] C[5, 2] + A[1, 6] C[6, 2]

         + A[1, 7] C[7, 2]]

        [A[2, 1] B[1, 1] + A[2, 2] B[2, 1] + A[2, 3] B[3, 1]

         + A[2, 4] B[4, 1] + A[2, 5] B[5, 1] + A[2, 6] B[6, 1]

         + A[2, 7] B[7, 1] + A[2, 1] C[1, 1] + A[2, 2] C[2, 1]

         + A[2, 3] C[3, 1] + A[2, 4] C[4, 1] + A[2, 5] C[5, 1]

         + A[2, 6] C[6, 1] + A[2, 7] C[7, 1] , A[2, 1] B[1, 2]

         + A[2, 2] B[2, 2] + A[2, 3] B[3, 2] + A[2, 4] B[4, 2]

         + A[2, 5] B[5, 2] + A[2, 6] B[6, 2] + A[2, 7] B[7, 2]

         + A[2, 1] C[1, 2] + A[2, 2] C[2, 2] + A[2, 3] C[3, 2]

         + A[2, 4] C[4, 2] + A[2, 5] C[5, 2] + A[2, 6] C[6, 2]

         + A[2, 7] C[7, 2]]

        [A[3, 1] B[1, 1] + A[3, 2] B[2, 1] + A[3, 3] B[3, 1]

         + A[3, 4] B[4, 1] + A[3, 5] B[5, 1] + A[3, 6] B[6, 1]

         + A[3, 7] B[7, 1] + A[3, 1] C[1, 1] + A[3, 2] C[2, 1]

         + A[3, 3] C[3, 1] + A[3, 4] C[4, 1] + A[3, 5] C[5, 1]

         + A[3, 6] C[6, 1] + A[3, 7] C[7, 1] , A[3, 1] B[1, 2]

         + A[3, 2] B[2, 2] + A[3, 3] B[3, 2] + A[3, 4] B[4, 2]

         + A[3, 5] B[5, 2] + A[3, 6] B[6, 2] + A[3, 7] B[7, 2]

         + A[3, 1] C[1, 2] + A[3, 2] C[2, 2] + A[3, 3] C[3, 2]

         + A[3, 4] C[4, 2] + A[3, 5] C[5, 2] + A[3, 6] C[6, 2]

         + A[3, 7] C[7, 2]]

> equal(map(expand, LS), map(expand, RS));

                                 true

> equal(LS, RS);

                                false

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

                                 [0    1]
                            T := [      ]
                                 [1    1]

> v := vector([1,1]);

                             v := [1, 1]

> evalm(T &* v);

                                [1, 2]

> evalm(T^10 &* v);

                              [89, 144]

> TT := T;

                               TT := T

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

                                  [1    1]
                            TT := [      ]
                                  [1    2]


                                  [2    3]
                            TT := [      ]
                                  [3    5]


                                 [13    21]
                           TT := [        ]
                                 [21    34]


                               [610     987]
                         TT := [           ]
                               [987    1597]


                            [1346269    2178309]
                      TT := [                  ]
                            [2178309    3524578]


                     [ 6557470319842    10610209857723]
               TT := [                                ]
                     [10610209857723    17167680177565]


  TT :=

        [155576970220531065681649693 , 251728825683549488150424261]

        [251728825683549488150424261 , 407305795904080553832073954]


  TT :=

        [87571595343018854458033386304178158174356588264390370 ,

        141693817714056513234709965875411919657707794958199867]

        [141693817714056513234709965875411919657707794958199867 ,

        229265413057075367692743352179590077832064383222590237]


  TT :=

        [277459222893057168553384709160828150293488720296478308619\

        14852073402148308000613611082094085891168867554589 , 448938\
        4531330994297807729816066062664618188362388623979126969446\

        6661322268805744081870933775586567858979269]

        [448938453133099429780772981606606266461818836238862397912\

        69694466661322268805744081870933775586567858979269 , 726397\
        6760261565983341576907674344167553075565353407065318454654\

        0063470576806357692953027861477736726533858]


  TT :=

        [278529355069959292393881241266809350935330735212370380691\
        3182668987369503203465183625616759613324452749958549669966\
        8821911178954250152084554694037312726521582408256284848181\

        31485544230827304940519132195299466733282 , 450669963367781\
        9813104383235728886049367860596218604830803023149600030645\
        7087213962487926091410303962448732665803450112195302093674\
        2558101987106764609420026228520234665586889971108924677841\

        3354004103631553925405243]

        [450669963367781981310438323572888604936786059621860483080\
        3023149600030645708721396248792609141030396244873266580345\
        0112195302093674255810198710676460942002622852023466558688\

        99711089246778413354004103631553925405243 , 729199318437741\
        2737043195648396979558721167948342308637716205818587400148\
        9121865798744093687543548489948318162503118934106481047924\
        4078947534047137736685242052602797514068703119663347760571\

        8294523235826853392138525]

> vv := evalm(TT &* v);

  vv := [729199318437741273704319564839697955872116794834230863771\
        6205818587400148912186579874409368754354848994831816250311\
        8934106481047924407894753404713773668524205260279751406870\

        31196633477605718294523235826853392138525, 1179869281805523\
        2550147578884125865608089028544560913468519228968187430794\
        6209079761232019778953852452397050828306569046301783141598\
        6637049521153902346105268281123032179655593090772272438413\

        1648527339458407317543768]

> vv[1];

  7291993184377412737043195648396979558721167948342308637716205818\
        5874001489121865798744093687543548489948318162503118934106\
        4810479244078947534047137736685242052602797514068703119663\
        3477605718294523235826853392138525

> ?fibonacci
> with(combinat);
Warning, new definition for Chi
Warning, new definition for fibonacci

  [Chi, bell, binomial, cartprod, character, choose, composition,

        conjpart, decodepart, encodepart, fibonacci, firstpart,

        graycode, inttovec, lastpart, multinomial, nextpart, numbcomb,

        numbcomp, numbpart, numbperm, partition, permute, powerset,

        prevpart, randcomb, randpart, randperm, stirling1, stirling2,

        subsets, vectoint]

> fibonacci(11);

                                  89

> fibonacci(2^10 + 1);

  7291993184377412737043195648396979558721167948342308637716205818\
        5874001489121865798744093687543548489948318162503118934106\
        4810479244078947534047137736685242052602797514068703119663\
        3477605718294523235826853392138525

> vv[1];

  7291993184377412737043195648396979558721167948342308637716205818\
        5874001489121865798744093687543548489948318162503118934106\
        4810479244078947534047137736685242052602797514068703119663\
        3477605718294523235826853392138525

> fibonacci(-1);

                                  1

> for i from -1 by -1 while i > -10 do print(fibonacci(i)); od;

                                  1


                                  -1


                                  2


                                  -3


                                  5


                                  -8


                                  13


                                 -21


                                  34

> evalm(T^(-10) &* v);

                              [34, -21]

>