Maths - Program

There are a number of open source programs that can work with groups. I have used Axiom, how to install Axiom here.

I have put user input in red:

(1) -> genA6 : LIST PERM INT := [cycle [1,2,3], cycle [2,3,4,5,6]]
 (1)  [(1 2 3),(2 3 4 5 6)]
 Type: List Permutation Integer

(2) -> pRA6 := permutationRepresentation(genA6,6)
      +0  0  1  0  0  0+ +1  0  0  0  0  0+
      |                | |                |
      |1  0  0  0  0  0| |0  0  0  0  0  1|
      |                | |                |
      |0  1  0  0  0  0| |0  1  0  0  0  0|
(2)  [|                |,|                |]
      |0  0  0  1  0  0| |0  0  1  0  0  0|
      |                | |                |
      |0  0  0  0  1  0| |0  0  0  1  0  0|
      |                | |                |
      +0  0  0  0  0  1+ +0  0  0  0  1  0+
 Type: List Matrix Integer

(3) -> sp0 := meatAxe(pRA6::(LIST MATRIX PF 2))
 A proper cyclic submodule is found.
 Transition matrix computed
 The inverse of the transition matrix computed
 Now transform the matrices
       +0  0  1  0  0+ +1  0  0  0  0+
       |             | |             |
       |1  0  0  0  0| |1  1  1  1  1|
       |             | |             |
(3)  [[|0  1  0  0  0|,|0  1  0  0  0|],[[1],[1]]]
       |             | |             |
       |0  0  0  1  0| |0  0  1  0  0|
       |             | |             |
       +0  0  0  0  1+ +0  0  0  1  0+
               Type: List List Matrix PrimeField 2


(4) -> sp1 := meatAxe sp0.1
 Fingerprint element in generated algebra is singular
 The generated cyclic submodule was not proper
 The generated cyclic submodule was not proper
 The generated cyclic submodule was not proper
 We know that all the cyclic submodules generated by all
 non-trivial element of the singular matrix under view are
 not proper, hence Norton's irreducibility test can be done:
 A proper cyclic submodule is found.
 Transition matrix computed
 The inverse of the transition matrix computed
 Now transform the matrices
 Representation is not irreducible and it will be split:
                 +0  1  0  0+ +0  1  1  1+
                 |          | |          |
                 |0  0  1  0| |1  1  0  1|
(4)  [[[1],[1]],[|          |,|          |]]
                 |1  0  0  0| |1  1  1  0|
                 |          | |          |
                 +0  0  0  1+ +1  1  1  1+
               Type: List List Matrix PrimeField 2


(5) -> isAbsolutelyIrreducible? sp1.2
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra has
               one-dimensional kernel
               We know that all the cyclic submodules generated by all
               non-trivial element of the singular matrix under view are
               not proper, hence Norton's irreducibility test can be done:
               The generated cyclic submodule was not proper
               Representation is absolutely irreducible
               (5)  true
               Type: Boolean


(6) -> d2211 := irreducibleRepresentation([2,2,1,1],genA6)
               (6)
 +1  0  0  - 1   1    0    0    0    0 + + 0    0   1   0   0  0   1   0  0+
 |                                     | |                                 |
 |0  1  0   1    0    1    0    0    0 | | 0    0   0   0   1  0  - 1  0  0|
 |                                     | |                                 |
 |0  0  1   0    1   - 1   0    0    0 | | 0    0   0   0   0  1   1   0  0|
 |                                     | |                                 |
 |0  0  0  - 1   0    0   - 1   0    0 | | 0    0   0   0   0  0   1   1  0|
 |                                     | |                                 |
[|0  0  0   0   - 1   0    0   - 1   0 |,| 0    0   0   0   0  0  - 1  0  1|]
 |                                     | |                                 |
 |0  0  0   0    0   - 1   0    0   - 1| | 0    0   0   0   0  0   1   0  0|
 |                                     | |                                 |
 |0  0  0   1    0    0    0    0    0 | |- 1   0   0   0   0  0  - 1  0  0|
 |                                     | |                                 |
 |0  0  0   0    1    0    0    0    0 | | 0   - 1  0   0   0  0   1   0  0|
 |                                     | |                                 |
 +0  0  0   0    0    1    0    0    0 + + 0    0   0  - 1  0  0  - 1  0  0+
      Type: List Matrix Integer

(7) -> d2211m2 := d2211:: (LIST MATRIX PF 2); sp2 := meatAxe d2211m2
     Fingerprint element in generated algebra is singular
     A proper cyclic submodule is found.
     Transition matrix computed
     The inverse of the transition matrix computed
     Now transform the matrices
                                   +1  0  0  0  0+ +1  1  1  0  0+
       +1  0  1  1+ +0  0  1  0+   |             | |             |
       |          | |          |   |0  1  1  1  1| |0  0  1  1  1|
       |0  1  0  1| |1  1  1  1|   |             | |             |
(7)  [[|          |,|          |],[|0  1  1  0  0|,|1  0  0  1  0|]]
       |1  1  0  0| |1  0  1  1|   |             | |             |
       |          | |          |   |0  1  0  1  0| |0  0  1  0  1|
       +0  1  0  0+ +0  1  0  1+   |             | |             |
                                   +0  1  1  1  0+ +1  0  0  1  1+
               Type: List List Matrix PrimeField 2


(8) -> isAbsolutelyIrreducible? sp2.1
               Random element in generated algebra has
               one-dimensional kernel
               We know that all the cyclic submodules generated by all
               non-trivial element of the singular matrix under view are
               not proper, hence Norton's irreducibility test can be done:
               The generated cyclic submodule was not proper
               Representation is absolutely irreducible
 (8)  true
               Type: Boolean


(9) -> areEquivalent? (sp1.2,sp2.1)
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra does
               not have a one-dimensional kernel
               Dimensions of kernels differ
 Representations are not equivalent.
 (9)  [0]
               Type: Matrix PrimeField 2


(10) -> dA6d16 := tensorProduct(sp1.2,sp2.1);meatAxe dA6d16
               Fingerprint element in generated algebra is non-singular 
               Fingerprint element in generated algebra is singular 
               The generated cyclic submodule was not proper 
               The generated cyclic submodule was not proper 
               The generated cyclic submodule was not proper 
               The generated cyclic submodule was not proper 
               The generated cyclic submodule was not proper 
               The generated cyclic submodule was not proper 
               The generated cyclic submodule was not proper 
               Fingerprint element in generated algebra is non-singular 
               Fingerprint element in generated algebra is singular 
               The generated cyclic submodule was not proper 
               The generated cyclic submodule was not proper 
               The generated cyclic submodule was not proper 
               The generated cyclic submodule was not proper 
               The generated cyclic submodule was not proper 
               The generated cyclic submodule was not proper 
               The generated cyclic submodule was not proper 
               Fingerprint element in generated algebra is singular 
               The generated cyclic submodule was not proper 
               The generated cyclic submodule was not proper 
               The generated cyclic submodule was not proper 
               We know that all the cyclic submodules generated by all 
               non-trivial element of the singular matrix under view are 
               not proper, hence Norton's irreducibility test can be done: 
               The generated cyclic submodule was not proper 
               Representation is irreducible, but we don't know 
               whether it is absolutely irreducible 
 (10)
               [ 
               +0  0  0  0  0  0  0  0  1  0  1  0  0  0  0  0+
               |                                              |
               |0  0  0  0  0  0  0  0  0  1  1  1  0  0  0  0|
               |                                              |
               |0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0|
               |                                              |
               |0  0  0  0  0  0  0  0  1  1  0  0  0  0  0  0|
               |                                              |
               |1  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0|
               |                                              |
               |0  1  1  1  0  0  0  0  0  0  0  0  0  0  0  0|
               |                                              |
               |1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
               |                                              |
               |1  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
               [|                                              |,
               |0  0  0  0  1  0  1  0  0  0  0  0  0  0  0  0| 
               |                                              | 
               |0  0  0  0  0  1  1  1  0  0  0  0  0  0  0  0| 
               |                                              | 
               |0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0| 
               |                                              | 
               |0  0  0  0  1  1  0  0  0  0  0  0  0  0  0  0| 
               |                                              | 
               |0  0  0  0  0  0  0  0  0  0  0  0  1  0  1  0| 
               |                                              | 
               |0  0  0  0  0  0  0  0  0  0  0  0  0  1  1  1| 
               |                                              | 
               |0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0| 
               |                                              | 
               +0  0  0  0  0  0  0  0  0  0  0  0  1  1  0  0+ 
               +0  0  0  0  0  1  1  0  0  1  1  0  0  1  1  0+ 
               |                                              | 
               |0  0  0  0  0  1  0  1  0  1  0  1  0  1  0  1| 
               |                                              | 
               |0  0  0  0  1  1  1  0  1  1  1  0  1  1  1  0| 
               |                                              | 
               |0  0  0  0  0  1  1  1  0  1  1  1  0  1  1  1| 
               |                                              | 
               |0  1  1  0  0  1  1  0  0  1  1  0  0  1  1  0|
               |                                              |
               |0  1  0  1  0  1  0  1  0  1  0  1  0  1  0  1|
               |                                              |
               |1  1  1  0  1  1  1  0  1  1  1  0  1  1  1  0|
               |                                              |
               |0  1  1  1  0  1  1  1  0  1  1  1  0  1  1  1|
               |                                              |]
               |0  1  1  0  0  0  0  0  0  1  1  0  0  1  1  0|
               |                                              |
               |0  1  0  1  0  0  0  0  0  1  0  1  0  1  0  1|
               |                                              |
               |1  1  1  0  0  0  0  0  1  1  1  0  1  1  1  0|
               |                                              |
               |0  1  1  1  0  0  0  0  0  1  1  1  0  1  1  1|
               |                                              |
               |0  1  1  0  0  1  1  0  0  0  0  0  0  1  1  0|
               |                                              |
               |0  1  0  1  0  1  0  1  0  0  0  0  0  1  0  1|
               |                                              |
               |1  1  1  0  1  1  1  0  0  0  0  0  1  1  1  0|
               |                                              |
               +0  1  1  1  0  1  1  1  0  0  0  0  0  1  1  1+
               ]
               Type: List List Matrix PrimeField 2

(11) -> isAbsolutelyIrreducible? dA6d16
               Random element in generated algebra does 
               not have a one-dimensional kernel 
               Random element in generated algebra does 
               not have a one-dimensional kernel 
               Random element in generated algebra does 
               not have a one-dimensional kernel 
               Random element in generated algebra does 
               not have a one-dimensional kernel 
               Random element in generated algebra does 
               not have a one-dimensional kernel 
               Random element in generated algebra does 
               not have a one-dimensional kernel 
               Random element in generated algebra does 
               not have a one-dimensional kernel 
               Random element in generated algebra does 
               not have a one-dimensional kernel 
               Random element in generated algebra does 
               not have a one-dimensional kernel 
               Random element in generated algebra does 
               not have a one-dimensional kernel 
               Random element in generated algebra does 
               not have a one-dimensional kernel 
               Random element in generated algebra does 
               not have a one-dimensional kernel 
               Random element in generated algebra does 
               not have a one-dimensional kernel 
               Random element in generated algebra does 
               not have a one-dimensional kernel 
               Random element in generated algebra does 
               not have a one-dimensional kernel 
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra does
               not have a one-dimensional kernel
               We have not found a one-dimensional kernel so far,
               as we do a random search you could try again
 (11)  false
               Type: Boolean


(12) -> sp3 := meatAxe (dA6d16:: (LIST MATRIX FF(2,2)))
               Fingerprint element in generated algebra is non-singular 
               Fingerprint element in generated algebra is singular 
               The generated cyclic submodule was not proper 
               The generated cyclic submodule was not proper 
               The generated cyclic submodule was not proper 
               The generated cyclic submodule was not proper 
               The generated cyclic submodule was not proper 
               The generated cyclic submodule was not proper 
               The generated cyclic submodule was not proper 
               Fingerprint element in generated algebra is non-singular 
               Fingerprint element in generated algebra is singular 
               The generated cyclic submodule was not proper 
               The generated cyclic submodule was not proper 
               The generated cyclic submodule was not proper 
               The generated cyclic submodule was not proper 
               The generated cyclic submodule was not proper 
               The generated cyclic submodule was not proper 
               The generated cyclic submodule was not proper 
               Fingerprint element in generated algebra is singular 
               The generated cyclic submodule was not proper 
               The generated cyclic submodule was not proper 
               A proper cyclic submodule is found. 
               Transition matrix computed 
               The inverse of the transition matrix computed 
               Now transform the matrices 
 (12)
[ 
 +  %A    %A + 1    0       %A      1     %A + 1    0     0 +
 |                                                          |
 |  0       0       %A    %A + 1    %A      %A      0     0 |
 |                                                          |
 |  %A    %A + 1    %A      1     %A + 1    0       0     0 |
 |                                                          |
 |  %A    %A + 1    %A      1       %A      0       0     0 |
[|                                                          |,
 |%A + 1    1       1       1       0       0     %A + 1  %A| 
 |                                                          | 
 |  0       0     %A + 1    1       0       0       %A    0 | 
 |                                                          | 
 |  1       0       1       1       0       0       0     0 | 
 |                                                          | 
 +  1       1       0       0       0       0       0     0 + 
 +  1       0       %A      0       1       1       %A    %A + 1+
 |                                                              |
 |  1     %A + 1    0       0       0     %A + 1    1     %A + 1|
 |                                                              |
 |  %A      1     %A + 1  %A + 1  %A + 1    1       %A      0   |
 |                                                              |
 |%A + 1  %A + 1    0       0       1     %A + 1    1       1   |
 |                                                              |]
 |  1       0     %A + 1    0       1       1       %A      %A  | 
 |                                                              | 
 |  0       0     %A + 1  %A + 1  %A + 1    1       1       %A  | 
 |                                                              | 
 |  0       0       1       0       0       1       0       1   | 
 |                                                              | 
 +  0       %A      0       %A      1     %A + 1  %A + 1    %A  + 
 , 
 +0     1       1     %A + 1  0  0  0  0+
 |                                      |
 |1     1     %A + 1    0     0  0  0  0|
 |                                      |
 |%A    0       0       0     0  0  0  0|
 |                                      |
 |1     %A      0       0     0  0  0  0|
[|                                      |,
 |%A  %A + 1    1       1     1  0  1  1|
 |                                      |
 |0     0       %A      1     0  1  0  1|
 |                                      |
 |%A    1       0       1     1  1  0  0|
 |                                      |
 +1     %A    %A + 1    %A    0  1  0  0+
 +%A + 1    1       %A      0       0     %A + 1    0       1   +
 |                                                              |
 |  0       %A      1       1       1       0     %A + 1    %A  |
 |                                                              |
 |  0     %A + 1    0     %A + 1  %A + 1    1     %A + 1    %A  |
 |                                                              |
 |  1     %A + 1    1     %A + 1    0       0     %A + 1    1   |
 |                                                              |]
 |  0       %A      0     %A + 1  %A + 1    0       0     %A + 1|
 |                                                              |
 |%A + 1    0     %A + 1    %A      0     %A + 1    0     %A + 1|
 |                                                              |
 |  0       1       0       1     %A + 1    0     %A + 1  %A + 1|
 |                                                              |
 +  %A      %A      %A      1       %A      %A      1     %A + 1+
  ]
               Type: List List Matrix FiniteField(2,2)


(13) -> isAbsolutelyIrreducible? sp3.1
               Random element in generated algebra does 
               not have a one-dimensional kernel 
               Random element in generated algebra does 
               not have a one-dimensional kernel
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra has
               one-dimensional kernel
               We know that all the cyclic submodules generated by all
               non-trivial element of the singular matrix under view are
               not proper, hence Norton's irreducibility test can be done:
               The generated cyclic submodule was not proper
               Representation is absolutely irreducible
 (13)  true
               Type: Boolean


(14) -> isAbsolutelyIrreducible? sp3.2
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra has
               one-dimensional kernel
               We know that all the cyclic submodules generated by all
               non-trivial element of the singular matrix under view are
               not proper, hence Norton's irreducibility test can be done:
               The generated cyclic submodule was not proper
               Representation is absolutely irreducible
 (14)  true
               Type: Boolean


(15) -> areEquivalent? (sp3.1,sp3.2)
               Random element in generated algebra does 
               not have a one-dimensional kernel 
               Random element in generated algebra does 
               not have a one-dimensional kernel 
               Random element in generated algebra does 
               not have a one-dimensional kernel 
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra does
               not have a one-dimensional kernel
               Random element in generated algebra has
               one-dimensional kernel
               There is no isomorphism, as the only possible one
               fails to do the necessary base change
 Representations are not equivalent.
 (15)  [0]
               Type: Matrix FiniteField(2,2)


(16) -> sp0.2 
 (16)  [[1],[1]]
               Type: List Matrix PrimeField 2


(17) -> sp1.2 
       +0  1  0  0+ +0  1  1  1+
       |          | |          |
       |0  0  1  0| |1  1  0  1|
(17)  [|          |,|          |]
       |1  0  0  0| |1  1  1  0| 
       |          | |          | 
       +0  0  0  1+ +1  1  1  1+ 
               Type: List Matrix PrimeField 2


(18) -> sp2.1 
       +1  0  1  1+ +0  0  1  0+
       |          | |          |
       |0  1  0  1| |1  1  1  1|
(18)  [|          |,|          |]
       |1  1  0  0| |1  0  1  1| 
       |          | |          | 
       +0  1  0  0+ +0  1  0  1+ 
               Type: List Matrix PrimeField 2
 
(19) -> sp3.1 
 (19)
 +  %A    %A + 1    0       %A      1     %A + 1    0     0 +
 |                                                          |
 |  0       0       %A    %A + 1    %A      %A      0     0 |
 |                                                          |
 |  %A    %A + 1    %A      1     %A + 1    0       0     0 |
 |                                                          |
 |  %A    %A + 1    %A      1       %A      0       0     0 |
[|                                                          |,
 |%A + 1    1       1       1       0       0     %A + 1  %A| 
 |                                                          | 
 |  0       0     %A + 1    1       0       0       %A    0 | 
 |                                                          | 
 |  1       0       1       1       0       0       0     0 | 
 |                                                          | 
 +  1       1       0       0       0       0       0     0 + 
 +  1       0       %A      0       1       1       %A    %A + 1+
 |                                                              |
 |  1     %A + 1    0       0       0     %A + 1    1     %A + 1|
 |                                                              |
 |  %A      1     %A + 1  %A + 1  %A + 1    1       %A      0   |
 |                                                              |
 |%A + 1  %A + 1    0       0       1     %A + 1    1       1   |
 |                                                              |]
 |  1       0     %A + 1    0       1       1       %A      %A  | 
 |                                                              | 
 |  0       0     %A + 1  %A + 1  %A + 1    1       1       %A  | 
 |                                                              | 
 |  0       0       1       0       0       1       0       1   | 
 |                                                              | 
 +  0       %A      0       %A      1     %A + 1  %A + 1    %A  + 
               Type: List Matrix FiniteField(2,2)


(20) -> sp3.2 
 (20)
               +0     1       1     %A + 1  0  0  0  0+
               |                                      |
               |1     1     %A + 1    0     0  0  0  0|
               |                                      |
               |%A    0       0       0     0  0  0  0|
               |                                      |
               |1     %A      0       0     0  0  0  0|
               [|                                      |,
               |%A  %A + 1    1       1     1  0  1  1|
               |                                      |
               |0     0       %A      1     0  1  0  1|
               |                                      |
               |%A    1       0       1     1  1  0  0|
               |                                      |
               +1     %A    %A + 1    %A    0  1  0  0+
 +%A + 1    1       %A      0       0     %A + 1    0       1   +
 |                                                              |
 |  0       %A      1       1       1       0     %A + 1    %A  |
 |                                                              |
 |  0     %A + 1    0     %A + 1  %A + 1    1     %A + 1    %A  |
 |                                                              |
 |  1     %A + 1    1     %A + 1    0       0     %A + 1    1   |
 |                                                              |]
 |  0       %A      0     %A + 1  %A + 1    0       0     %A + 1|
 |                                                              |
 |%A + 1    0     %A + 1    %A      0     %A + 1    0     %A + 1|
 |                                                              |
 |  0       1       0       1     %A + 1    0     %A + 1  %A + 1|
 |                                                              |
 +  %A      %A      %A      1       %A      %A      1     %A + 1+
               Type: List Matrix FiniteField(2,2)


(21) -> dA6d16
 (21)
               +0  0  0  0  1  0  1  1  0  0  0  0  0  0  0  0+
               |                                              |
               |0  0  0  0  0  1  0  1  0  0  0  0  0  0  0  0|
               |                                              |
               |0  0  0  0  1  1  0  0  0  0  0  0  0  0  0  0|
               |                                              |
               |0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0|
               |                                              |
               |0  0  0  0  0  0  0  0  1  0  1  1  0  0  0  0|
               |                                              |
               |0  0  0  0  0  0  0  0  0  1  0  1  0  0  0  0|
               |                                              |
               |0  0  0  0  0  0  0  0  1  1  0  0  0  0  0  0|
               |                                              |
               |0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0|
               [|                                              |,
               |1  0  1  1  0  0  0  0  0  0  0  0  0  0  0  0| 
               |                                              | 
               |0  1  0  1  0  0  0  0  0  0  0  0  0  0  0  0| 
               |                                              | 
               |1  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0| 
               |                                              | 
               |0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0| 
               |                                              | 
               |0  0  0  0  0  0  0  0  0  0  0  0  1  0  1  1| 
               |                                              | 
               |0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  1| 
               |                                              | 
               |0  0  0  0  0  0  0  0  0  0  0  0  1  1  0  0| 
               |                                              | 
               +0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0+ 
               +0  0  0  0  0  0  1  0  0  0  1  0  0  0  1  0+ 
               |                                              | 
               |0  0  0  0  1  1  1  1  1  1  1  1  1  1  1  1| 
               |                                              | 
               |0  0  0  0  1  0  1  1  1  0  1  1  1  0  1  1| 
               |                                              | 
               |0  0  0  0  0  1  0  1  0  1  0  1  0  1  0  1| 
               |                                              |
               |0  0  1  0  0  0  1  0  0  0  0  0  0  0  1  0|
               |                                              |
               |1  1  1  1  1  1  1  1  0  0  0  0  1  1  1  1|
               |                                              |
               |1  0  1  1  1  0  1  1  0  0  0  0  1  0  1  1|
               |                                              |
               |0  1  0  1  0  1  0  1  0  0  0  0  0  1  0  1|
               |                                              |]
               |0  0  1  0  0  0  1  0  0  0  1  0  0  0  0  0|
               |                                              |
               |1  1  1  1  1  1  1  1  1  1  1  1  0  0  0  0|
               |                                              |
               |1  0  1  1  1  0  1  1  1  0  1  1  0  0  0  0|
               |                                              |
               |0  1  0  1  0  1  0  1  0  1  0  1  0  0  0  0|
               |                                              |
               |0  0  1  0  0  0  1  0  0  0  1  0  0  0  1  0|
               |                                              |
               |1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1|
               |                                              |
               |1  0  1  1  1  0  1  1  1  0  1  1  1  0  1  1|
               |                                              |
               +0  1  0  1  0  1  0  1  0  1  0  1  0  1  0  1+
               Type: List Matrix PrimeField 2
             

metadata block
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Correspondence about this page

Book Shop - Further reading.

Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them.

flag flag flag flag flag flag The Princeton Companion to Mathematics - This is a big book that attempts to give a wide overview of the whole of mathematics, inevitably there are many things missing, but it gives a good insight into the history, concepts, branches, theorems and wider perspective of mathematics. It is well written and, if you are interested in maths, this is the type of book where you can open a page at random and find something interesting to read. To some extent it can be used as a reference book, although it doesn't have tables of formula for trig functions and so on, but where it is most useful is when you want to read about various topics to find out which topics are interesting and relevant to you.

 

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