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ExactCouples :: excerptLES

excerptLES -- displays a few entries of a long exact sequence

Synopsis

Description

The encoding of a long exact sequence as a module is described in detail in longExactSequence

i1 : R = QQ[d]/d^2;
i2 : M = coker map(R^{-1,-1,-1,-1,-1,0,0,0,0},R^{-1,-1,-1,-2,-2,-2,-2,-2},
         {{0,0,0,d,0,0,0,0},{0,0,0,0,d,0,0,0},{0,0,0,0,0,d,0,0},
          {0,0,0,0,0,0,d,0},{0,0,0,0,0,0,0,d},{-4*d,4*d,4*d,0,0,0,0,0},
          {5*d,0,0,0,0,0,0,0},{0,5*d,0,0,0,0,0,0},{0,0,5*d,0,0,0,0,0}});
i3 : N = coker map(R^{-1,-1,0,0,0,1,1},R^{0,-1,-1,-2,-2},
         {{0,0,0,d,0},{0,0,0,0,d},{0,0,-4*d,0,0},{0,d,0,0,0},
          {0,0,3*d,0,0},{0,0,0,0,0},{d,0,0,0,0}});
i4 : f = map(N, M, {{1,1,1,1,1,0,0,0,0},{1,1,1,1,1,0,0,0,0},{d,d,d,d,d,-14,-12,4,4},
                    {0,0,0,0,0,1,1,1,1},{0,0,0,0,0,3,3,3,3},{0,0,0,0,0,d,d,d,0},
                    {0,0,0,0,0,0,0,0,0}});

o4 : Matrix
i5 : LES = longExactSequence f;
warning: clearing value of symbol f to allow access to subscripted variables based on it
       : debug with expression   debug 3406   or with command line option   --debug 3406
i6 : expectExactCouple LES;
i7 : excerptLES(0,2,LES)

o7 =               .- ->  0                                           
           0      (      
                   \     

                           2              1        0                \ 
                   .- -> QQ  - - - - -> QQ       - - ->       0  - -' 
     | 0 0 0 0 1 |(           | 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 |
                           2              5  | 0 0 0 0 0 |     5    \ 
                   .- -> QQ  - - - - -> QQ  - - - - - - - -> QQ  - -' 
       | 0 0 1 |  (           | 0 1 |
       | 0 0 0 |   \          | 0 0 |
                              | 0 0 |
                              | 0 0 |
                              | 0 0 |

                                               | 0 1 0 |
                                               | 0 0 1 |
                           1              3    | 0 0 0 |       3    \ 
                   .- -> QQ   - - - ->  QQ    - - - - - ->   QQ  - -' 
           0      (            | 1 |
                   \           | 0 |
                               | 0 |

                                                                    \ 
                                                              0  - -' 

See also

Ways to use excerptLES:

For the programmer

The object excerptLES is a method function.