GAP (Polenta) - Chapter 5: Information Messages

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5 Information Messages
5.1 Info Class
5.1-1 InfoPolenta
5.2 Example

### 5 Information Messages

It is possible to get informations about the status of the computation of the functions of Chapter 2 of this manual.

#### 5.1 Info Class

##### 5.1-1 InfoPolenta

`‣ InfoPolenta` | ( info class )

is the Info class of the Polenta package (for more details on the Info mechanism see Section Reference: Info Functions of the GAP Reference Manual). With the help of the function `SetInfoLevel(InfoPolenta,level)` you can change the info level of `InfoPolenta`.

- If `InfoLevel( InfoPolenta )` is equal to 0 then no information messages are displayed.

- If `InfoLevel( InfoPolenta )` is equal to 1 then basic informations about the process are provided. For further background on the displayed informations we refer to [Ass03] (publicly available via the Internet address http://www.icm.tu-bs.de/ag_algebra/software/assmann/diploma.pdf).

- If `InfoLevel( InfoPolenta )` is equal to 2 then, in addition to the basic information, the generators of computed subgroups and module series are displayed.

#### 5.2 Example

    gap> SetInfoLevel( InfoPolenta, 1 );

    gap> PcpGroupByMatGroup( PolExamples(11) );
    #I  Determine a constructive polycyclic sequence
        for the input group ...
    #I
    #I  Chosen admissible prime: 3
    #I
    #I  Determine a constructive polycyclic sequence
        for the image under the p-congruence homomorphism ...
    #I  finished.
    #I  Finite image has relative orders [ 3, 2, 3, 3, 3 ].
    #I
    #I  Compute normal subgroup generators for the kernel
        of the p-congruence homomorphism ...
    #I  finished.
    #I
    #I  Compute the radical series ...
    #I  finished.
    #I  The radical series has length 4.
    #I
    #I  Compute the composition series ...
    #I  finished.
    #I  The composition series has length 5.
    #I
    #I  Compute a constructive polycyclic sequence
        for the induced action of the kernel to the composition series ...
    #I  finished.
    #I  This polycyclic sequence has relative orders [  ].
    #I
    #I  Calculate normal subgroup generators for the
        unipotent part ...
    #I  finished.
    #I
    #I  Determine a constructive polycyclic  sequence
        for the unipotent part ...
    #I  finished.
    #I  The unipotent part has relative orders
    #I  [ 0, 0, 0 ].
    #I
    #I  ... computation of a constructive
        polycyclic sequence for the whole group finished.
    #I
    #I  Compute the relations of the polycyclic
        presentation of the group ...
    #I  Compute power relations ...
    #I  ... finished.
    #I  Compute conjugation relations ...
    #I  ... finished.
    #I  Update polycyclic collector ...
    #I  ... finished.
    #I  finished.
    #I
    #I  Construct the polycyclic presented group ...
    #I  finished.
    #I
    Pcp-group with orders [ 3, 2, 3, 3, 3, 0, 0, 0 ]

    gap> SetInfoLevel( InfoPolenta, 2 );

    gap> PcpGroupByMatGroup( PolExamples(11) );
    #I  Determine a constructive polycyclic sequence
        for the input group ...
    #I
    #I  Chosen admissible prime: 3
    #I
    #I  Determine a constructive polycyclic sequence
        for the image under the p-congruence homomorphism ...
    #I  finished.
    #I  Finite image has relative orders [ 3, 2, 3, 3, 3 ].
    #I
    #I  Compute normal subgroup generators for the kernel
        of the p-congruence homomorphism ...
    #I  finished.
    #I  The normal subgroup generators are
    #I  [ [ [ 1, -3/2, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 3 ], [ 0, 0, 0, 1 ] ],
      [ [ 1, 0, 0, 24 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ],
      [ [ 1, 3, 3, 15 ], [ 0, 1, 0, 6 ], [ 0, 0, 1, -6 ], [ 0, 0, 0, 1 ] ],
      [ [ 1, 3, 3, 9 ], [ 0, 1, 0, 6 ], [ 0, 0, 1, -6 ], [ 0, 0, 0, 1 ] ],
      [ [ 1, 3/2, 3/2, 3/2 ], [ 0, 1, 0, 3 ], [ 0, 0, 1, -3 ], [ 0, 0, 0, 1 ] ],
      [ [ 1, -3/2, 9/2, -69/2 ], [ 0, 1, 0, 9 ], [ 0, 0, 1, 3 ], [ 0, 0, 0, 1 ] ]
        , [ [ 1, 0, 0, -24 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ],
      [ [ 1, -3, -3, -9 ], [ 0, 1, 0, -6 ], [ 0, 0, 1, 6 ], [ 0, 0, 0, 1 ] ],
      [ [ 1, -3, -3, -15 ], [ 0, 1, 0, -6 ], [ 0, 0, 1, 6 ], [ 0, 0, 0, 1 ] ],
      [ [ 1, -3, 0, 9 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 6 ], [ 0, 0, 0, 1 ] ],
      [ [ 1, -3, -3, -9 ], [ 0, 1, 0, -6 ], [ 0, 0, 1, 6 ], [ 0, 0, 0, 1 ] ],
      [ [ 1, -3, 0, 9 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 6 ], [ 0, 0, 0, 1 ] ],
      [ [ 1, -3/2, -3/2, -9/2 ], [ 0, 1, 0, -3 ], [ 0, 0, 1, 3 ], [ 0, 0, 0, 1 ]
         ],
      [ [ 1, -3, -3, -12 ], [ 0, 1, 0, -6 ], [ 0, 0, 1, 6 ], [ 0, 0, 0, 1 ] ],
      [ [ 1, 3, -3/2, -21 ], [ 0, 1, 0, -3 ], [ 0, 0, 1, -6 ], [ 0, 0, 0, 1 ] ],
      [ [ 1, 3/2, 3/2, 9/2 ], [ 0, 1, 0, 3 ], [ 0, 0, 1, -3 ], [ 0, 0, 0, 1 ] ] ]
    #I
    #I  Compute the radical series ...
    #I  finished.
    #I  The radical series has length 4.
    #I  The radical series is
    #I  [ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ],
      [ [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 0, 0, 1 ] ],
      [  ] ]
    #I
    #I  Compute the composition series ...
    #I  finished.
    #I  The composition series has length 5.
    #I  The composition series is
    #I  [ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ],
      [ [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ],
      [ [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 0, 0, 1 ] ], [  ] ]
    #I
    #I  Compute a constructive polycyclic sequence
        for the induced action of the kernel to the composition series ...
    #I  finished.
    #I  This polycyclic sequence has relative orders [  ].
    #I
    #I  Calculate normal subgroup generators for the
        unipotent part ...
    #I  finished.
    #I  The normal subgroup generators for the unipotent part are
    #I  [ [ [ 1, -3/2, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 3 ], [ 0, 0, 0, 1 ] ],
      [ [ 1, 0, 0, 24 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ],
      [ [ 1, 3, 3, 15 ], [ 0, 1, 0, 6 ], [ 0, 0, 1, -6 ], [ 0, 0, 0, 1 ] ],
      [ [ 1, 3, 3, 9 ], [ 0, 1, 0, 6 ], [ 0, 0, 1, -6 ], [ 0, 0, 0, 1 ] ],
      [ [ 1, 3/2, 3/2, 3/2 ], [ 0, 1, 0, 3 ], [ 0, 0, 1, -3 ], [ 0, 0, 0, 1 ] ],
      [ [ 1, -3/2, 9/2, -69/2 ], [ 0, 1, 0, 9 ], [ 0, 0, 1, 3 ], [ 0, 0, 0, 1 ] ]
        , [ [ 1, 0, 0, -24 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ],
      [ [ 1, -3, -3, -9 ], [ 0, 1, 0, -6 ], [ 0, 0, 1, 6 ], [ 0, 0, 0, 1 ] ],
      [ [ 1, -3, -3, -15 ], [ 0, 1, 0, -6 ], [ 0, 0, 1, 6 ], [ 0, 0, 0, 1 ] ],
      [ [ 1, -3, 0, 9 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 6 ], [ 0, 0, 0, 1 ] ],
      [ [ 1, -3, -3, -9 ], [ 0, 1, 0, -6 ], [ 0, 0, 1, 6 ], [ 0, 0, 0, 1 ] ],
      [ [ 1, -3, 0, 9 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 6 ], [ 0, 0, 0, 1 ] ],
      [ [ 1, -3/2, -3/2, -9/2 ], [ 0, 1, 0, -3 ], [ 0, 0, 1, 3 ], [ 0, 0, 0, 1 ]
         ],
      [ [ 1, -3, -3, -12 ], [ 0, 1, 0, -6 ], [ 0, 0, 1, 6 ], [ 0, 0, 0, 1 ] ],
      [ [ 1, 3, -3/2, -21 ], [ 0, 1, 0, -3 ], [ 0, 0, 1, -6 ], [ 0, 0, 0, 1 ] ],
      [ [ 1, 3/2, 3/2, 9/2 ], [ 0, 1, 0, 3 ], [ 0, 0, 1, -3 ], [ 0, 0, 0, 1 ] ] ]
    #I
    #I  Determine a constructive polycyclic  sequence
        for the unipotent part ...
    #I  finished.
    #I  The unipotent part has relative orders
    #I  [ 0, 0, 0 ].
    #I
    #I  ... computation of a constructive
        polycyclic sequence for the whole group finished.
    #I
    #I  Compute the relations of the polycyclic
        presentation of the group ...
    #I  Compute power relations ...
    .....
    #I  ... finished.
    #I  Compute conjugation relations ...
    ..............................................
    #I  ... finished.
    #I  Update polycyclic collector ...
    #I  ... finished.
    #I  finished.
    #I
    #I  Construct the polycyclic presented group ...
    #I  finished.
    #I
    Pcp-group with orders [ 3, 2, 3, 3, 3, 0, 0, 0 ]

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