Quelle info.xml Sprache: XML

<Chapter Label="Information Messages">
<Heading>Information Messages</Heading>

It is possible to get informations about the status of the computation of the
functions of Chapter <Ref Chap="Methods for matrix groups"/> of this manual.


<Section Label="Info Class">
<Heading>Info Class</Heading>

<ManSection>
<InfoClass Name="InfoPolenta"/>
<Description>

is the Info class of the &Polenta; package (for more details on the Info mechanism
see Section <Ref Sect="Info Functions" BookName="Reference"/> of the &GAP; Reference Manual).
With the help of the function
<C>SetInfoLevel(InfoPolenta,<A>level</A>)</C> you can change
the info level of <C>InfoPolenta</C>.

<List>
<Item>
  If  <C>InfoLevel( InfoPolenta )</C> is equal to 0
then no information
  messages are displayed.
</Item>

<Item>
  If <C>InfoLevel( InfoPolenta )</C> is equal to 1 then basic informations
  about the process are provided. For further background on the displayed
  informations we refer to  <Cite Key="Assmann"/> (publicly available via the
  Internet address <URL>http://www.icm.tu-bs.de/ag_algebra/software/assmann/diploma.pdf</URL>).
</Item>

<Item>
  If <C>InfoLevel( InfoPolenta )</C> is equal to 2 then, in addition to the
  basic information, the generators of computed subgroups and module series
  are displayed.
</Item>
</List>
</Description>
</ManSection>

</Section>


<Section Label="Example">
<Heading>Example</Heading>

<Example><![CDATA[
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 ]
]]></Example>

</Section>
</Chapter>

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