<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>
