| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/polenta/doc/ (Algebra von RWTH Aachen Version 4.15.1©) Datei vom 10.3.2025 mit Größe 7 kB |
|
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.pd </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> ¤ Dauer der Verarbeitung: 0.14 Sekunden (vorverarbeitet) ¤*© Formatika GbR, Deutschland |
|
2026-03-28