decomp(1)

1decomp(1)                        User Commands                       decomp(1)
2
3
4

NAME

6       decomp - decompose a module
7

SYNOPSIS

9       decomp [OPTIONS] <Module> <Endo>
10

DESCRIPTION

12       This program decomposes a module Module into its direct summands, using
13       the head of the endomorphism ring, Endo.  It assumes that the  endomor‐
14       phism  ring and its left regular representation has already been calcu‐
15       lated using mkhom(1).  It also expects  that  chop(1),  pwkond(1),  and
16       rad(1) have been run on the left regular representation.
17
18       Decomp produces three types of output files:
19
20       · A basis of the module reflecting the decomposition is written to Mod‐
21         ule.dec.  With respect to this basis, the generators  have  a  block-
22         diagonal  structure  with the blocks corresponding to the direct sum‐
23         mands.
24
25       · If you use the -t option, decomp calculates the action of the genera‐
26         tors  with  respect to the decomposition basis, and writes it to Mod‐
27         ule.dec.1, Module.dec.2,....
28
29       · If you use the -a option, the program also calculates the  action  of
30         the generators on each direct summand, i.e., the blocks of the matri‐
31         ces above.  They are written to Module.Comp.1, Module.Comp.2, and  so
32         on, where Comp is the name of the direct summand, containing the iso‐
33         morphism type (dimension plus one letter) and a number counting  iso‐
34         morphic summands that occur more than once in the decomposition.
35

OPTIONS

37       -Q     Quiet, no messages.
38
39       -V     Verbose, more messages.
40
41       -T <MaxTime>
42              Set CPU time limit
43
44       -t     Write transformed generators.
45
46       -a     Write the action on the direct summands.
47

IMPLEMENTATION DETAILS

49       The algorithm used by this program was developed by Magdolna Szöke; see
50       "Examining Green Correspondents of Weight Modules",  Aachener  Beiträge
51       zur Mathematik, Band 24, Wissenschaftsverlag Mainz, Aachen, 1998.
52

INPUT FILES

54       Module.{1,2,...}
55              Generators on Module.
56
57       Module.cfinfo
58              Constituent info file for Module.
59
60       Endo.{1,2,...}
61              k-Basis of the endomorphism ring.
62
63       Endo.gens.{1,2,...}
64              Generating system of the endomorphism ring.
65
66       Endo.lrr.{1,2,...}
67              Left regular representation of the endomorphism ring.
68
69       Endo.lrr.cfinfo
70              Constituent  info  file  for  Endo.lrr after running chop(1) and
71              pwkond(1).
72
73       Endo.lrr.soc
74              Basis of the socle of Endo.lrr, made by soc(1).
75

OUTPUT FILES

77       Module.dec
78              Basis of Module reflecting the decomposition.
79
80       Module.dec.{1,2,...}
81              Generators in the decomposition basis (with -t).
82
83       Module.Comp.{1,2,...}
84              Generators on the components (with -a).
85