decomp man page
decomp — decompose a module
Synopsis
decomp [Options] <Module> <Endo>
Description
This program decomposes a module Module into its direct summands, using the head of the endomorphism ring, Endo. It assumes that the endomorphism ring and its left regular representation has already been calculated using mkhom(1). It also expects that chop(1), pwkond(1), and rad(1) have been run on the left regular representation.
Decomp produces three types of output files:
- A basis of the module reflecting the decomposition is written to Module.dec. With respect to this basis, the generators have a block-diagonal structure with the blocks corresponding to the direct summands.
- If you use the -t option, decomp calculates the action of the generators with respect to the decomposition basis, and writes it to Module.dec.1, Module.dec.2,....
- If you use the -a option, the program also calculates the action of the generators on each direct summand, i.e., the blocks of the matrices above. They are written to Module.Comp.1, Module.Comp.2, and so on, where Comp is the name of the direct summand, containing the isomorphism type (dimension plus one letter) and a number counting isomorphic summands that occur more than once in the decomposition.
Options
- -Q
Quiet, no messages.
- -V
Verbose, more messages.
- -T <MaxTime>
Set CPU time limit
- -t
Write transformed generators.
- -a
Write the action on the direct summands.
Implementation Details
The algorithm used by this program was developed by Magdolna Szöke; see "Examining Green Correspondents of Weight Modules", Aachener Beiträge zur Mathematik, Band 24, Wissenschaftsverlag Mainz, Aachen, 1998.
Input Files
- Module.{1,2,...}
Generators on Module.
- Module.cfinfo
Constituent info file for Module.
- Endo.{1,2,...}
k-Basis of the endomorphism ring.
- Endo.gens.{1,2,...}
Generating system of the endomorphism ring.
- Endo.lrr.{1,2,...}
Left regular representation of the endomorphism ring.
- Endo.lrr.cfinfo
Constituent info file for Endo.lrr after running chop(1) and pwkond(1).
- Endo.lrr.soc
Basis of the socle of Endo.lrr, made by soc(1).