# 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*.cfinfoConstituent 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.cfinfoConstituent info file for

*Endo*.lrr after running chop(1) and pwkond(1).*Endo*.lrr.socBasis of the socle of

*Endo*.lrr, made by soc(1).