From 09e4b5d9c6774ab4e99ed766928cf6f842c3994e Mon Sep 17 00:00:00 2001 From: Max Horn Date: Fri, 27 Mar 2026 18:36:29 +0100 Subject: [PATCH] Remove dev/smtx.tex Its content is subsumed by the Meataxe documentation in the ref manual, as well as code comments --- dev/smtx.tex | 250 --------------------------------------------------- 1 file changed, 250 deletions(-) delete mode 100644 dev/smtx.tex diff --git a/dev/smtx.tex b/dev/smtx.tex deleted file mode 100644 index 188d6e2c3f..0000000000 --- a/dev/smtx.tex +++ /dev/null @@ -1,250 +0,0 @@ -\documentclass[12pt]{article} -\usepackage{fullpage} -\usepackage{palatcm} -\def\smtxcmd#1{\subsubsection*{{\tt #1}}} -\title{The Smash MeatAxe for {\sf GAP4}} -\author{Alexander Hulpke} -\date{November 19, 1996} -\def\SMTX{{\sf SMTX}} -\begin{document} -\maketitle -The {\sf Smash}-MeatAxe {\SMTX} is a modification of the MeatAxe in the {\sf -Smash} share library, originally written by Derek Holt and Sarah Rees. It is -adapted to {\sf GAP4} -(where it is intended to become the standard library MeatAxe -unless someone else is willing to write a better one) and works according to -the standardized MeatAxe interface. This document describes the implemented -features as well as some internal routines that resemble features of the -old {\sf Smash}-MeatAxe.\\ -If you feel that routines for certain functions are missing {\em please ask -me before writing them yourself. There might be some internal feature that -allows easy addition already available!}\\ -The routines will only work if the module given is a full row vector space.\\ -The routines from {\SMTX} are selected by setting {\verb+ MTX:=SMTX;+}. - -\section*{Commands} -\smtxcmd{SMTX.SubQuotActions(matrices,sub,dim,subdim,one,type)} -is the working horse of the basic chopping routines: {\tt matrices} is a -list of matrices in dimension {\tt dim}, {\tt sub} is the basis of a -subspace in dimension {\tt subdim}. The respective one is given by {\tt -one}. The integer {\tt type} finally encodes in its binary decomposition -which actions are to be performed: 1 stands for subspace action, 2 for -factor action and 4 for action of the full module -on a subspace adapted basis. The routine -returns a record with components (if applicable): {\tt smatrices}, {\tt -qmatrices} and {\tt nmatrices} giving new matrices for the three possible -actions and {\tt nbasis} an extension of the basis given in {\tt sub} with -respect to which the action is performed.\\ -The routine returns {\tt fail} if {\tt sub} is not a proper subspace.\\ -The basis given in {\tt sub} must be normed!\\ -There are a couple of further routines that basically just call -SubQuotActions to provide several layers of interfacing (and also return -{\tt fail} if {\tt sub} is not a submodule basis): - -\smtxcmd{SMTX.InducedAction(module,sub[,type])} -just calls {\tt SubQuotActions}, but returns module actions instead of -matrices and returns the computed results in a list in sequence -(sub,quot,both,basis) instead of record components. If no {\tt type} is -given, it is assumed to be 7.\\ -The basis given in {\tt sub} must be normed! - -\smtxcmd{SMTX.SubGModuleAction(sub,matrices)} -computes matrices for just the subspace action. SCHEDULED FOR ELIMINATION! - -\smtxcmd{SMTX.InducedActionSubmodule(module,sub)} -creates a new module corresponding to the action of {\tt module} on {\tt sub}. - -\smtxcmd{SMTX.InducedActionSubmoduleNB(module,sub)} -Dito, but the basis in {\tt sub} must be normed. - -\smtxcmd{SMTX.InducedActionFactorModule(module,sub[,compl])} -creates a new module corresponding to the action of {\tt module} on the -factor of {\tt sub}. If {\tt compl} is given, it has to be a basis of a -(vectorspace-)complement of {\tt sub}. The action then will correspond to -{\tt compl}. - -\smtxcmd{SMTX.ProperSubmoduleBasis(module)} -returns the action on a proper submodule and {\tt fail} if none exists. - -\smtxcmd{SMTX.SMCoRaEl(matrices,ngens,newgenlist,dim,F)} -internally used to create a random element -PROBABLY NOT AN END-USER FUNCTION. JUST LISTED AS PARTS OF SMASH MIGHT STILL -CONTAINED DUPLICATE CODE PUT HEREIN. - -\smtxcmd{SMTX.IrreducibilityTest(module)} -Tests for irreducibility and sets a subbasis if reducible. It neither sets -an irreducibility flag, nor tests it. Thus the routine also can simply be -called to obtain a random submodule. - -\smtxcmd{SMTX.IsIrreducible(module)} -if necessary calls the irreducibility test and sets a flag to be returned -otherwise. The existence of the flag can be checked with -{\tt SMTX.HasIsIrreducible} - -\smtxcmd{SMTX.AbsoluteIrreducibilityTest(module)} -Tests for absolute irreducibility and sets splitting field degree. It -neither sets an absolute irreducibility flag, nor tests it. - -\smtxcmd{SMTX.IsAbsolutelyIrreducible(module)} -if necessary calls the absolute irreducibility test and sets a flag to be -returned otherwise. The existence of the flag can be checked with -{\tt SMTX.HasIsAbsolutelyIrreducible} - -\smtxcmd{SMTX.RandomIrreducibleSubGModule(module)} -returns the module action on a random irreducible submodule. - -\smtxcmd{SMTX.GoodElementGModule(module)} -finds an element with minimal possible nullspace dimension if {\tt module} -is known to be irreducible - -\smtxcmd{SMTX.CompleteBasis(module,pbasis)} -extends {\tt pbasis} to a basis of the full space by action of {\tt module}. -It returns whether it succeeded. - -\smtxcmd{SMTX.DegreeFieldExt(module)} -returns the degree of the splitting field extension. - -\smtxcmd{SMTX.DegreeSplittingField(module)} -returns the degree of the splitting field extension over the prime field - -\smtxcmd{SMTX.CollectedFactors(module)} -returns a list giving all irreducible composition factors with their -frequencies. - -\smtxcmd{SMTX.CompositionFactors(module)} -returns a list of composition factors in ascending order - -\smtxcmd{SMTX.Distinguish(cf,nr)} -Let {\tt cf} be the output of {\tt SMTX.CollectedFactors}. This routine -tries to find a group algebra element that has nullity zero on all -composition factors except {\tt nr}. - -\smtxcmd{SMTX.MinimalSubGModule(module,cf,nr)} -returns the basis of a minimal submodule of {\tt module} containing the -indicated composition factor. It assumes {\tt Distinguish} has been called -already - -\smtxcmd{SMTX.Isomorphism(module1,module2)} -returns an isomorphism from module1 to module2 (if any exists) and {\tt -fail} otherwise. It needs that one of the modules is known to be -ireducible. It implicitly assumes that the same group is acting, otherwise -the results are unpredictable. -The isomorphism is given by a matrix $M$, whose rows give the images of the -standard basis vectors of module2 in the standard basis of module1. That is, -conjugation of the generators of {\tt module2} with $M$ yields the -generators of {\tt module1}. - -\smtxcmd{SMTX.IsEquivalent(module1,module2)} -tests two irreducible modules for equivalence. - -\smtxcmd{SMTX.MatrixSum(matrices1,matrices2)} -creates the direct sum of two matrix lists - -\smtxcmd{SMTX.Homomorphisms(module1,module2)} -returns a basis of all homomorphisms from the irreducible module {\tt -module1} to {\tt module2}. - -\smtxcmd{SMTX.SortHomGModule(module1,module2,homs)} -Function to sort the output of {\tt Homomorphisms} - -\smtxcmd{SMTX.MinimalSubGModules(module1,module2[,max])} -returns (at most {\tt max}) bases of submodules of module2 which are -isomorphic to the irreducible {\tt module1}. - -\smtxcmd{SMTX.BasesCompositionSeries(module)} -returns a list of bases of submodules in a composition series in ascending -order - -\smtxcmd{SMTX.BasesMinimalSubmodules(module)} -returns a list of bases of all minimal submodules - -\smtxcmd{SMTX.BasesMaximalSubmodules(module)} -returns a list of bases of all maximal submodules - -\smtxcmd{SMTX.BasesMinimalSupermodules(module,sub)} -returns a list of bases of all minimal supermodules of the submodule given by -the basis {\tt sub}. - -\smtxcmd{SMTX.BasesSubmodules(module)} -returns a list containing a basis for every submodule - -\smtxcmd{SMTX.Setter(string)} -returns a setter function for the component {\tt smashMeataxe.(string)}. - -\smtxcmd{SMTX.Getter(string)} -returns a getter function for the component {\tt smashMeataxe.(string)}. - -\subsection*{Flags} - -The following getter routines access internal flags. For each routine, the -appropriate setters name is prefixed with {\tt Set}. - -\smtxcmd{SMTX.Subbasis} -Basis of a submodule - -\smtxcmd{SMTX.AlgEl} -list {\tt[newgens,coefflist]} giving an algrebra element used for chopping - -\smtxcmd{SMTX.AlgElMat} -matrix thereof - -\smtxcmd{SMTX.AlgElCharPol} -minimal polynomial thereof - -\smtxcmd{SMTX.AlgElCharPolFac} -used factor thereof - -\smtxcmd{SMTX.AlgElNullspaceVec} -nullspace of the matrix evaluated under this factor - -\smtxcmd{SMTX.AlgElNullspaceDimension} -dimension thereof - -\smtxcmd{SMTX.CentMat} - -\smtxcmd{SMTX.CentMatMinPoly} - -\newpage - -\section*{Translation of old names} -\begin{tabular}{ll} -Old&New\\ -\hline -ChopGMod&SMTX.CollectedFactors\\ -CompleteBasis&SMTX.CompleteBasis\\ -Distinguish&SMTX.Distinguish\\ -EnlargeIrreducibleGModule&${}^\dag$\\ -FieldGenCentMat&${}^\dag$\\ -FrobAction&SMTX.FrobeniusAction\\ -GoodElMod&SMTX.GoodElementGModule\\ -HomGMod&SMTX.Homomorphisms\\ -IsAbsIrredGMod&SMTX.AbsoluteIrreducibilityTest${}^\dag$\\ -&SMTX.IsAbsolutelyIrreducible${}^\dag$\\ -IsIrredGMod&SMTX.IrreducibilityTest${}^\dag$\\ -&SMTX.IsIrreducible${}^\dag$\\ -IsomGMod&SMTX.Isomorphism(module1,module2)\\ -MatSum&SMTX.MatrixSum\\ -MinSub&SMTX.MinimalSubGModule\\ -MinSubGMods&SMTX.MinimalSubGModules\\ -OrthogVec&SMTX.OrthogonalVector\\ -QuotGMod&SMTX.InducedActionFactorModule\\ -RandomIrredSubGMod&SMTX.RandomIrreducibleSubGModule\\ -SetAlgElCharPolFacFlag&SMTX.SetAlgElCharPolFac\\ -SetAlgElCharPolFlag&SMTX.SetAlgElCharPol\\ -SetAlgElFlag&SMTX.SetAlgEl\\ -SetAlgElMatFlag&SMTX.SetAlgElMat\\ -SetAlgElNullspaceDimFlag&SMTX.SetAlgElNullspaceDimension\\ -SetAlgElNullspaceVecFlag&SMTX.SetAlgElNullspaceVec\\ -SetCentMatFlag&SMTX.SetCentMat\\ -SetCentMatMinPolyFlag&SMTX.SetCentMatMinPoly\\ -SetSubbasisFlag&SMTX.SetSubbasis\\ -SortHomGMod&SMTX.SortHomGModule\\ -SpinBasis&SMTX.SpinnedBasis\\ -SubGMod&SMTX.InducedActionSubmodule\\ -SubGModAction&SMTX.SubGModuleAction\\ -SubQuotGMod&SMTX.InducedAction\\ -\end{tabular}\\ -All functions return {\tt fail} to indicate impossibility to perform instead -of {\tt false}.\\ -\dag indicates that the performed functions were slightly changed. -\end{document}