|
#############################################################################
#
# This is the SCSCP server configuration file.
# The service provider can start the server just by the command
# $ gap myserver.g
#
#############################################################################
#############################################################################
#
# Load necessary packages and read external files.
# Put here and other commands if needed.
#
#############################################################################
LogTo(); # to close log file if it was opened from .gaprc
LoadPackage("scscp");
LoadPackage("factint");
LoadPackage("anupq");
LoadPackage("cvec");
LoadPackage("cubefree");
#############################################################################
#
# Procedures and functions available for the SCSCP server
# (you can also install procedures contained in other files,
# including standard GAP procedures and functions) by adding
# appropriate calls to InstallSCSCPprocedure below.
#
#############################################################################
#############################################################################
#
# IdGroupByGenerators( <list of permutations> )
#
# Returns the number of the group, generated by given permutations,
# in the GAP Small Groups Library.
#
IdGroupByGenerators:=function( permlist )
return IdGroup( Group( permlist ) );
end;
#############################################################################
#
# QuillenSeriesByIdGroup( [ ord, nr] )
#
# Let G:=SmallGroup( ord, nr ) be a p-group of order p^n. It was proved in
# [D.Quillen, The spectrum of an equivariant cohomology ring II, Ann. of
# Math., (2) 94 (1984), 573-602] that the number of conjugacy classes of
# maximal elementary abelian subgroups of given rank is determined by the
# group algebra KG.
# The function calculates this numbers for each possible rank and returns
# a list of the length n, where i-th element corresponds to the number of
# conjugacy classes of maximal elementary abelian subgroups of the rank i.
#
QuillenSeriesByIdGroup := function( id )
local G, qs, latt, msl, ccs, ccs_repr, i, x, n;
G := SmallGroup( id );
latt := LatticeSubgroups(G);
msl := MinimalSupergroupsLattice(latt);
ccs := ConjugacyClassesSubgroups(latt);
ccs_repr := List(ccs, Representative);
qs := [];
for i in [ 1 .. LogInt( Size(G), PrimePGroup(G) ) ] do
qs[i]:=0;
od;
for i in [ 1 .. Length(ccs_repr) ] do
if IsElementaryAbelian( ccs_repr[i] ) then
if ForAll( msl[i],
x -> IsElementaryAbelian( ccs[x[1]][x[2]] ) = false ) then
n := LogInt( Size(ccs_repr[i]), PrimePGroup(G) );
qs[n] := qs[n] + 1;
fi;
fi;
od;
return [ id, qs ];
end;
PointImages:=function( G, n )
local g;
return Set( List( GeneratorsOfGroup(G), g -> n^g ) );
end;
SCSCPadditionService:=function(a,b)
return a+b;
end;
#############################################################################
#
# Installation of procedures to make them available for WS
# (you can also install procedures contained in other files,
# including standard GAP procedures and functions)
#
#############################################################################
# Simple procedures for tests and demos
InstallSCSCPprocedure( "Identity", x -> x, "Identity procedure for tests", 1, 1 );
InstallSCSCPprocedure( "WS_Factorial", Factorial, "See ?Factorial in GAP", 1, 1 );
InstallSCSCPprocedure( "addition", SCSCPadditionService, "to add two integers", 2, 2 );
InstallSCSCPprocedure( "WS_Phi", Phi, "Euler's totient function, see ?Phi in GAP", 1, 1 );
InstallSCSCPprocedure( "Length", Length, 1, 1 );
InstallSCSCPprocedure( "Size", Size, 1, 1 );
InstallSCSCPprocedure( "Determinant", Determinant );
InstallSCSCPprocedure( "NrConjugacyClasses", NrConjugacyClasses, 1, 1 );
InstallSCSCPprocedure( "SylowSubgroup", SylowSubgroup, 2, 2 );
InstallSCSCPprocedure( "IsPrimeInt", IsPrimeInt, 1, 1 );
InstallSCSCPprocedure( "NrSmallGroups", NrSmallGroups, 1, 1 );
InstallSCSCPprocedure( "NumberCFGroups", NumberCFGroups, 1, 2 );
InstallSCSCPprocedure( "NumberCFSolvableGroups", NumberCFSolvableGroups, 1, 2 );
# Group identification in the GAP small group library
InstallSCSCPprocedure( "GroupIdentificationService", IdGroupByGenerators,
"Accepts a list of permutations and returns IdGroup of the group they generate", 1, infinity );
InstallSCSCPprocedure( "WS_IdGroup", IdGroup, "See ?IdGroup in GAP", 1, 1 );
InstallSCSCPprocedure( "WS_QUIT_GAP", QUIT_GAP, "quit GAP", 0, 1 );
###########################################################################
#
# IdGroup512ByCode( <pcgs code of the group> )
#
# The function accepts the integer number that is the code for pcgs of
# a group of order 512 and returns the number of this group in the
# GAP Small Groups library. It is assumed that the client will make sure
# that the code really corresponds to the group of order 512, since this
# can not be checked from the code itself.
#
# This function requires ANUPQ package for IdStandardPresented512Group.
#
if ARCH_IS_UNIX() then
IdGroup512ByCode:=function( code )
local G, F, H;
G := PcGroupCode( code, 512 );
F := PqStandardPresentation( G );
H := PcGroupFpGroup( F );
return IdStandardPresented512Group( H );
end;
InstallSCSCPprocedure( "IdGroup512ByCode", IdGroup512ByCode,
"Identification of groups of order 512 using the ANUPQ package", 1, 1 );
fi;
InstallSCSCPprocedure( "MatrixGroup", Group );
# Important MIP (modular isomorphism problem for group algebras of finite p-group
# over the field of p elements) invariant
InstallSCSCPprocedure( "QuillenSeriesByIdGroup", QuillenSeriesByIdGroup,
"Quillen series of a finite p-group given by IdGroup (list of two integers)", 1, 1 );
# Service used to compute automorphism groups of transformation semigroups with
# the MONOID package, which requires the GRAPE package, and the latter requires
# the external program 'nauty' by Brendan D. McKay
InstallSCSCPprocedure( "WS_AutomorphismGroup", AutomorphismGroup, 1, 1 );
# GAP group libraries
InstallSCSCPprocedure( "WS_AlternatingGroup", AlternatingGroup );
InstallSCSCPprocedure( "WS_SymmetricGroup", SymmetricGroup );
InstallSCSCPprocedure( "WS_SmallGroup", SmallGroup );
InstallSCSCPprocedure( "WS_TransitiveGroup", TransitiveGroup );
InstallSCSCPprocedure( "WS_PrimitiveGroup", PrimitiveGroup );
InstallSCSCPprocedure( "MathieuGroup", MathieuGroup );
# Multiplication services
InstallSCSCPprocedure( "WS_Mult", function(a,b) return a*b; end );
InstallSCSCPprocedure( "WS_MultMatrix",
function(a,b)
if not IsMatrix(a) or not IsMatrix(b) then
Error( "The argument must be a matrix!" );
else
return a*b;
fi;
end );
# Lattice of subgroups
InstallSCSCPprocedure( "WS_LatticeSubgroups", LatticeSubgroups, 1, 1 );
# Series of factorisation methods from the GAP package FactInt
InstallSCSCPprocedure("WS_FactorsTD", FactorsTD,
"FactorsTD from FactInt package, see ?FactorsTD in GAP", 1, 2 );
InstallSCSCPprocedure("WS_FactorsPminus1", FactorsPminus1,
"FactorsPminus1 from FactInt package, see ?FactorsPminus1 in GAP", 1, 4 );
InstallSCSCPprocedure("WS_FactorsPplus1", FactorsPplus1,
"FactorsPplus1 from FactInt package, see ?FactorsPplus1 in GAP", 1, 4 );
InstallSCSCPprocedure("WS_FactorsECM", FactorsECM,
"FactorsECM from FactInt package, see ?FactorsECM in GAP", 1, 5 );
InstallSCSCPprocedure("WS_FactorsCFRAC", FactorsCFRAC,
"FactorsCFRAC from FactInt package, see ?FactorsCFRAC in GAP", 1, 1 );
InstallSCSCPprocedure("WS_FactorsMPQS", FactorsMPQS,
"FactorsMPQS from FactInt package, see ?FactorsMPQS in GAP", 1, 1 );
InstallSCSCPprocedure("WS_ConwayPolynomial", ConwayPolynomial, "See ?ConwayPolynomial in GAP", 2, 2 );
InstallSCSCPprocedure( "PointImages", PointImages,
"1st argument is a permutation group G, 2nd is an integer n. Returns the set of images of n under generators of G", 2, 2 );
#############################################################################
#
# procedures for the UnitLib package for the parallel computation of the
# normalized unit group of a modular group algebra of a finite p-group
# from the GAP small groups library
#
if LoadPackage("unitlib") = true then
InstallSCSCPprocedure( "NormalizedUnitCFpower", NormalizedUnitCFpower );
InstallSCSCPprocedure( "NormalizedUnitCFcommutator", NormalizedUnitCFcommutator );
fi;
#############################################################################
#
# procedure to test pickling/unpickling from the IO package for data encoding
#
IO_UnpickleStringAndPickleItBack:=function( picklestr )
return( IO_PickleToString( IO_UnpickleFromString( picklestr ) ) );
end;
InstallSCSCPprocedure( "IO_UnpickleStringAndPickleItBack", IO_UnpickleStringAndPickleItBack,
"To test how pickling format from IO package may be used for data transmitting (see ?IO_Pickle, ?IO_Unpickle)", 1, 1 );
############################################################################
#
# Setting up the service for parallel computation
# of minimal distance of a linear code
#
SCSCPMINDISTG:=fail;
SCSCPMINDISTF:=fail;
SCSCPMINDISTzero:=fail;
InstallSCSCPprocedure("ResetMinimumDistanceService",
function( G, F, zero )
SCSCPMINDISTG:=IO_UnpickleFromString(G);
SCSCPMINDISTF:=F;
SCSCPMINDISTzero:=IO_UnpickleFromString(zero);
return true;
end);
InstallSCSCPprocedure(
"AClosestVectorCombinationsMatFFEVecFFE",
i -> WeightVecFFE( AClosestVectorCombinationsMatFFEVecFFE(
SCSCPMINDISTG, SCSCPMINDISTF, SCSCPMINDISTzero, i, 1) ) );
#############################################################################
#
# Finally, we start the SCSCP server.
#
#############################################################################
RunSCSCPserver( SCSCPserverAddress, SCSCPserverPort );
[ Dauer der Verarbeitung: 0.31 Sekunden
(vorverarbeitet)
]
|
