|
#############################################################################
##
## This file is part of GAP, a system for computational discrete algebra.
## This file's authors include Volkmar Felsch.
##
## Copyright of GAP belongs to its developers, whose names are too numerous
## to list here. Please refer to the COPYRIGHT file for details.
##
## SPDX-License-Identifier: GPL-2.0-or-later
##
## This file contains the declarations of operations for the GAP library of
## irreducible maximal finite integral matrix groups.
##
#############################################################################
##
#V InfoImf
##
## is the info class for the imf functions
## (see~"Info Functions").
##
DeclareInfoClass( "InfoImf" );
#############################################################################
##
## Some global variables.
##
#############################################################################
##
#F IsImfMatrixGroup( <G> )
##
DeclareFilter( "IsImfMatrixGroup" );
#############################################################################
##
#A ImfRecord( <G> )
##
DeclareAttribute( "ImfRecord", IsGroup, "mutable" );
#############################################################################
##
## list of global variables not thought for the user
##
#############################################################################
##
#F BaseShortVectors( <orbit> ) . . . . . . . . . . . . . . . . . . . . . . .
##
## 'BaseShortVectors' expects as argument an orbit of short vectors under
## some imf matrix group of dimension dim, say. This orbit can be
## considered as a set of generatos of a dim-dimensional Q-vectorspace.
## 'BaseShortVectors' determines a subset B of <orbit> which is a base
## of that vectorspace, and it returns a list of two lists containing
##
## - a list of the position numbers with respect to <orbit> of the elements
## of the base B and
## - the base change matrix B^-1.
##
## Both will be needed by the function 'ImfPermutationToMatrix'.
##
DeclareGlobalFunction( "BaseShortVectors" );
#############################################################################
##
#F DisplayImfInvariants( <dim>, <q> ) . . . . . . . . . . . . . . . . . . .
#F DisplayImfInvariants( <dim>, <q>, <z> ) . . . . . . . . . . . . . . . . .
##
## 'DisplayImfInvariants' displays some Z-class invariants of the specified
## classes of irreducible maximal finite integral matrix groups in some
## easily readable format.
##
## The default value of z is 1. If any of the arguments is zero, the routine
## loops over all legal values of the respective parameter.
##
DeclareGlobalFunction( "DisplayImfInvariants" );
#############################################################################
##
#F DisplayImfReps( <dim>, <q>, <z> ) . . . . . . . . . . . . . . . . . . . .
##
## 'DisplayImfReps' is a subroutine of the 'DisplayImfInvariants' command.
## It displays some Z-class invariants of the zth Z-classes in the qth
## Q-class of the irreducible maximal finite integral matrix groups of
## dimension dim.
##
## If an argument z = 0 has been specified, then all classes in the given
## Q-class will be displayed, otherwise just the zth Z-class is displayed.
##
## This subroutine is considered to be an internal one. Hence the arguments
## are not checked for being in range. Moreover, it is assumed that the imf
## main list IMFList has already been loaded.
##
DeclareGlobalFunction( "DisplayImfReps" );
#############################################################################
##
#F ImfInvariants( <dim>, <q> ) . . . . . . . . . . . . . . . . . . . . . . .
#F ImfInvariants( <dim>, <q>, <z> ) . . . . . . . . . . . . . . . . . . . .
##
## 'ImfInvariants' returns a record of Z-class invariants of the zth Z-class
## in the qth Q-class of irreducible maximal finite integral matrix groups
## of dimension dim. The default value of z is 1.
##
## Assume that G is a representative group of the specified Z-class. Then
## the resulting record contains the following components:
##
## size group size of G,
## isSolvable true, if G is solvable,
## isomorphismType isomorphism type of G,
## elementaryDivisors elementary divisors of G,
## minimalNorm norm of the short vectors associated to G,
## sizesOrbitsShortVectors a list of the sizes of the orbits of short
## vectors associated to G,
## maximalQClass Q-class number of corresponding rational imf
## class (only if it is different from q).
##
## If a value z > 1 has been specified for a dimension for which no Z-class
## representatives are available, the function will display an appropriate
## message and return the value 'false'.
##
DeclareGlobalFunction( "ImfInvariants" );
#############################################################################
##
#F IMFLoad( <dim> ) . . . . . . . . load a secondary file of the imf library
##
## 'IMFLoad' loads the imf main list and, if dim > 0, the list of matrices
## containing the Gram matrices and the lists of generators for the
## irreducible maximal finite integral matrix groups of dimension <dim>.
## Nothing is done if the required lists have already been loaded.
##
## 'IMFLoad' finds the files in the directory specified by 'GRPNAME'. This
## variable is set in the init file 'LIBNAME/\"init.g\"'.
##
## The given dimension is not checked to be in range.
##
DeclareGlobalFunction( "IMFLoad" );
#############################################################################
##
#F ImfMatrixGroup( <dim>, <q> ) . . . . . . . . . . . . . . . . . . . . . .
#F ImfMatrixGroup( <dim>, <q>, <z> ) . . . . . . . . . . . . . . . . . . . .
##
## 'ImfMatrixGroup' returns the representative of the zth Z-class in the qth
## Q-class of the irreducible maximal finite integral matrix groups of
## dimension dim. The default value of z is 1.
##
## If a value z > 1 has been specified for a dimension for which no Z-class
## representatives are available, the function will display an appropriate
## message and return the value 'false'.
##
DeclareGlobalFunction( "ImfMatrixGroup" );
#############################################################################
##
#F ImfNumberQClasses( <dim> ) . . . . . . . . . . . . . . . . . . . . . . .
##
## 'ImfNumberQClasses' returns the number of available Q-classes of
## irreducible maximal finite subgroups of dimension dim, i. e., the number
## of Q-classes of irreducible maximal finite subgroups of GL(dim,Z), if dim
## is at most 11 or a prime, or the number of Q-classes of irreducible
## maximal finite subgroups of GL(dim,Q), else.
##
DeclareGlobalFunction( "ImfNumberQClasses" );
#############################################################################
##
#F ImfNumberQQClasses( <dim> ) . . . . . . . . . . . . . . . . . . . . . . .
##
## 'ImfNumberQQClasses' returns the number of Q-classes of irreducible
## maximal finite subgroups of GL(dim,Q).
##
DeclareGlobalFunction( "ImfNumberQQClasses" );
#############################################################################
##
#F ImfNumberZClasses( <dim>, <q> ) . . . . . . . . . . . . . . . . . . . . .
##
## 'ImfNumberZClasses' returns the number of available class representatives
## in the qth Q-class of irreducible maximal finite integral matrix groups
## of dimension dim, i. e., the number of Z-classes in that Q-class, if dim
## is at most 11 or a prime, or just the value 1, else.
##
DeclareGlobalFunction( "ImfNumberZClasses" );
#############################################################################
##
#F ImfPositionNumber( [ <dim>, <q> ] ) . . . . . . . . . . . . . . . . . . .
#F ImfPositionNumber( [ <dim>, <q>, <z> ] ) . . . . . . . . . . . . . . . .
##
## 'ImfPositionNumber' loads the imf main list if it is not yet available.
## Then it checks the given arguments and returns the position number of the
## specified Z-class representative within the list of all representatives
## of dimension dim which is still in the original order as submitted to
## us by LehrstuhL B. The default value of z is 1.
##
DeclareGlobalFunction( "ImfPositionNumber" );
#############################################################################
##
#F OrbitShortVectors( <gens>, <rep> ) . . . . . . . . . . . . . . . . . . .
##
## 'OrbitShortVectors' is a subroutine of the 'PermGroupImfGroup' command.
## It returns the orbit of the short vector <rep> under the matrix group
## generators given in list <gens>.
##
DeclareGlobalFunction( "OrbitShortVectors" );
#############################################################################
##
#F IsomorphismPermGroupImfGroup( <M> ) . . . . . . . . . . . . . . . . . . .
#F IsomorphismPermGroupImfGroup( <M>, <n> ) . . . . . . . . . . . . . . . .
##
## 'IsomorphismPermGroupImfGroup' returns an isomorphism from the given
## irreducible maximal finite integral matrix group to the permutation grou
## induced by the action of M on its nth orbit on the set of short vectors.
## The default value of n is 1.
##
DeclareGlobalFunction( "IsomorphismPermGroupImfGroup" );
[ Dauer der Verarbeitung: 0.37 Sekunden
(vorverarbeitet)
]
|
