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#############################################################################
##
#W ilatgrp.gd XGAP library Max Neunhoeffer
##
##
#Y Copyright 1998, Max Neunhoeffer, Aachen, Germany
##
## This file contains code to display a subgroup lattice interactively.
##
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##
#I Info class "GraphicLattice"
##
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DeclareInfoClass( "GraphicLattice" );
SetInfoLevel(GraphicLattice,1); # we normally show our messages
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##
#P KnowsAllLevels . . . . . . . . . . . . . . . whether all levels are known
##
## FIXME...
DeclareFilter( "KnowsAllLevels" );
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##
##
## FIXME...
#F HasHasseProperty . . . . . . . . . . . . . . . whether lattice has Hasse
DeclareFilter( "HasseProperty" );
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##
#F CanCompareSubgroups . . . . . . . . . . whether we can compare subgroups
##
## FIXME...
DeclareFilter( "CanCompareSubgroups");
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##
#O GGLSylowSubgroup(<grp>) . . . . . . asks for prime, calls SylowSubgroup
##
## This operation just asks for a prime by a little dialog and calls then
## SylowSubgroup. Returns its result.
##
DeclareOperation( "GGLSylowSubgroup", [ IsGroup ] );
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##
#O GGLEpimorphisms(<sheet>,<grp>) . . . pops up box to choose on which group
##
## This operations brings up a text selector where one can choose several
## types of groups to calculate epimorphisms onto.
##
DeclareOperation( "GGLEpimorphisms", [ IsGraphicSheet, IsGroup ] );
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##
#O GGLLowIndexSubgroups(<sheet>,<grp>) . . pops up box to choose max. index
##
## This operations brings up a dialog, in which one can choose the maximal
## index for the subgroups that are searched.
##
DeclareOperation( "GGLLowIndexSubgroups", [ IsGraphicSheet, IsGroup ] );
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##
#O GGLPresentation(<sheet>,<grp>) . . . asks for presentation for subgroup
##
## This operation makes a presentation for the group <grp> and returns a
## short description of it.
##
DeclareOperation( "GGLPresentation", [ IsGraphicSheet, IsGroup ] );
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##
#O GGLAbelianPQuotient(<sheet>,<grp>) . . . . . asks for p and calls library
##
## This operation asks for a prime p and runs then the library operations
## to calculate abelian prime quotients.
##
DeclareOperation( "GGLAbelianPQuotient", [ IsGraphicSheet, IsGroup ] );
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##
#O GGLPrimeQuotient(<sheet>,<grp>) . asks for p and class and calls library
##
## This operation asks for a prime p and a class cl and runs then the
## library operations to calculate prime quotients up to class cl.
##
DeclareOperation( "GGLPrimeQuotient", [ IsGraphicSheet, IsGroup ] );
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##
#O GGLEpiQuotientSystem . . . . . . . . . . calculates the epimorphism to qs
##
## obsolete!?!
##
DeclareSynonym( "GGLEpiQuotientSystem", EpimorphismQuotientSystem );
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##
#O GGLKernelQuotientSystem . . . . . . . calculates the kernel of epi to qs
##
## obsolete!?!
##
DeclareOperation( "GGLKernelQuotientSystem", [ IsQuotientSystem ] );
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##
#O GGLCompareSubgroups(<sheet>,<grplist>) . . . . . . . . compares subgroups
##
## This operation lets the GAP library compare the selected subgroups.
## The new information about equality or inclusion of one in the other resp.
## is included into the graphic lattice. This can lead to the merging of
## vertices. No new vertices are included into the lattice.
##
DeclareOperation( "GGLCompareSubgroups", [IsGraphicSheet, IsList ]);
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##
#O GGLTestConjugacy(<sheet>,<grplist>) . . . . . test conjugacy of subgroups
##
## This operation lets the GAP library test the selected conjugacy classes
## of subgroups. If new information about conjugacy is found, classes are
## merged.
##
DeclareOperation( "GGLTestConjugacy", [IsGraphicSheet, IsList ]);
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##
## Constructors:
##
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##
#F GGLMakeSubgroupsMenu( <sheet>, <config> ) . . . . . makes subgroups menu
##
## This function is used to generate a menu out of the configuration data.
##
DeclareGlobalFunction( "GGLMakeSubgroupsMenu" );
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##
#O GraphicSubgroupLattice(<G>) . . . . displays subgroup lattice graphically
#O GraphicSubgroupLattice(<G>,<def>) . . . . . . . . . . same with defaults
##
## Displays a graphic poset which shows (parts of) the subgroup lattice of
## the group <group>. Normally only the whole group and the trivial group are
## shown (behaviour of "InteractiveLattice" in xgap3). Returns a
## IsGraphicSubgroupLattice object. Calls DecideSubgroupLatticeType. See
## there for details.
##
if not IsBound(GraphicSubgroupLattice) then
DeclareOperation( "GraphicSubgroupLattice", [ IsGroup ] );
DeclareOperation( "GraphicSubgroupLattice", [ IsGroup, IsRecord ] );
fi;
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##
#O DecideSubgroupLatticeType ( <grp> ) . decides about the type of a lattice
##
## This operation is called while creation of a new graphic subgroup lattice.
## It has to decide about the type of the lattice. That means it has to
## decide 5 questions:
## 1) Are all levels known right from the beginning?
## 2) Has the lattice the HasseProperty?
## 3) Can we test two subgroups for equality reasonably cheaply?
## 4) Shall we create a vertex for the trivial subgroup at the beginning?
## 5) What menu operations are possible?
## 6) What information is displayed on RightClick?
## Returns a list. The first four entries are boolean values for questions
## 1-4. Note that if the answer to 2 is true, then the answer to 3 must also
## be true. The fifth and sixth entry are configuration lists as explained
## in the configuration section of "ilatgrp.gi" for menu operations and
## info displays respectively.
DeclareOperation( "DecideSubgroupLatticeType", [ IsGroup ] );
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##
## Methods for manipulating the poset:
##
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##
#O InsertVertex( <sheet>, <grp>, <conj>, <hint> ) . . . . insert new vertex
##
## Insert the group <grp> as a new vertex into the sheet. If
## CanCompareSubgroups is set for the lattice, we check, if the group is
## already in the lattice or if we already have a conjugate subgroup.
## If the lattice has the HasseProperty, then this new vertex is sorted
## into the poset. So we check for all vertices on higher levels, if
## the new vertex is contained and for all vertices on lower levels,
## if they are contained in the new vertex. We try then to add edges to
## the appropriate vertices. If the lattice does not have the HasseProperty,
## nothing is done with respect to the connections of any vertex.
## Returns list with vertex as first entry and a flag as second, which
## says, if this vertex was inserted right now or has already been there.
## <hint> is a list of x coordinates which should give some hint for the
## choice of the new x coordinate. It can for example be the x coordinates
## of those groups which were parameter for the operation which calculated
## the group. <hints> can be empty but must always be a list!
## If the lattice does not have CanCompareSubgroups and <conj> is a vertex
## we put the new vertex into the class of this vertex. Otherwise <conj>
## should either be false or fail.
## `InsertVertex' can return `fail', if `CanComputeIndex' *and*
## `CanComputeSize' return `false' for the subgroup.
##
DeclareOperation( "InsertVertex", [IsGraphicSheet, IsGroup, IsObject, IsList]);
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##
#O NewInclusionInfo( <sheet>, <v1>, <v2> ) . . . . . . . . . . v1 lies in v2
##
## For graphic group lattices without the HasseProperty we cannot calculate
## all inclusion information for each new vertex. This operation is the
## proposed method to enter an inclusion information which normally comes
## out of the process of subgroup calculation into the poset. It should
## normally only be called if one conjectures or knows that v1 is a
## maximal subobject with respect to the current poset, but the methods
## for this operation first check, if there is already a way from v1 up
## to v2. If this is the case, nothing is done. Otherwise we have to check,
## if this new connection can be established: If v2 lies in a lower level
## than v1 (of course those two levels are not comparable, so by definition
## both subgroups must lie in a level of their own!) then, we try
## to move the level of v1 into a new level right below that of v2. If
## that does not work we try to move the level of v2 right over the level
## of v1. If that does not work check if we know that v2 is contained in v1
## In this case we call MergeVertices. Otherwise we finally give up and
## display an info!
## Now we draw the connection but have to make sure, that this new connection
## does not close a circle such that there is an edge in the poset which
## connects a vertex "below" v1 to a vertex "over" v2. Therefore we
## calculate all vertices lying "below" v1 and "over" v2 and disconnect
## them pairwise. This is all done by means of posets and not by means
## of groups. There are no group inclusion checks performed!
DeclareOperation( "NewInclusionInfo",
[ IsGraphicSheet, IsGraphicObject, IsGraphicObject ] );
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##
#O MergeVertices( <sheet>, <v1>, <v2> ) . . . . . . . . . . . merge vertices
##
## For graphic group lattices without the HasseProperty we cannot calculate
## all inclusion information for each new vertex. If we don't have
## CanCompareSubgroups either, we have to think of the case where we have two
## vertices to which belongs the same group respectively. If we come to
## know this, then we have to fix this situation by merging vertices.
## This operation does exactly this *without* further checks. The vertex
## having the lower (that is older) serial number survives and inherits all
## inclusion information the other one has. This in turn is deleted.
##
DeclareOperation( "MergeVertices",
[ IsGraphicSheet, IsGraphicObject, IsGraphicObject ] );
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##
## The following operations are menu functions for GraphicSubgroupLattices:
##
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##
#O GGLMenuOperation (<sheet>, <menu>, <entry>) . . . is called from the menu
##
## This operation is called for all so called "menu operations" the user
## wants to perform on lattices. It is highly configurable with respect
## to the input and output and the GAP-Operation which is actually performed
## on the selected subgroups. See the configuration section in "ilatgrp.gi"
## for an explanation.
##
DeclareOperation( "GGLMenuOperation", [ IsGraphicSheet, IsMenu, IsString ]);
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##
#O GGLRightClickPopup (<sheet>, <vertex>, <x>, <y>) . . . . . . . . . . . .
## . . . . . . . . . . . . . . . . . . . called if user does a right click
##
## This is called if the user does a right click on a vertex or somewhere
## else on the sheet. This operation is highly configurable with respect
## to the Attributes of groups it can display/calculate. See the
## configuration section in "ilatgrp.gi" for an explanation.
##
DeclareOperation( "GGLRightClickPopup",
[ IsGraphicSheet, IsObject, IsInt, IsInt ] );
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##
## Operations to switch between graphics and GAP calculations:
##
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##
#O SelectedGroups(<sheet>) . . . . . . . . returns list of selected groups
##
## Uses the `Selected' operation to get a list of vertices and returns the
## corresponding list of subgroups.
##
DeclareOperation( "SelectedGroups", [ IsGraphicSheet ] );
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##
#O SelectGroups( <sheet>, <list> ) . . . . . . . . select subgroups in list
##
## Uses the `Select' operation to select exactly those vertices to which
## the subgroups in the supplied list belong. Be careful: We use
## `IsIdenticalObj' here because comparison must be fast. If a subgroup is
## not yet as vertex in the lattice, only a warning is printed. If two
## or more vertices have the subgroup as associated group, only one of them
## is selected.
##
DeclareOperation( "SelectGroups", [ IsGraphicSheet, IsList ] );
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