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############################################################################
##
## elements/blocks.gi
## Copyright (C) 2013-2022 James D. Mitchell
##
## Licensing information can be found in the README file of this package.
##
#############################################################################
##
#############################################################################
# Blocks are stored internally as a list consisting of:
#
# [ nr of blocks, internal rep of blocks, transverse blocks ]
#
# <nr of blocks> is a non-negative integer, <internal rep of blocks>[i] = j if
# <i> belongs to the <j>th block, <transverse blocks>[j] = 1 if block <j> is
# transverse and 0 if it is not.
#############################################################################
#############################################################################
# GAP level - directly using interface to C/C++ level
#############################################################################
InstallMethod(LeftBlocks, "for a bipartition", [IsBipartition],
BIPART_LEFT_BLOCKS);
InstallMethod(RightBlocks, "for a bipartition", [IsBipartition],
BIPART_RIGHT_BLOCKS);
InstallMethod(ExtRepOfObj, "for blocks", [IsBlocks], BLOCKS_EXT_REP);
InstallMethod(ChooseHashFunction, "for blocks",
[IsBlocks, IsInt],
{_, hashlen} -> rec(func := BLOCKS_HASH, data := hashlen));
InstallMethod(DegreeOfBlocks, "for blocks", [IsBlocks], BLOCKS_DEGREE);
InstallMethod(RankOfBlocks, "for blocks", [IsBlocks], BLOCKS_RANK);
InstallMethod(NrBlocks, "for blocks", [IsBlocks], BLOCKS_NR_BLOCKS);
InstallMethod(\=, "for blocks", [IsBlocks, IsBlocks], BLOCKS_EQ);
InstallMethod(\<, "for blocks", [IsBlocks, IsBlocks], BLOCKS_LT);
InstallMethod(ProjectionFromBlocks, "for blocks", [IsBlocks], BLOCKS_PROJ);
InstallMethod(OnRightBlocks, "for blocks and a bipartition",
[IsBlocks, IsBipartition], BLOCKS_RIGHT_ACT);
InstallMethod(OnLeftBlocks, "for blocks and a bipartition",
[IsBlocks, IsBipartition], BLOCKS_LEFT_ACT);
#############################################################################
# GAP level - NOT directly using interface to C/C++ level
#############################################################################
InstallMethod(AsDigraph, "for blocks", [IsBlocks],
function(blocks)
local ext, out, block, i;
ext := ExtRepOfObj(blocks);
out := List([1 .. DegreeOfBlocks(blocks)], x -> []);
for block in ext do
if block[1] > 0 then # transverse block
for i in block do
out[i] := ShallowCopy(block);
RemoveSet(out[i], i);
od;
else
for i in block do
out[-i] := block * -1;
od;
fi;
od;
return Digraph(out);
end);
InstallMethod(CanonicalBlocks, "for blocks", [IsBlocks],
function(blocks)
local gr, canon, scc, rep, i;
gr := AsDigraph(blocks);
gr := OnDigraphs(gr, BlissCanonicalLabelling(gr));
canon := [];
scc := DigraphStronglyConnectedComponents(gr).comps;
canon := ShallowCopy(scc);
for i in [1 .. Length(scc)] do
rep := scc[i][1];
if IsDigraphEdge(gr, [rep, rep]) then
canon[i] := -1 * canon[i];
fi;
od;
return BLOCKS_NC(canon);
end);
# not a synonym since NrTransverseBlocks applies to a bipartition also
InstallMethod(NrTransverseBlocks, "for blocks", [IsBlocks], RankOfBlocks);
# Printing, viewing etc . . .
InstallMethod(String, "for blocks", [IsBlocks],
x -> Concatenation("BLOCKS_NC(", String(ExtRepOfObj(x)), ")"));
InstallMethod(ViewObj, "for blocks", [IsBlocks],
function(blocks)
local ext, str, i;
ext := ExtRepOfObj(blocks);
if Length(ext) > 0 then
Print("<blocks: ");
if ext[1][1] < 0 then
Print(-1 * ext[1]);
else
str := JoinStringsWithSeparator(List(ext[1], String), "*, ");
Print("[ ", str, "* ]");
fi;
for i in [2 .. Length(ext)] do
if ext[i][1] < 0 then
Print(", ", -1 * ext[i]);
else
str := JoinStringsWithSeparator(List(ext[i], String), "*, ");
Print(", [ ", str, "* ]");
fi;
od;
else
Print("<empty blocks");
fi;
Print(">");
end);
InstallMethod(PrintObj, "for blocks", [IsBlocks], 10,
function(blocks)
Print(PrintString(blocks));
end);
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