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Implement IsJoinIrreducible and IsMeetIrreducible #910

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Implement IsJoinIrreducible and IsMeetIrreducible #910

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46836b9
Naive implementation of IsJoinIrreducible and IsMeetIrreducible
ThatOtherAndrew Mar 20, 2026
3bb2bb8
Optimise join/meet irreducible functions
ThatOtherAndrew Mar 20, 2026
7b7d883
Add error handling inspired by existing .gi files
ThatOtherAndrew Mar 20, 2026
6c07453
Expand tests with LLM assistance
ThatOtherAndrew Mar 20, 2026
8cf99ca
Integrate joinmeetirreducible into oper.gi/oper.gd
ThatOtherAndrew Mar 20, 2026
2c37a4b
Remove dirty whitespace from tst/standard/oper.tst
ThatOtherAndrew Mar 20, 2026
8ae6cba
Add joinmeetirreducible tests to tst/standard/oper.tst
ThatOtherAndrew Mar 20, 2026
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3 changes: 3 additions & 0 deletions gap/oper.gd
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Original file line number Diff line number Diff line change
Expand Up @@ -161,3 +161,6 @@ DeclareOperation("PartialOrderDigraphJoinOfVertices",
[IsDigraph, IsPosInt, IsPosInt]);
DeclareOperation("PartialOrderDigraphMeetOfVertices",
[IsDigraph, IsPosInt, IsPosInt]);

DeclareOperation("IsJoinIrreducible", [IsDigraph, IsPosInt]);
DeclareOperation("IsMeetIrreducible", [IsDigraph, IsPosInt]);
32 changes: 32 additions & 0 deletions gap/oper.gi
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Expand Up @@ -2720,6 +2720,38 @@ function(D, i, j)
return fail;
end);

InstallMethod(IsJoinIrreducible,
"for a digraph and a positive integer",
[IsDigraph, IsPosInt],
function(D, v)
local hasse;
if not IsPartialOrderDigraph(D) then
ErrorNoReturn("the 1st argument <D> must satisfy IsPartialOrderDigraph,");
elif not v in DigraphVertices(D) then
ErrorNoReturn("the 2nd argument <v> must be a vertex of the ",
"1st argument <D>,");
fi;
hasse := DigraphReflexiveTransitiveReduction(DigraphMutableCopyIfMutable(D));
# join-irreducible iff at most one lower cover in the Hasse diagram
return InDegreeOfVertexNC(hasse, v) <= 1;
end);

InstallMethod(IsMeetIrreducible,
"for a digraph and a positive integer",
[IsDigraph, IsPosInt],
function(D, v)
local hasse;
if not IsPartialOrderDigraph(D) then
ErrorNoReturn("the 1st argument <D> must satisfy IsPartialOrderDigraph,");
elif not v in DigraphVertices(D) then
ErrorNoReturn("the 2nd argument <v> must be a vertex of the ",
"1st argument <D>,");
fi;
hasse := DigraphReflexiveTransitiveReduction(DigraphMutableCopyIfMutable(D));
# meet-irreducible iff at most one upper cover in the Hasse diagram
return OutDegreeOfVertexNC(hasse, v) <= 1;
end);

InstallMethod(DigraphKings, "for a digraph and a positive integer",
[IsDigraph, IsPosInt],
function(D, n)
Expand Down
121 changes: 112 additions & 9 deletions tst/standard/oper.tst
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Original file line number Diff line number Diff line change
Expand Up @@ -17,6 +17,7 @@
#@local out, out1, out2, out3, p1, p2, path, preorder, qr, r, res, rtclosure, t
#@local tclosure, u1, u2, x
#@local p, q, idp, idt, M
#@local b2, chain, lattice, m3
gap> START_TEST("Digraphs package: standard/oper.tst");
gap> LoadPackage("digraphs", false);;

Expand Down Expand Up @@ -1514,18 +1515,18 @@ gap> gr := ChainDigraph(5);
<immutable chain digraph with 5 vertices>
gap> DigraphRandomWalk(gr, 2, 100);
[ [ 2, 3, 4, 5 ], [ 1, 1, 1 ] ]
gap> DigraphRandomWalk(gr, 2, 2);
gap> DigraphRandomWalk(gr, 2, 2);
[ [ 2, 3, 4 ], [ 1, 1 ] ]
gap> DigraphRandomWalk(gr, 5, 100);
[ [ 5 ], [ ] ]
gap> gr := CompleteBipartiteDigraph(10, 8);;
gap> DigraphRandomWalk(gr, 3, 0);
gap> DigraphRandomWalk(gr, 3, 0);
[ [ 3 ], [ ] ]
gap> DigraphRandomWalk(gr, 19, 5);
Error, the 2nd argument <v> must be a vertex of the 1st argument <D>,
gap> DigraphRandomWalk(gr, 123, 5);
Error, the 2nd argument <v> must be a vertex of the 1st argument <D>,
gap> DigraphRandomWalk(gr, 3, -1);
gap> DigraphRandomWalk(gr, 3, -1);
Error, the 3rd argument <t> must be a non-negative int,

# DigraphLayers
Expand Down Expand Up @@ -1822,6 +1823,108 @@ fail
gap> PartialOrderDigraphJoinOfVertices(gr1, 3, 4);
fail

# IsJoinIrreducible, IsMeetIrreducible

# The pentagon lattice N5: 1 < {2, 3}, 3 < 4, {2, 4} < 5
gap> gr := Digraph([[2, 3], [5], [4], [5], []]);
<immutable digraph with 5 vertices, 5 edges>
gap> lattice := DigraphReflexiveTransitiveClosure(gr);
<immutable preorder digraph with 5 vertices, 13 edges>
gap> IsJoinIrreducible(lattice, 1);
true
gap> IsJoinIrreducible(lattice, 2);
true
gap> IsJoinIrreducible(lattice, 3);
true
gap> IsJoinIrreducible(lattice, 4);
true
gap> IsJoinIrreducible(lattice, 5);
false
gap> IsMeetIrreducible(lattice, 1);
false
gap> IsMeetIrreducible(lattice, 2);
true
gap> IsMeetIrreducible(lattice, 3);
true
gap> IsMeetIrreducible(lattice, 4);
true
gap> IsMeetIrreducible(lattice, 5);
true

# A 4-element chain: every element is doubly irreducible
gap> chain := DigraphReflexiveTransitiveClosure(ChainDigraph(4));
<immutable preorder digraph with 4 vertices, 10 edges>
gap> IsJoinIrreducible(chain, 1);
true
gap> IsJoinIrreducible(chain, 2);
true
gap> IsJoinIrreducible(chain, 3);
true
gap> IsJoinIrreducible(chain, 4);
true
gap> IsMeetIrreducible(chain, 1);
true
gap> IsMeetIrreducible(chain, 2);
true
gap> IsMeetIrreducible(chain, 3);
true
gap> IsMeetIrreducible(chain, 4);
true

# The Boolean lattice B2: 1 < {2, 3} < 4
gap> b2 := DigraphReflexiveTransitiveClosure(Digraph([[2, 3], [4], [4], []]));
<immutable preorder digraph with 4 vertices, 9 edges>
gap> IsJoinIrreducible(b2, 1);
true
gap> IsJoinIrreducible(b2, 2);
true
gap> IsJoinIrreducible(b2, 3);
true
gap> IsJoinIrreducible(b2, 4);
false
gap> IsMeetIrreducible(b2, 1);
false
gap> IsMeetIrreducible(b2, 2);
true
gap> IsMeetIrreducible(b2, 3);
true
gap> IsMeetIrreducible(b2, 4);
true

# The M3 lattice: 1 < {2, 3, 4} < 5
gap> m3 := DigraphReflexiveTransitiveClosure(Digraph([[2, 3, 4], [5], [5], [5], []]));
<immutable preorder digraph with 5 vertices, 12 edges>
gap> IsJoinIrreducible(m3, 1);
true
gap> IsJoinIrreducible(m3, 2);
true
gap> IsJoinIrreducible(m3, 3);
true
gap> IsJoinIrreducible(m3, 4);
true
gap> IsJoinIrreducible(m3, 5);
false
gap> IsMeetIrreducible(m3, 1);
false
gap> IsMeetIrreducible(m3, 2);
true
gap> IsMeetIrreducible(m3, 3);
true
gap> IsMeetIrreducible(m3, 4);
true
gap> IsMeetIrreducible(m3, 5);
true

# Error handling
gap> IsJoinIrreducible(CycleDigraph(3), 1);
Error, the 1st argument <D> must satisfy IsPartialOrderDigraph,
gap> IsMeetIrreducible(CycleDigraph(3), 1);
Error, the 1st argument <D> must satisfy IsPartialOrderDigraph,
gap> IsJoinIrreducible(Digraph([[1]]), 2);
Error, the 2nd argument <v> must be a vertex of the 1st argument <D>,
gap> IsMeetIrreducible(Digraph([[1]]), 2);
Error, the 2nd argument <v> must be a vertex of the 1st argument <D>,

# DigraphClosure
gap> gr := Digraph([[4, 5, 6, 7, 9], [7, 3], [2, 6, 7, 9, 10],
> [5, 6, 7, 1, 9], [1, 4, 6, 7], [7, 1, 3, 4, 5],
Expand Down Expand Up @@ -2460,9 +2563,9 @@ gap> ConormalProduct(CycleDigraph(2), CycleDigraph(8));
#HomomorphicProduct
gap> D := Digraph([[2, 3], [1, 3, 3], [1, 2, 2]]);
<immutable multidigraph with 3 vertices, 8 edges>
gap> HomomorphicProduct(D, D);
gap> HomomorphicProduct(D, D);
Error, the 1st argument (a digraph) must not satisfy IsMultiDigraph
gap> DigraphSymmetricClosure(CycleDigraph(6));
gap> DigraphSymmetricClosure(CycleDigraph(6));
<immutable symmetric digraph with 6 vertices, 12 edges>
gap> HomomorphicProduct(PetersenGraph(), last);
<immutable digraph with 60 vertices, 1080 edges>
Expand Down Expand Up @@ -2525,7 +2628,7 @@ gap> StrongProduct(NullDigraph(0), CompleteDigraph(3));
<immutable empty digraph with 0 vertices>
gap> D1 := Digraph([[2], [1, 3, 4], [2, 5], [2, 5], [3, 4]]);
<immutable digraph with 5 vertices, 10 edges>
gap> D2 := Digraph([[2], [1, 3, 4], [2], [2]]);
gap> D2 := Digraph([[2], [1, 3, 4], [2], [2]]);
<immutable digraph with 4 vertices, 6 edges>
gap> LexicographicProduct(D1, D2);
<immutable digraph with 20 vertices, 190 edges>
Expand All @@ -2545,7 +2648,7 @@ gap> OutNeighbours(last);
[ 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20 ],
[ 9, 10, 11, 12, 13, 14, 15, 16, 18 ],
[ 9, 10, 11, 12, 13, 14, 15, 16, 18 ] ]
gap> LexicographicProduct(ChainDigraph(3), CycleDigraph(7));
gap> LexicographicProduct(ChainDigraph(3), CycleDigraph(7));
<immutable digraph with 21 vertices, 119 edges>

# SwapDigraphs
Expand Down Expand Up @@ -3032,7 +3135,7 @@ Error, expected an edge between the 2nd and 3rd arguments (vertices) 1 and

# DigraphContractEdge: Edge is a looped edge (u = v)
gap> D := DigraphByEdges([[1, 1], [2, 1], [1, 2]]);;
gap> DigraphVertexLabels(D);;
gap> DigraphVertexLabels(D);;
gap> C := DigraphContractEdge(D, 1, 1);
Error, The 2nd argument <u> must not be equal to the 3rd argument <v>
gap> DigraphHasLoops(D);
Expand Down Expand Up @@ -3196,7 +3299,7 @@ Error, expected an edge between the 2nd and 3rd arguments (vertices) 1 and

# DigraphContractEdge: Edge is a looped edge (u = v) (mutable)
gap> D := DigraphByEdges(IsMutableDigraph, [[1, 1], [2, 1], [1, 2]]);;
gap> DigraphVertexLabels(D);;
gap> DigraphVertexLabels(D);;
gap> DigraphContractEdge(D, 1, 1);
Error, The 2nd argument <u> must not be equal to the 3rd argument <v>
gap> DigraphHasLoops(D);
Expand Down