From 50f28ca1af0398a587254a696f02e887442a2eff Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Meike=20Wei=C3=9F?= <meike.weiss@rwth-aachen.de>
Date: Thu, 12 Sep 2024 16:45:48 +0200
Subject: [PATCH 1/2] bug fix

---
 gap/Paths/paths.gd | 14 ++++++++++++++
 gap/Paths/paths.gi | 26 ++++++++++++++++++++------
 2 files changed, 34 insertions(+), 6 deletions(-)

diff --git a/gap/Paths/paths.gd b/gap/Paths/paths.gd
index ac091d19..526a9f25 100644
--- a/gap/Paths/paths.gd
+++ b/gap/Paths/paths.gd
@@ -1308,6 +1308,20 @@ DeclareAttribute( "AllTwoWaistsOfComplex", IsTwistedPolygonalComplex);
 #! gap> AllThreeWaistsOfComplex(Tetrahedron());
 #! [  ]
 #! @EndExampleSession
+#! As another example we consider the following simplicial surface:
+#! @BeginExampleSession
+#! gap> umbdesc:=[ (1,4,6,7,5,3), (1,7,5,8,2,3), (1,7,6,8,2,4),(2,4,6,8,5,3) ];;
+#! gap> s:=SimplicialSurfaceByUmbrellaDescriptor(umbdesc);;
+#! gap> AllThreeWaistsOfComplex(s);
+#! [ ( v2, E1, v3, E6, v1, E11, v2 ),
+#!   ( v1, E1, v4, E8, v2, E10, v1 ),
+#!   ( v3, E2, v2, E6, v1, E9, v3 ),
+#!   ( v1, E2, v4, E7, v3, E12, v1 ),
+#!   ( v2, E3, v4, E4, v3, E12, v2 ),
+#!   ( v3, E3, v4, E5, v2, E10, v3 ),
+#!   ( v4, E4, v1, E8, v2, E9, v4 ),
+#!   ( v4, E5, v1, E7, v3, E11, v4 )]
+#! @EndExampleSession
 #!
 #! @Returns a set of closed vertex-edge-paths
 #! @Arguments complex
diff --git a/gap/Paths/paths.gi b/gap/Paths/paths.gi
index 9f3aec5c..11fe1f84 100644
--- a/gap/Paths/paths.gi
+++ b/gap/Paths/paths.gi
@@ -1011,12 +1011,26 @@ end
 InstallMethod( AllThreeWaistsOfComplex, "for a twisted polygonal complex",
     [IsTwistedPolygonalComplex],
     function( surface )
-        local w,eof,waists;
-        waists:=Combinations(Edges(surface),3);
-        waists:=Filtered(waists,w->Length(Union(VerticesOfEdges(surface){w}))=3);
-        waists:=Filtered(waists,w->Filtered(EdgesOfFaces(surface),
-        eof->Length(Intersection(w,eof))>=2)=[]);
-        return List(waists,w->VertexEdgePathByEdges(surface,w));
+        local w,voe1,voe2,voe3,v1,v2,v3,eof,waists,verticesOfEdges,facesOfEdges,temp;
+         verticesOfEdges:=VerticesOfEdges(surface);
+         facesOfEdges:=FacesOfEdges(surface);
+         waists:=Combinations(InnerEdges(surface),3);
+         waists:=Filtered(waists,w->Length(Union(verticesOfEdges{w}))=3);
+         waists:=Filtered(waists,w->Length(Union(facesOfEdges{w}))=6);
+         temp:=waists;
+         waists:=[];
+         for w in temp do 
+            voe1:=verticesOfEdges[w[1]];
+            voe2:=verticesOfEdges[w[2]];
+            voe3:=verticesOfEdges[w[3]];
+ 		    v1:=Intersection(voe1,voe2)[1];
+            v2:=Intersection(voe2,voe3)[1];
+            v3:=Intersection(voe1,voe3)[1];
+            if Length(Set([v1,v2,v3]))=3 then 
+ 			    Add(waists,[v1,w[1],v2,w[2],v3,w[3],v1]);
+ 		    fi;
+         od;
+         return List(waists,w->VertexEdgePathNC(surface,w));
 end
 );
 

From 0aec9ea016974f4e9f8bf0228f8effb5a7eb2248 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Meike=20Wei=C3=9F?= <meike.weiss@rwth-aachen.de>
Date: Thu, 12 Sep 2024 17:08:13 +0200
Subject: [PATCH 2/2] fixed error

---
 gap/Paths/paths.gd | 12 ++++--------
 gap/Paths/paths.gi |  2 +-
 2 files changed, 5 insertions(+), 9 deletions(-)

diff --git a/gap/Paths/paths.gd b/gap/Paths/paths.gd
index 526a9f25..5b56936e 100644
--- a/gap/Paths/paths.gd
+++ b/gap/Paths/paths.gd
@@ -1313,14 +1313,10 @@ DeclareAttribute( "AllTwoWaistsOfComplex", IsTwistedPolygonalComplex);
 #! gap> umbdesc:=[ (1,4,6,7,5,3), (1,7,5,8,2,3), (1,7,6,8,2,4),(2,4,6,8,5,3) ];;
 #! gap> s:=SimplicialSurfaceByUmbrellaDescriptor(umbdesc);;
 #! gap> AllThreeWaistsOfComplex(s);
-#! [ ( v2, E1, v3, E6, v1, E11, v2 ),
-#!   ( v1, E1, v4, E8, v2, E10, v1 ),
-#!   ( v3, E2, v2, E6, v1, E9, v3 ),
-#!   ( v1, E2, v4, E7, v3, E12, v1 ),
-#!   ( v2, E3, v4, E4, v3, E12, v2 ),
-#!   ( v3, E3, v4, E5, v2, E10, v3 ),
-#!   ( v4, E4, v1, E8, v2, E9, v4 ),
-#!   ( v4, E5, v1, E7, v3, E11, v4 )]
+#! [ ( v1, E1, v2, E6, v3, E11, v1 ), ( v2, E1, v1, E8, v4, E10, v2 ),
+#!   ( v1, E2, v3, E6, v2, E9, v1 ), ( v3, E2, v1, E7, v4, E12, v3 ),
+#!   ( v3, E3, v2, E4, v4, E12, v3 ), ( v2, E3, v3, E5, v4, E10, v2 ),
+#!   ( v2, E4, v4, E8, v1, E9, v2 ), ( v3, E5, v4, E7, v1, E11, v3 ) ]
 #! @EndExampleSession
 #!
 #! @Returns a set of closed vertex-edge-paths
diff --git a/gap/Paths/paths.gi b/gap/Paths/paths.gi
index 11fe1f84..5e15486e 100644
--- a/gap/Paths/paths.gi
+++ b/gap/Paths/paths.gi
@@ -1027,7 +1027,7 @@ InstallMethod( AllThreeWaistsOfComplex, "for a twisted polygonal complex",
             v2:=Intersection(voe2,voe3)[1];
             v3:=Intersection(voe1,voe3)[1];
             if Length(Set([v1,v2,v3]))=3 then 
- 			    Add(waists,[v1,w[1],v2,w[2],v3,w[3],v1]);
+ 			    Add(waists,[v3,w[1],v1,w[2],v2,w[3],v3]);
  		    fi;
          od;
          return List(waists,w->VertexEdgePathNC(surface,w));