From 2b47fbb61cf370bddf9d56bf9a92335c5b7c507f Mon Sep 17 00:00:00 2001 From: Flynn Fehre Date: Thu, 9 Mar 2023 19:40:04 +0100 Subject: [PATCH 01/44] Added DrawConvexFacegraphToTikz --- doc/Image_convex_facegraph_Double6Gon.tex | 47 +++++ gap/PolygonalComplexes/drawing.gd | 17 ++ gap/PolygonalComplexes/drawing.gi | 228 ++++++++++++++++++++++ gap/PolygonalComplexes/embedding.gd | 64 ++++++ 4 files changed, 356 insertions(+) create mode 100644 doc/Image_convex_facegraph_Double6Gon.tex diff --git a/doc/Image_convex_facegraph_Double6Gon.tex b/doc/Image_convex_facegraph_Double6Gon.tex new file mode 100644 index 00000000..a919f0e3 --- /dev/null +++ b/doc/Image_convex_facegraph_Double6Gon.tex @@ -0,0 +1,47 @@ +\begin{tikzpicture}[vertexBall, edgeDouble=nolabels, faceStyle=nolabels, scale=4] + +\coordinate (V1) at (1. , 0.); +\coordinate (V2) at (0.5000000010362841 , 0.8660254031861397); +\coordinate (V3) at (-0.4999999979274318 , 0.8660254049810364); +\coordinate (V4) at (-1. , 3.589793029841612e-09); +\coordinate (V5) at (-0.5000000041451365 , -0.866025401391243); +\coordinate (V6) at (0.4999999948185802 , -0.8660254067759328); +\coordinate (V7) at (0.8333333326424773 , -5.982988363998724e-10); +\coordinate (V8) at (0.3888888898100303 , 0.7216878361878827); +\coordinate (V9) at (-0.4351851836499495 , 0.6976315766169703); +\coordinate (V10) at (-0.8225308646325142 , -0.02806563506918342); +\coordinate (V11) at (-0.3870884810657467 , -0.7263654412350147); +\coordinate (V12) at (0.4077074718085085 , -0.698411178156174); +\draw[edge] (V1) -- node[edgeLabel] {$1$} (V6); +\draw[edge] (V1) -- node[edgeLabel] {$2$} (V2); +\draw[edge] (V2) -- node[edgeLabel] {$3$} (V3); +\draw[edge] (V3) -- node[edgeLabel] {$4$} (V4); +\draw[edge] (V4) -- node[edgeLabel] {$5$} (V5); +\draw[edge] (V5) -- node[edgeLabel] {$6$} (V6); +\draw[edge] (V1) -- node[edgeLabel] {$7$} (V7); +\draw[edge] (V6) -- node[edgeLabel] {$8$} (V12); +\draw[edge] (V7) -- node[edgeLabel] {$9$} (V12); +\draw[edge] (V2) -- node[edgeLabel] {$10$} (V8); +\draw[edge] (V7) -- node[edgeLabel] {$11$} (V8); +\draw[edge] (V3) -- node[edgeLabel] {$12$} (V9); +\draw[edge] (V8) -- node[edgeLabel] {$13$} (V9); +\draw[edge] (V4) -- node[edgeLabel] {$14$} (V10); +\draw[edge] (V9) -- node[edgeLabel] {$15$} (V10); +\draw[edge] (V5) -- node[edgeLabel] {$16$} (V11); +\draw[edge] (V10) -- node[edgeLabel] {$17$} (V11); +\draw[edge] (V11) -- node[edgeLabel] {$18$} (V12); +% Draw the faces +\vertexLabelR{V1}{left}{$1$} +\vertexLabelR{V2}{left}{$2$} +\vertexLabelR{V3}{left}{$3$} +\vertexLabelR{V4}{left}{$4$} +\vertexLabelR{V5}{left}{$5$} +\vertexLabelR{V6}{left}{$6$} +\vertexLabelR{V7}{left}{$7$} +\vertexLabelR{V8}{left}{$8$} +\vertexLabelR{V9}{left}{$9$} +\vertexLabelR{V10}{left}{$10$} +\vertexLabelR{V11}{left}{$11$} +\vertexLabelR{V12}{left}{$12$} +\end{tikzpicture} + diff --git a/gap/PolygonalComplexes/drawing.gd b/gap/PolygonalComplexes/drawing.gd index e50ce384..1f09d3f9 100644 --- a/gap/PolygonalComplexes/drawing.gd +++ b/gap/PolygonalComplexes/drawing.gd @@ -999,3 +999,20 @@ DrawFacegraphToTikz( oct, #! its own). #! @EndChunk +#! @BeginChunk DrawConvexFacegraphToTikz_example +#! @BeginLog +double6Gon := SimplicialSurfaceByVerticesInFaces([[1,2,3],[1,3,4],[1,4,5], +[1,5,6],[1,6,7],[1,2,7],[2,3,8],[3,4,8],[4,5,8],[5,6,8],[6,7,8],[2,7,8]]);; +#! @EndLog +#! +#! +#! \input{Image_Double6gon.tex} +#! +#! @BeginLog +DrawConvexFacegraphToTikz( double6Gon, "convex_facegraph_Double6Gon.tex" );; +#! @EndLog +#! +#! +#! \input{Image_convex_facegraph_Double6Gon.tex} +#! +#! @EndChunk \ No newline at end of file diff --git a/gap/PolygonalComplexes/drawing.gi b/gap/PolygonalComplexes/drawing.gi index f6942b07..427b5dec 100644 --- a/gap/PolygonalComplexes/drawing.gi +++ b/gap/PolygonalComplexes/drawing.gi @@ -2024,3 +2024,231 @@ InstallOtherMethod( DrawFacegraphToTikz, ); +InstallMethod( DrawConvexFacegraphToTikz, + "for a closed vertex-faithful simplicial sphere, a file name and a record", + [IsSimplicialSurface, IsString, IsRecord], + function(surf, name, record) + local graph, SplitListPosition, ThreeSplitListPosition, InFilterFunc, IntersectionFilterFunc, CorrectFacesOfVertexFilter, WeightedCentric, TwoWeightedCentric, MainHelp, RegularPolygon, DrawConvexFaceGraph, DrawGraph; + if not( IsClosedSurface(surf) and IsVertexFaithful(surf) and EulerCharacteristic(surf)=2) and not IsBound(printRecord.faceCoordinates2D) then + return fail; + fi; + + SplitListPosition := function(list, v) # help function + local i, res1, res2; + res1:=[]; + res2:=[]; + for i in [2..v] do + Add(res1,list[i]); + od; + for i in [v..Length(list)] do + Add(res2, list[i]); + od; + Add(res1,list[1]); + Add(res2, list[1]); + return [res1,res2]; + end; + + ThreeSplitListPosition := function(list, v, w) # helpt function + local i, res1, res2, res3; + if w > v then + res1 := []; + res2 := []; + res3 := []; + for i in [2..v] do + Add(res1,list[i]); + od; + for i in [v..w] do + Add(res2, list[i]); + od; + for i in [w..Length(list)] do + Add(res3, list[i]); + od; + Add(res1, list[1]); + Add(res2, list[1]); + Add(res3, list[1]); + elif w < v then + res1 := []; + res2 := []; + res3 := []; + for i in [2..w] do + Add(res1,list[i]); + od; + for i in [w..v] do + Add(res2, list[i]); + od; + for i in [v..Length(list)] do + Add(res3, list[i]); + od; + Add(res1, list[1]); + Add(res2, list[1]); + Add(res3, list[1]); + fi; + return [res1, res2, res3]; + end; + + InFilterFunc := function(cur1, cur2, list) # help function + if cur1 in list and cur2 in list then + return true; + else + return false; + fi; + end; + + IntersectionFilterFunc := function(faceGraph, list) # help function + if not IsEmpty(Intersection(faceGraph, list)) then + return true; + else + return false; + fi; + end; + + CorrectFacesOfVertexFilter := function(cur1, cur2, faceGraph, list) # help function + return InFilterFunc(cur1, cur2, list) and IntersectionFilterFunc(faceGraph, list); + end; + + WeightedCentric := function(list) # help function + return Float(2/3)*list[1]+Float(1/6)*(list[2]+list[3]); + end; + + TwoWeightedCentric := function(list) # help function + local res; + res := []; + Add(res, Float(2/3)*list[1] + Float(5/18)*list[2] + Float(1/18)*list[3]); + Add(res, Float(2/3)*list[1] + Float(1/18)*list[2] + Float(5/18)*list[3]); + return res; + end; + + MainHelp := function(surf, cur, faceGraph) #surf simp. surface, cur list of lists of [v,[x,y]], faceGraph list of [v,[x,y]] with the added vertices of wanted faceGraph + local n, mainHelp1, mainHelp2, cur1, cur2, curi, mainHelpi, i, v, newv, res, neighbours, verticesOfFaceGraph, correctFacesOfVertex, toSplitVertex, toSplitVertex1, toSplitVertex2, toSplitVertexPos, toSplitVertexPos1, toSplitVertexPos2, alreadyPositionedVertices; + if Length(cur) >= 2 then # More than one convex drawing plane + res := []; + faceGraph := MainHelp(surf, [cur[1]], faceGraph)[2]; + for i in [1..Length(cur)] do + mainHelpi := MainHelp(surf, [cur[i]], faceGraph); + curi := mainHelpi[1]; + res := Concatenation(res, curi); + faceGraph := Set(Concatenation(faceGraph, mainHelpi[2])); + od; + return [res, faceGraph]; + elif Length(cur)=1 then # Only one convex drawing plane + cur := cur[1]; + n:=Length(cur); + if n < 2 then + return [[[]], faceGraph]; + fi; + neighbours := NeighbourFacesOfFace(surf, cur[1][1]); + verticesOfFaceGraph := List(faceGraph, x -> x[1]); + if Length(Intersection(verticesOfFaceGraph, neighbours)) = 2 then # 2 neighbours of cur[1] have been positioned already + if Length(neighbours) = 2 then # There are only 2 neighbours which means no vertex has to be positioned + Remove(cur, 1); + else # There are 3 neighbours which means there is a new vertex that has to be positioned + for v in neighbours do + if not v in verticesOfFaceGraph then + newv := [v, WeightedCentric([cur[1][2], cur[2][2], cur[n][2]])]; + Add(faceGraph, newv); + Remove(cur, 1); + Add(cur, newv); + fi; + od; + fi; + return [[cur], faceGraph]; + elif Length(Intersection(verticesOfFaceGraph, neighbours)) = 1 then # 1 neighbour of cur[1] has been positioned already + if Length(neighbours) = 1 then # There is only 1 neighbour which means no vertex has to be positioned + Remove(cur, 1); + elif Length(neighbours) = 2 then # There are only 2 neighbours which means 1 vertex has to be positioned + for v in neighbours do + if not v in verticesOfFaceGraph then + newv := [v, WeightedCentric([cur[1][2], cur[2][2], cur[n][2]])]; + Add(faceGraph, newv); + Remove(cur, 1); + Add(cur, newv); + fi; + od; + else # There are 3 neighbours which means 2 vertices have to be positioned + correctFacesOfVertex := Filtered(FacesOfVertices(surf), x -> CorrectFacesOfVertexFilter(cur[1][1], cur[2][1], List(faceGraph, y -> y[1]), x)); + for v in Difference(Difference(neighbours, correctFacesOfVertex[1]), verticesOfFaceGraph) do + newv := [v, TwoWeightedCentric([cur[1][2], cur[2][2], cur[n][2]])[2]]; + Add(faceGraph, newv); + Add(cur, newv); + od; + for v in Difference(Intersection(neighbours, correctFacesOfVertex[1]), verticesOfFaceGraph) do + newv := [v, TwoWeightedCentric([cur[1][2], cur[2][2], cur[n][2]])[1]]; + Add(faceGraph, newv); + Add(cur, newv); + od; + fi; + Remove(cur, 1); + return [[cur], faceGraph]; + elif Length(Intersection(verticesOfFaceGraph, neighbours)) = 3 then # 3 neighbours of cur[1] have been positioned already + alreadyPositionedVertices := Difference(neighbours, [cur[2][1], cur[n][1]]); + if Length(Intersection(List(cur, x -> x[1]), alreadyPositionedVertices)) = 2 then # case 3: edge slices convex drawing plane in three and splits it + toSplitVertex1 := Intersection(List(cur, x -> x[1]), alreadyPositionedVertices)[1]; + toSplitVertex2 := Intersection(List(cur, x -> x[1]), alreadyPositionedVertices)[2]; + toSplitVertexPos1 := Position(List(cur, x -> x[1]), toSplitVertex1); + toSplitVertexPos2 := Position(List(cur, x -> x[1]), toSplitVertex2); + return [ThreeSplitListPosition(cur, toSplitVertexPos1, toSplitVertexPos2), faceGraph]; + elif Length(Intersection(List(cur, x -> x[1]), alreadyPositionedVertices)) = 1 then # case 2: edge slices convex drawing plane in two and splits it + toSplitVertex := Intersection(List(cur, x -> x[1]), alreadyPositionedVertices)[1]; + toSplitVertexPos := Position(List(cur, x -> x[1]), toSplitVertex); + return [SplitListPosition(cur, toSplitVertexPos), faceGraph]; + elif Length(Intersection(List(cur, x -> x[1]), alreadyPositionedVertices)) = 0 then # case 1: edge does not violate convex drawing plane + Remove(cur, 1); + return [[cur], faceGraph]; + else + # Print("Failure at 3 neighbours of cur[1] have been positioned already!"); + Error(); + fi; + fi; + fi; + end; + + RegularPolygon := function(list) #returns vertices of a regular polygon as a list of [vert, [x,y]] + local n, res, i; + res:=[]; + n:=Length(list); + for i in [1..n] do + Add(res,[list[i],[Cos(2*3.14159265*((i-1)/n)),Sin(2*3.14159265*((i-1)/n))]]); + od; + return res; + end; + + DrawConvexFaceGraph := function(surf) + local cur, faceGraph, path, mainHelp, maxPathPos; + maxPathPos := PositionMaximum(List(UmbrellaPathsOfVertices(surf), x -> Length(FacesAsList(x)))); + path := UmbrellaPathOfVertex(surf, maxPathPos); # Start with the biggest UmbrellaPath + # path := UmbrellaPathOfVertex(surf, Vertices(surf)[1]); # Start with the UmbrellaPath of the vertex 1 + cur := [RegularPolygon(FacesAsList(path))]; + faceGraph := RegularPolygon(FacesAsList(path)); + while Length(faceGraph) x[1]); + if "scale" in RecNames(record) and "faceCoordinates2D" in RecNames(record) then + return DrawFacegraphToTikz(surf, name, record); + elif (not "scale" in RecNames(record)) and "faceCoordinates2D" in RecNames(record) then + record.scale := 4; + elif "scale" in RecNames(record) and (not "faceCoordinates2D" in RecNames(record)) then + record.faceCoordinates2D := List(graph, x -> x[2]); + else + record.faceCoordinates2D := List(graph, x -> x[2]); + record.scale := 4; + fi; + + return DrawFacegraphToTikz(surf, name, record); + + end +); + +InstallOtherMethod( DrawConvexFacegraphToTikz, + "for a simplicial surface and a file name", + [IsSimplicialSurface, IsString], + function(surf, name) + return DrawConvexFacegraphToTikz(surf, name, rec()); + end +); diff --git a/gap/PolygonalComplexes/embedding.gd b/gap/PolygonalComplexes/embedding.gd index 8be9e2a3..cd9940fa 100644 --- a/gap/PolygonalComplexes/embedding.gd +++ b/gap/PolygonalComplexes/embedding.gd @@ -363,3 +363,67 @@ DeclareOperation( "DrawFacegraphToTikz", [IsSimplicialSurface ,IsString,IsRecord #! @Subsection Output control #! @SubsectionLabel DrawFacegraphToTikz_Output #! @InsertChunk DrawFacegraphToTikz_Output +#! +#! @BeginGroup DrawConvexFacegraphToTikz +#! @Description +#! Draw the face graph of the given surface into a tex-file (using TikZ). +#! An introduction to the use of this method (along with several examples) +#! can be found at the start of section . +#! If surface is a simplicial vertex faithful sphere and the function +#! is used without the argument printRecord, then the drawing printed +#! into file is a planar embedding of the face graph of surface, +#! where the vertices of the surface are identified by the faces of the +#! embedding. DrawConvexFacegraphToTikz differs from DrawFacegraphToTikz +#! () by constructing the face graph +#! by successively manipulating a convex drawing plane and calculating new face coordinates. +#! The new coordinates are then drawn with DrawFacegraphToTikz. +#! This results in an embedding which maps the faces +#! of one of the largest umbrella paths on the outer ring as a +#! regular polygon. Trying to use the function for a surface that is not a +#! vertex-faithful sphere results in returning fail. +#! +#! * If the given file does not end in .tex the ending +#! .tex will be added to it. +#! * The given file will be overwritten without asking if it already exists. +#! If you don't have permission to write in that file, this method will +#! throw an error. +#! * The particulars of the drawing are determined by the +#! given printRecord. If this is not given and surface is a +#! simplicial sphere, the default settings are used. +#! * The printRecord will be modified and returned by this method. +#! It contains the data to recreate the drawing of the surface. +#! +#! +#! There are several parameters to change the output of this method. +#! Since the design of the parameters is the design of the parameters +#! of DrawFacegraphToTikz(), +#! one can also refer to the corresponding subsections for a better +#! understanding. +#! There are the following classes of parameters: +#! * Colours +#! (): Change the +#! colours of edges and faces represented as vertices. +#! * Labels +#! (): Modify the labels +#! of vertices, edges and faces. +#! * Scale +#! (): These +#! parameters control the size of the drawing. +#! * faceCoordinates2D +#! (): +#! Modify the 2D-coordinates of the faces. +#! * Geodesics +#! (): Draw the +#! geodesics of the simplicial surface into the file. +#! * Output control +#! (): Modify how the +#! &LaTeX;-output behaves and how much information is printed to the +#! console. +#! +#! Consider the following example of the double-6-gon: +#! @InsertChunk DrawConvexFacegraphToTikz_example +#! +#! @Returns a record +#! @Arguments surface, file[, printRecord] +DeclareOperation( "DrawConvexFacegraphToTikz", [IsSimplicialSurface, IsString, IsRecord]); +#! @EndGroup \ No newline at end of file From 78c321b769fe5f46451fb8842308164ff13de38c Mon Sep 17 00:00:00 2001 From: Flynn Fehre Date: Sat, 11 Mar 2023 10:30:30 +0100 Subject: [PATCH 02/44] changed WeightedCentric for improved space between the facenodes --- gap/PolygonalComplexes/drawing.gi | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/gap/PolygonalComplexes/drawing.gi b/gap/PolygonalComplexes/drawing.gi index 427b5dec..69474205 100644 --- a/gap/PolygonalComplexes/drawing.gi +++ b/gap/PolygonalComplexes/drawing.gi @@ -2107,14 +2107,14 @@ InstallMethod( DrawConvexFacegraphToTikz, end; WeightedCentric := function(list) # help function - return Float(2/3)*list[1]+Float(1/6)*(list[2]+list[3]); + return Float(1/2)*list[1]+Float(1/4)*(list[2]+list[3]); end; TwoWeightedCentric := function(list) # help function local res; res := []; - Add(res, Float(2/3)*list[1] + Float(5/18)*list[2] + Float(1/18)*list[3]); - Add(res, Float(2/3)*list[1] + Float(1/18)*list[2] + Float(5/18)*list[3]); + Add(res, Float(1/2)*list[1] + Float(7/18)*list[2] + Float(2/18)*list[3]); + Add(res, Float(1/2)*list[1] + Float(2/18)*list[2] + Float(7/18)*list[3]); return res; end; From e30293b9e075b9c69e1b7533ad2e8285840de35c Mon Sep 17 00:00:00 2001 From: Flynn Fehre Date: Thu, 18 May 2023 13:44:43 +0200 Subject: [PATCH 03/44] first correction --- gap/PolygonalComplexes/drawing.gi | 17 +++++++++++++---- 1 file changed, 13 insertions(+), 4 deletions(-) diff --git a/gap/PolygonalComplexes/drawing.gi b/gap/PolygonalComplexes/drawing.gi index 69474205..cebcd12f 100644 --- a/gap/PolygonalComplexes/drawing.gi +++ b/gap/PolygonalComplexes/drawing.gi @@ -2048,7 +2048,7 @@ InstallMethod( DrawConvexFacegraphToTikz, return [res1,res2]; end; - ThreeSplitListPosition := function(list, v, w) # helpt function + ThreeSplitListPosition := function(list, v, w) # help function local i, res1, res2, res3; if w > v then res1 := []; @@ -2130,9 +2130,9 @@ InstallMethod( DrawConvexFacegraphToTikz, faceGraph := Set(Concatenation(faceGraph, mainHelpi[2])); od; return [res, faceGraph]; - elif Length(cur)=1 then # Only one convex drawing plane + elif Length(cur) = 1 then # Only one convex drawing plane cur := cur[1]; - n:=Length(cur); + n := Length(cur); if n < 2 then return [[[]], faceGraph]; fi; @@ -2142,13 +2142,21 @@ InstallMethod( DrawConvexFacegraphToTikz, if Length(neighbours) = 2 then # There are only 2 neighbours which means no vertex has to be positioned Remove(cur, 1); else # There are 3 neighbours which means there is a new vertex that has to be positioned + alreadyPositionedVertices := Difference(neighbours, [cur[2][1], cur[n][1]]); + if Length(Intersection(List(cur, x -> x[1]), alreadyPositionedVertices)) = 1 then # case 2: edge slices convex drawing plane in two and splits it + toSplitVertex := Intersection(List(cur, x -> x[1]), alreadyPositionedVertices)[1]; + toSplitVertexPos := Position(List(cur, x -> x[1]), toSplitVertex); + return [SplitListPosition(cur, toSplitVertexPos), faceGraph]; + fi; for v in neighbours do - if not v in verticesOfFaceGraph then + if v=25 then Error(); fi; # debug + if (not v in verticesOfFaceGraph) then # and (ForAny(VerticesOfFace(surf, v), faceVertex -> Length(Intersection(List(cur, x -> x[1]), FacesAsList(UmbrellaPathOfVertex(surf, faceVertex)))) >= 3)) newv := [v, WeightedCentric([cur[1][2], cur[2][2], cur[n][2]])]; Add(faceGraph, newv); Remove(cur, 1); Add(cur, newv); fi; + if v=25 then Error(); fi; # debug od; fi; return [[cur], faceGraph]; @@ -2252,3 +2260,4 @@ InstallOtherMethod( DrawConvexFacegraphToTikz, return DrawConvexFacegraphToTikz(surf, name, rec()); end ); + From f0319a97d0479ae1730d11b1e1f0e6457f4d7609 Mon Sep 17 00:00:00 2001 From: Flynn Fehre Date: Sat, 20 May 2023 14:23:36 +0200 Subject: [PATCH 04/44] solved an error with DrawConvexFacegraphToTikz and added a new parameter 'spread' for this function --- gap/PolygonalComplexes/drawing.gd | 46 ++++++- gap/PolygonalComplexes/drawing.gi | 198 +++++++++++------------------- 2 files changed, 117 insertions(+), 127 deletions(-) diff --git a/gap/PolygonalComplexes/drawing.gd b/gap/PolygonalComplexes/drawing.gd index 1f09d3f9..14f009fd 100644 --- a/gap/PolygonalComplexes/drawing.gd +++ b/gap/PolygonalComplexes/drawing.gd @@ -899,11 +899,15 @@ DrawFacegraphToTikz( tetra, "facegraph_oct_rescaled", pr);; #! * faceCoordinates2D: Modify the coordinates of the faces which are #! represented as vertices in the embedding. #! +#! * spread (Only available for DrawConvexFacegraphToTikz +#! ): Modify the spread of +#! the coordinates. +#! #! We will exemplify them with the tetrahedron to make clear how the parameters #! work: #! #! @BeginLog -tetra :=SimplicialSurfaceByVerticesInFaces([[1,2,3],[1,2,4], +tetra := SimplicialSurfaceByVerticesInFaces([[1,2,3],[1,2,4], [1,3,4],[2,3,4]]);; DrawFacegraphToTikz(tetra, "facegraph_tetrahedron");; #! @EndLog @@ -931,6 +935,46 @@ DrawFacegraphToTikz(tetra, #! #! #! +#! +#! spread(Only available for DrawConvexFacegraphToTikz +#! ): Modifies the position of the +#! vertices representing the faces. The spread parameter can be chosen as a float in the +#! interval (0, 1). Choosing the parameter outside the interval results in +#! an error. Choosing a number close to 1 modifies the face coordinates such +#! that they tend torwards the outer ring of the face graph. Choosing a number +#! close to 0 modifies the face coordinates such that they tend torwards the +#! middle of the face graph. The default spread is set at 0.5. +#! +#! We will exemplify this parameter with the icosahedron. +#! @BeginLog +icosahedron := SimplicialSurfaceByVerticesInFaces([ [ 1, 2, 3 ], [ 1, 2, 4 ], + [ 1, 4, 5 ], [ 1, 5, 6 ], [ 1, 3, 6 ], [ 2, 3, 7 ], [ 2, 4, 8 ], [ 4, 5, 9 ], + [ 5, 6, 10 ], [ 3, 6, 11 ], [ 2, 7, 8 ], [ 4, 8, 9 ], [ 5, 9, 10 ], [ 6, 10, 11 ], + [ 3, 7, 11 ], [ 7, 8, 12 ], [ 8, 9, 12 ], [ 9, 10, 12 ], [ 10, 11, 12 ], + [ 7, 11, 12 ] ]);; +DrawConvexFacegraphToTikz(icosahedron, "convex_facegraph_icosahedron_default_spread");; +#! @EndLog +#! +#! \input{_TIKZ_convex_facegraph_icosahedron_default_spread.tex} +#! +#! +#! @BeginLog +pr := rec(spread := 0.3);; +DrawConvexFacegraphToTikz(icosahedron, + "convex_facegraph_icosahedron_low_spread", pr);; +#! @EndLog +#! +#! \input{_TIKZ_convex_facegraph_icosahedron_low_spread.tex} +#! +#! +#! @BeginLog +pr := rec(spread := 0.7);; +DrawConvexFacegraphToTikz(icosahedron, + "convex_facegraph_icosahedron_high_spread", pr);; +#! @EndLog +#! +#! \input{_TIKZ_convex_facegraph_icosahedron_high_spread.tex} +#! #! @EndChunk diff --git a/gap/PolygonalComplexes/drawing.gi b/gap/PolygonalComplexes/drawing.gi index cebcd12f..05cd943d 100644 --- a/gap/PolygonalComplexes/drawing.gi +++ b/gap/PolygonalComplexes/drawing.gi @@ -2028,8 +2028,10 @@ InstallMethod( DrawConvexFacegraphToTikz, "for a closed vertex-faithful simplicial sphere, a file name and a record", [IsSimplicialSurface, IsString, IsRecord], function(surf, name, record) - local graph, SplitListPosition, ThreeSplitListPosition, InFilterFunc, IntersectionFilterFunc, CorrectFacesOfVertexFilter, WeightedCentric, TwoWeightedCentric, MainHelp, RegularPolygon, DrawConvexFaceGraph, DrawGraph; - if not( IsClosedSurface(surf) and IsVertexFaithful(surf) and EulerCharacteristic(surf)=2) and not IsBound(printRecord.faceCoordinates2D) then + local graph, SplitListPosition, InFilterFunc, + IntersectionFilterFunc, CorrectFacesOfVertexFilter, WeightedCentricParameters, + TwoWeightedCentricParameters, MainHelp, RegularPolygon, DrawConvexFaceGraph, DrawGraph, q; + if not (IsClosedSurface(surf) and IsVertexFaithful(surf) and EulerCharacteristic(surf) = 2) and not IsBound(printRecord.faceCoordinates2D) then return fail; fi; @@ -2038,52 +2040,15 @@ InstallMethod( DrawConvexFacegraphToTikz, res1:=[]; res2:=[]; for i in [2..v] do - Add(res1,list[i]); + Add(res1, list[i]); od; - for i in [v..Length(list)] do + for i in [(v + 1)..Length(list)] do Add(res2, list[i]); od; - Add(res1,list[1]); + Add(res1, list[1]); Add(res2, list[1]); - return [res1,res2]; - end; - - ThreeSplitListPosition := function(list, v, w) # help function - local i, res1, res2, res3; - if w > v then - res1 := []; - res2 := []; - res3 := []; - for i in [2..v] do - Add(res1,list[i]); - od; - for i in [v..w] do - Add(res2, list[i]); - od; - for i in [w..Length(list)] do - Add(res3, list[i]); - od; - Add(res1, list[1]); - Add(res2, list[1]); - Add(res3, list[1]); - elif w < v then - res1 := []; - res2 := []; - res3 := []; - for i in [2..w] do - Add(res1,list[i]); - od; - for i in [w..v] do - Add(res2, list[i]); - od; - for i in [v..Length(list)] do - Add(res3, list[i]); - od; - Add(res1, list[1]); - Add(res2, list[1]); - Add(res3, list[1]); - fi; - return [res1, res2, res3]; + Add(res2, list[v]); + return [res1, res2]; end; InFilterFunc := function(cur1, cur2, list) # help function @@ -2106,105 +2071,81 @@ InstallMethod( DrawConvexFacegraphToTikz, return InFilterFunc(cur1, cur2, list) and IntersectionFilterFunc(faceGraph, list); end; - WeightedCentric := function(list) # help function - return Float(1/2)*list[1]+Float(1/4)*(list[2]+list[3]); + WeightedCentricParameters := function(list, p) # help function + return Float(p)*list[1] + Float((1-p)/2)*(list[2] + list[3]); end; - TwoWeightedCentric := function(list) # help function + TwoWeightedCentricParameters := function(list, p, q) # help function local res; res := []; - Add(res, Float(1/2)*list[1] + Float(7/18)*list[2] + Float(2/18)*list[3]); - Add(res, Float(1/2)*list[1] + Float(2/18)*list[2] + Float(7/18)*list[3]); + Add(res, p*list[1] + (1-p)*q*list[2] + (1-p)*(1-q)*list[3]); + Add(res, p*list[1] + (1-p)*(1-q)*list[2] + (1-p)*q*list[3]); return res; end; - MainHelp := function(surf, cur, faceGraph) #surf simp. surface, cur list of lists of [v,[x,y]], faceGraph list of [v,[x,y]] with the added vertices of wanted faceGraph - local n, mainHelp1, mainHelp2, cur1, cur2, curi, mainHelpi, i, v, newv, res, neighbours, verticesOfFaceGraph, correctFacesOfVertex, toSplitVertex, toSplitVertex1, toSplitVertex2, toSplitVertexPos, toSplitVertexPos1, toSplitVertexPos2, alreadyPositionedVertices; + RegularPolygon := function(list) #returns vertices of a regular polygon as a list of [vert, [x,y]] + local n, res, i; + res := []; + n := Length(list); + for i in [1..n] do + Add(res, [list[i], [Cos(2*3.14159265*((i-1)/n)), Sin(2*3.14159265*((i-1)/n))]]); + od; + return res; + end; + + MainHelp := function(surf, cur, faceGraph, spread, q) + local res, mainHelpi, curi, curLength, i, toSplitVertex, toSplitVertexPos, nodesOfFaceGraph, alreadyPositionedNeighbours, neighbours, v, newv, correctFacesOfVertex; if Length(cur) >= 2 then # More than one convex drawing plane res := []; - faceGraph := MainHelp(surf, [cur[1]], faceGraph)[2]; for i in [1..Length(cur)] do - mainHelpi := MainHelp(surf, [cur[i]], faceGraph); + mainHelpi := MainHelp(surf, [cur[i]], faceGraph, spread, q); curi := mainHelpi[1]; res := Concatenation(res, curi); faceGraph := Set(Concatenation(faceGraph, mainHelpi[2])); od; return [res, faceGraph]; - elif Length(cur) = 1 then # Only one convex drawing plane - cur := cur[1]; - n := Length(cur); - if n < 2 then + else # Only one convex drawing plane + cur := cur[1]; # deabstracting the only current list + curLength := Length(cur); + if curLength < 2 then return [[[]], faceGraph]; - fi; - neighbours := NeighbourFacesOfFace(surf, cur[1][1]); - verticesOfFaceGraph := List(faceGraph, x -> x[1]); - if Length(Intersection(verticesOfFaceGraph, neighbours)) = 2 then # 2 neighbours of cur[1] have been positioned already - if Length(neighbours) = 2 then # There are only 2 neighbours which means no vertex has to be positioned - Remove(cur, 1); - else # There are 3 neighbours which means there is a new vertex that has to be positioned - alreadyPositionedVertices := Difference(neighbours, [cur[2][1], cur[n][1]]); - if Length(Intersection(List(cur, x -> x[1]), alreadyPositionedVertices)) = 1 then # case 2: edge slices convex drawing plane in two and splits it - toSplitVertex := Intersection(List(cur, x -> x[1]), alreadyPositionedVertices)[1]; - toSplitVertexPos := Position(List(cur, x -> x[1]), toSplitVertex); - return [SplitListPosition(cur, toSplitVertexPos), faceGraph]; - fi; - for v in neighbours do - if v=25 then Error(); fi; # debug - if (not v in verticesOfFaceGraph) then # and (ForAny(VerticesOfFace(surf, v), faceVertex -> Length(Intersection(List(cur, x -> x[1]), FacesAsList(UmbrellaPathOfVertex(surf, faceVertex)))) >= 3)) - newv := [v, WeightedCentric([cur[1][2], cur[2][2], cur[n][2]])]; + else + neighbours := NeighbourFacesOfFace(surf, cur[1][1]); + nodesOfFaceGraph := List(faceGraph, x -> x[1]); + alreadyPositionedNeighbours := Difference(neighbours, [cur[2][1], cur[curLength][1]]); + if Length(Intersection(List(cur, x -> x[1]), alreadyPositionedNeighbours)) = 0 then # case 1: edge does not violate convex drawing plane + if Length(Intersection(nodesOfFaceGraph, neighbours)) = 1 then # Only one neighbour has been positioned already, so 2 more have to be added + correctFacesOfVertex := Filtered(FacesOfVertices(surf), x -> CorrectFacesOfVertexFilter(cur[1][1], cur[2][1], List(faceGraph, y -> y[1]), x)); + for v in Difference(Difference(neighbours, correctFacesOfVertex[1]), nodesOfFaceGraph) do + newv := [v, TwoWeightedCentricParameters([cur[1][2], cur[2][2], cur[curLength][2]], spread, q)[2]]; Add(faceGraph, newv); - Remove(cur, 1); Add(cur, newv); - fi; - if v=25 then Error(); fi; # debug - od; - fi; - return [[cur], faceGraph]; - elif Length(Intersection(verticesOfFaceGraph, neighbours)) = 1 then # 1 neighbour of cur[1] has been positioned already - if Length(neighbours) = 1 then # There is only 1 neighbour which means no vertex has to be positioned - Remove(cur, 1); - elif Length(neighbours) = 2 then # There are only 2 neighbours which means 1 vertex has to be positioned - for v in neighbours do - if not v in verticesOfFaceGraph then - newv := [v, WeightedCentric([cur[1][2], cur[2][2], cur[n][2]])]; + od; + for v in Difference(Intersection(neighbours, correctFacesOfVertex[1]), nodesOfFaceGraph) do + newv := [v, TwoWeightedCentricParameters([cur[1][2], cur[2][2], cur[curLength][2]], spread, q)[1]]; Add(faceGraph, newv); - Remove(cur, 1); Add(cur, newv); - fi; - od; - else # There are 3 neighbours which means 2 vertices have to be positioned - correctFacesOfVertex := Filtered(FacesOfVertices(surf), x -> CorrectFacesOfVertexFilter(cur[1][1], cur[2][1], List(faceGraph, y -> y[1]), x)); - for v in Difference(Difference(neighbours, correctFacesOfVertex[1]), verticesOfFaceGraph) do - newv := [v, TwoWeightedCentric([cur[1][2], cur[2][2], cur[n][2]])[2]]; - Add(faceGraph, newv); - Add(cur, newv); - od; - for v in Difference(Intersection(neighbours, correctFacesOfVertex[1]), verticesOfFaceGraph) do - newv := [v, TwoWeightedCentric([cur[1][2], cur[2][2], cur[n][2]])[1]]; - Add(faceGraph, newv); - Add(cur, newv); - od; - fi; - Remove(cur, 1); - return [[cur], faceGraph]; - elif Length(Intersection(verticesOfFaceGraph, neighbours)) = 3 then # 3 neighbours of cur[1] have been positioned already - alreadyPositionedVertices := Difference(neighbours, [cur[2][1], cur[n][1]]); - if Length(Intersection(List(cur, x -> x[1]), alreadyPositionedVertices)) = 2 then # case 3: edge slices convex drawing plane in three and splits it - toSplitVertex1 := Intersection(List(cur, x -> x[1]), alreadyPositionedVertices)[1]; - toSplitVertex2 := Intersection(List(cur, x -> x[1]), alreadyPositionedVertices)[2]; - toSplitVertexPos1 := Position(List(cur, x -> x[1]), toSplitVertex1); - toSplitVertexPos2 := Position(List(cur, x -> x[1]), toSplitVertex2); - return [ThreeSplitListPosition(cur, toSplitVertexPos1, toSplitVertexPos2), faceGraph]; - elif Length(Intersection(List(cur, x -> x[1]), alreadyPositionedVertices)) = 1 then # case 2: edge slices convex drawing plane in two and splits it - toSplitVertex := Intersection(List(cur, x -> x[1]), alreadyPositionedVertices)[1]; + od; + Remove(cur, 1); + return [[cur], faceGraph]; + elif Length(Intersection(nodesOfFaceGraph, neighbours)) = 2 then # Only two neighbours have been positioned already, so 1 more has to be added + for v in neighbours do + if not v in nodesOfFaceGraph then # and (ForAny(VerticesOfFace(surf, v), faceVertex -> Length(Intersection(List(cur, x -> x[1]), FacesAsList(UmbrellaPathOfVertex(surf, faceVertex)))) >= 3)) + newv := [v, WeightedCentricParameters([cur[1][2], cur[2][2], cur[curLength][2]], spread)]; + Add(faceGraph, newv); + Remove(cur, 1); + Add(cur, newv); + fi; + od; + return [[cur], faceGraph]; + elif Length(Intersection(nodesOfFaceGraph, neighbours)) = 3 then # All three neighbours have been positioned already, so no more have to be added + Remove(cur, 1); + return [[cur], faceGraph]; + fi; + else # case 2: edge slices convex drawing plane in two and splits it + toSplitVertex := Intersection(List(cur, x -> x[1]), alreadyPositionedNeighbours)[1]; toSplitVertexPos := Position(List(cur, x -> x[1]), toSplitVertex); return [SplitListPosition(cur, toSplitVertexPos), faceGraph]; - elif Length(Intersection(List(cur, x -> x[1]), alreadyPositionedVertices)) = 0 then # case 1: edge does not violate convex drawing plane - Remove(cur, 1); - return [[cur], faceGraph]; - else - # Print("Failure at 3 neighbours of cur[1] have been positioned already!"); - Error(); fi; fi; fi; @@ -2220,22 +2161,28 @@ InstallMethod( DrawConvexFacegraphToTikz, return res; end; - DrawConvexFaceGraph := function(surf) + DrawConvexFaceGraph := function(surf, spread, q) local cur, faceGraph, path, mainHelp, maxPathPos; maxPathPos := PositionMaximum(List(UmbrellaPathsOfVertices(surf), x -> Length(FacesAsList(x)))); path := UmbrellaPathOfVertex(surf, maxPathPos); # Start with the biggest UmbrellaPath # path := UmbrellaPathOfVertex(surf, Vertices(surf)[1]); # Start with the UmbrellaPath of the vertex 1 cur := [RegularPolygon(FacesAsList(path))]; faceGraph := RegularPolygon(FacesAsList(path)); - while Length(faceGraph)= Float(1) or record.spread <= Float(0) then + Error("The spread parameter has to be chosen in the interval (0, 1) !"); + fi; + q := Float(7/9); # another parameter that controls the spread but probably not important enough to let the user control it. q must be chosen in the interval ((1/2), 1). + graph := DrawConvexFaceGraph(surf, Float(record.spread), q); SortBy(graph, x -> x[1]); if "scale" in RecNames(record) and "faceCoordinates2D" in RecNames(record) then return DrawFacegraphToTikz(surf, name, record); @@ -2249,7 +2196,6 @@ InstallMethod( DrawConvexFacegraphToTikz, fi; return DrawFacegraphToTikz(surf, name, record); - end ); From 1f6f96ab6a6352dc7967bd06cb9a58ef63fde358 Mon Sep 17 00:00:00 2001 From: Flynn Fehre Date: Sat, 20 May 2023 19:43:29 +0200 Subject: [PATCH 05/44] minor corrections --- gap/PolygonalComplexes/drawing.gd | 21 +++++++++++---------- 1 file changed, 11 insertions(+), 10 deletions(-) diff --git a/gap/PolygonalComplexes/drawing.gd b/gap/PolygonalComplexes/drawing.gd index 14f009fd..cb9f8b13 100644 --- a/gap/PolygonalComplexes/drawing.gd +++ b/gap/PolygonalComplexes/drawing.gd @@ -932,11 +932,8 @@ DrawFacegraphToTikz(tetra, #! #! \input{_TIKZ_facegraph_tetrahedron_Coordinates.tex} #! -#! #! -#! -#! -#! spread(Only available for DrawConvexFacegraphToTikz +#! spread (Only available for DrawConvexFacegraphToTikz #! ): Modifies the position of the #! vertices representing the faces. The spread parameter can be chosen as a float in the #! interval (0, 1). Choosing the parameter outside the interval results in @@ -947,12 +944,14 @@ DrawFacegraphToTikz(tetra, #! #! We will exemplify this parameter with the icosahedron. #! @BeginLog -icosahedron := SimplicialSurfaceByVerticesInFaces([ [ 1, 2, 3 ], [ 1, 2, 4 ], - [ 1, 4, 5 ], [ 1, 5, 6 ], [ 1, 3, 6 ], [ 2, 3, 7 ], [ 2, 4, 8 ], [ 4, 5, 9 ], - [ 5, 6, 10 ], [ 3, 6, 11 ], [ 2, 7, 8 ], [ 4, 8, 9 ], [ 5, 9, 10 ], [ 6, 10, 11 ], - [ 3, 7, 11 ], [ 7, 8, 12 ], [ 8, 9, 12 ], [ 9, 10, 12 ], [ 10, 11, 12 ], - [ 7, 11, 12 ] ]);; -DrawConvexFacegraphToTikz(icosahedron, "convex_facegraph_icosahedron_default_spread");; +icosahedron := SimplicialSurfaceByVerticesInFaces([ [ 1, 2, 3 ], + [ 1, 2, 4 ], [ 1, 4, 5 ], [ 1, 5, 6 ], [ 1, 3, 6 ], [ 2, 3, 7 ], + [ 2, 4, 8 ], [ 4, 5, 9 ], [ 5, 6, 10 ], [ 3, 6, 11 ], + [ 2, 7, 8 ], [ 4, 8, 9 ], [ 5, 9, 10 ], [ 6, 10, 11 ], + [ 3, 7, 11 ], [ 7, 8, 12 ], [ 8, 9, 12 ], [ 9, 10, 12 ], + [ 10, 11, 12 ], [ 7, 11, 12 ] ]);; +DrawConvexFacegraphToTikz(icosahedron, +"convex_facegraph_icosahedron_default_spread");; #! @EndLog #! #! \input{_TIKZ_convex_facegraph_icosahedron_default_spread.tex} @@ -975,6 +974,8 @@ DrawConvexFacegraphToTikz(icosahedron, #! #! \input{_TIKZ_convex_facegraph_icosahedron_high_spread.tex} #! +#! +#! #! @EndChunk From 679f7245ce9e2939175fa12efcf4d83d4950e094 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Meike=20Wei=C3=9F?= Date: Mon, 2 Oct 2023 15:15:07 +0200 Subject: [PATCH 06/44] Adaptation of SubcomplexByFaces to edge-coloured complexes --- gap/PolygonalComplexes/modification.gd | 11 ++++++++++ gap/PolygonalComplexes/modification.gi | 28 ++++++++++++++++++++++---- 2 files changed, 35 insertions(+), 4 deletions(-) diff --git a/gap/PolygonalComplexes/modification.gd b/gap/PolygonalComplexes/modification.gd index 8e68605a..48f8c05f 100755 --- a/gap/PolygonalComplexes/modification.gd +++ b/gap/PolygonalComplexes/modification.gd @@ -576,6 +576,17 @@ DeclareOperation( "SplitEdgePathNC", [IsPolygonalComplex, IsVertexEdgePath and I #! The NC-version does not check whether the given set of faces #! actually consists only of faces in complex. It also does not #! check whether the result of SubsurfaceByFaces is a surface. +#! +#! In Chapter edge colouring will be introduced. +#! If we compute a subcomplex of an edge-coloured complex, it will be edge-coloured again, +#! induced by the edge-colouring of the given complex. +#! @BeginExampleSession +#! gap> colEdges:=[ 1, 2, 1, 2, 1, 2, 3, 3, 3, 3, 3, 3 ];; +#! gap> colSurface:=EdgeColouredPolygonalComplex(hex,colEdges); +#! tame coloured surface (MMB with 7 vertices, 12 edges and 6 faces) +#! gap> SubsurfaceByFaces(colSurface,[1,2]); +#! tame coloured surface (BMB with 4 vertices, 5 edges and 2 faces) +#! @EndExampleSession #! #! @Returns a twisted polygonal complex #! @Arguments complex, faces diff --git a/gap/PolygonalComplexes/modification.gi b/gap/PolygonalComplexes/modification.gi index ef540ba2..132b5f1e 100755 --- a/gap/PolygonalComplexes/modification.gi +++ b/gap/PolygonalComplexes/modification.gi @@ -498,7 +498,8 @@ InstallOtherMethod( SubcomplexByFaces, InstallMethod( SubcomplexByFacesNC, "for a polygonal complex and a set of faces", [IsPolygonalComplex, IsSet], function(complex, subfaces) - local subVertices, subEdges, newVerticesOfEdges, newEdgesOfFaces, e, f; + local subVertices, subEdges, newVerticesOfEdges, newEdgesOfFaces, e, f, + subcomplex, colEdges, colEdgesSub, edge; subEdges := __SIMPLICIAL_UnionSets( EdgesOfFaces(complex){subfaces} ); @@ -514,8 +515,18 @@ InstallMethod( SubcomplexByFacesNC, "for a polygonal complex and a set of faces" newEdgesOfFaces[f] := EdgesOfFaces(complex)[f]; od; - return PolygonalComplexByDownwardIncidenceNC( subVertices, subEdges, + subcomplex:=PolygonalComplexByDownwardIncidenceNC( subVertices, subEdges, subfaces, newVerticesOfEdges, newEdgesOfFaces ); + if IsEdgeColouredPolygonalComplex(complex) then + colEdges:=ColoursOfEdges(complex); + colEdgesSub:=[]; + for edge in Edges(subcomplex) do + colEdgesSub[edge]:=colEdges[edge]; + od; + subcomplex:=EdgeColouredPolygonalComplexNC(subcomplex,colEdgesSub); + fi; + + return subcomplex; end ); InstallMethod( SubcomplexByFacesNC, @@ -523,7 +534,7 @@ InstallMethod( SubcomplexByFacesNC, [IsTwistedPolygonalComplex, IsSet], function(complex, subfaces) local remChambers, vofC, eofC, fofC, c, zeroClass, oneClass, - twoClass, cl; + twoClass, cl, subcomplex, colEdges, colEdgesSub, edge; remChambers := Union( ChambersOfFaces(complex){subfaces} ); vofC := []; @@ -541,7 +552,16 @@ InstallMethod( SubcomplexByFacesNC, twoClass := Set(twoClass); twoClass := Difference(twoClass, [[]]); - return TwistedPolygonalComplexByChamberRelationsNC( vofC, eofC, fofC, zeroClass, oneClass, twoClass ); + subcomplex:=TwistedPolygonalComplexByChamberRelationsNC( vofC, eofC, fofC, zeroClass, oneClass, twoClass ); + if IsEdgeColouredTwistedPolygonalComplex(complex) then + colEdges:=ColoursOfEdges(complex); + colEdgesSub:=[]; + for edge in Edges(subcomplex) do + colEdgesSub[edge]:=colEdges[edge]; + od; + subcomplex:=EdgeColouredTwistedPolygonalComplexNC(subcomplex,colEdgesSub); + fi; + return subcomplex; end ); InstallOtherMethod( SubcomplexByFacesNC, From 1defacc9f7a162444d1af58fe5e5eb83a94bd300 Mon Sep 17 00:00:00 2001 From: Lukas Schnelle Date: Wed, 24 Jan 2024 12:20:31 +0100 Subject: [PATCH 07/44] add function to return all coordinates of a printrecord --- gap/PolygonalComplexes/animating.gd | 5 ++++- gap/PolygonalComplexes/animating.gi | 8 ++++++++ 2 files changed, 12 insertions(+), 1 deletion(-) diff --git a/gap/PolygonalComplexes/animating.gd b/gap/PolygonalComplexes/animating.gd index 67ce9b83..85b8861e 100644 --- a/gap/PolygonalComplexes/animating.gd +++ b/gap/PolygonalComplexes/animating.gd @@ -143,12 +143,15 @@ DeclareOperation( "SetVertexCoordinates3DNC", [IsSimplicialSurface, IsList, IsRe #! The 3D-coordinates of vertex vertex has to have the format [x,y,z]. #! If the format of the coordinates is not correct, then an error is shown. #! This can happen, if the NC version is used to store the 3D-coordinates. -#! The NC-version does not check the coordinate format saved in the print record. +#! The NC-version does not check the coordinate format saved in the print record. +#! The GetAllVertexCoordinates3DNC command returns all coordinates from the print record without checking them as a list. #! @Returns a list #! @Arguments surface, vertex, printRecord DeclareOperation( "GetVertexCoordinates3D", [IsSimplicialSurface, IsPosInt, IsRecord] ); #! @Arguments surface, vertex, printRecord DeclareOperation( "GetVertexCoordinates3DNC", [IsSimplicialSurface, IsPosInt, IsRecord] ); +#! @Arguments surface, printRecord +DeclareOperation( "GetAllVertexCoordinates3DNC", [IsSimplicialSurface, IsRecord] ); #! @EndGroup #! @BeginGroup DrawSurfaceToJavaScript diff --git a/gap/PolygonalComplexes/animating.gi b/gap/PolygonalComplexes/animating.gi index 9a01ddd2..e3fb62fe 100644 --- a/gap/PolygonalComplexes/animating.gi +++ b/gap/PolygonalComplexes/animating.gi @@ -88,6 +88,14 @@ InstallMethod( GetVertexCoordinates3DNC, RedispatchOnCondition(GetVertexCoordinates3DNC, true, [IsTwistedPolygonalComplex, IsPosInt, IsRecord], [IsSimplicialSurface], 0); +InstallMethod( GetAllVertexCoordinates3DNC, + "for a simplicial surfaceand a record", + [IsSimplicialSurface, IsRecord], + function(surface, printRecord) + return printRecord.vertexCoordinates3D; + end +); + InstallMethod( CalculateParametersOfInnerCircle, "for a simplicial surface and a record", From ac7cd5c010d00847f7e8ebbe7f28b9549955384a Mon Sep 17 00:00:00 2001 From: Lukas Schnelle Date: Wed, 24 Jan 2024 12:20:52 +0100 Subject: [PATCH 08/44] add myself as author --- PackageInfo.g | 10 ++++++++++ 1 file changed, 10 insertions(+) diff --git a/PackageInfo.g b/PackageInfo.g index 4470a478..c0103aad 100644 --- a/PackageInfo.g +++ b/PackageInfo.g @@ -66,6 +66,16 @@ Persons := [ PostalAddress := "--", Place := "Aachen", Institution := "Chair of Algebra and Representation Theory", + ), + rec( + IsAuthor := true, + IsMaintainer := true, + FirstNames := "Lukas", + LastName := "Schnelle", + Email := "lukas.schnelle1@rwth-aachen.de", + PostalAddress := "--", + Place := "Aachen", + Institution := "Chair of Algebra and Representation Theory", ), rec( LastName := "GAP Team", From 772bfc640c06f07b2470aadb228b7fdb9ca35aa5 Mon Sep 17 00:00:00 2001 From: Lukas Schnelle Date: Wed, 24 Jan 2024 14:02:11 +0100 Subject: [PATCH 09/44] address comments from MeikeWeiss --- gap/PolygonalComplexes/animating.gd | 2 +- gap/PolygonalComplexes/animating.gi | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/gap/PolygonalComplexes/animating.gd b/gap/PolygonalComplexes/animating.gd index 85b8861e..f01b0e32 100644 --- a/gap/PolygonalComplexes/animating.gd +++ b/gap/PolygonalComplexes/animating.gd @@ -144,7 +144,7 @@ DeclareOperation( "SetVertexCoordinates3DNC", [IsSimplicialSurface, IsList, IsRe #! If the format of the coordinates is not correct, then an error is shown. #! This can happen, if the NC version is used to store the 3D-coordinates. #! The NC-version does not check the coordinate format saved in the print record. -#! The GetAllVertexCoordinates3DNC command returns all coordinates from the print record without checking them as a list. +#! The GetAllVertexCoordinates3DNC method returns all coordinates from the print record without checking them as a list. #! @Returns a list #! @Arguments surface, vertex, printRecord DeclareOperation( "GetVertexCoordinates3D", [IsSimplicialSurface, IsPosInt, IsRecord] ); diff --git a/gap/PolygonalComplexes/animating.gi b/gap/PolygonalComplexes/animating.gi index e3fb62fe..d0e8c648 100644 --- a/gap/PolygonalComplexes/animating.gi +++ b/gap/PolygonalComplexes/animating.gi @@ -89,7 +89,7 @@ RedispatchOnCondition(GetVertexCoordinates3DNC, true, [IsTwistedPolygonalComplex [IsSimplicialSurface], 0); InstallMethod( GetAllVertexCoordinates3DNC, - "for a simplicial surfaceand a record", + "for a simplicial surface and a record", [IsSimplicialSurface, IsRecord], function(surface, printRecord) return printRecord.vertexCoordinates3D; From 0ddc4a5d900b1df2a029653b16ed3e3e2eccc7ab Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Meike=20Wei=C3=9F?= Date: Wed, 14 Feb 2024 15:56:49 +0100 Subject: [PATCH 10/44] corrected IsWaist --- gap/Paths/paths.gd | 7 +++++-- gap/Paths/paths.gi | 33 ++++++++++++++++++++++++++------- 2 files changed, 31 insertions(+), 9 deletions(-) diff --git a/gap/Paths/paths.gd b/gap/Paths/paths.gd index 416e637c..112ec37b 100644 --- a/gap/Paths/paths.gd +++ b/gap/Paths/paths.gd @@ -1197,7 +1197,10 @@ DeclareAttribute( "ViewInformation", IsEdgeFacePath ); #! @Section Waists #! @SectionLabel Waists #! This section deals with a specific type of closed vertex-edge-paths, namely waists. -#! A n-waist is a closed vertex-edge path of length n such that all edges are inner and no two are incident to the same face. +#! A n-waist is a closed vertex-edge path of length n such that all edges are inner and no two are incident to the same face. +#! Moreover, a simplicial surface X can only have a n-waist for n>3 if X does not have a 3-waist and the vertex-edge path describing the n-waist must be distance-faithful. +#! A closed vertex-edge path P is distance-faithful if for any two vertices of P at least one shortest edge path between them is contained in P. +#! #! This will be illustrated on the following double tetrahedron: #! #! <img src="./images/_Wrapper_Image_Example3Waist-1.svg"> </img> @@ -1305,7 +1308,7 @@ DeclareAttribute( "AllThreeWaistsOfComplex", IsTwistedPolygonalComplex); #! For example, consider the double tetrahedron from the start of section : #! @BeginExampleSession #! gap> AllWaistsOfComplex(doubleTetra); -#! [ ( v5, E10, v4, E7, v3, E8, v5 ), ( v5, E12, v6, E9, v3, E8, v5 ) ] +#! [ ( v4, E7, v3, E8, v5, E10, v4 ), ( v5, E8, v3, E9, v6, E12, v5 ) ] #! @EndExampleSession #! #! @Returns a set of closed vertex-edge-paths diff --git a/gap/Paths/paths.gi b/gap/Paths/paths.gi index f2060662..32cec17a 100644 --- a/gap/Paths/paths.gi +++ b/gap/Paths/paths.gi @@ -951,9 +951,9 @@ InstallMethod(ShiftCyclicPath, InstallMethod(IsWaist, "for a complex and a vertex-edge path", [IsTwistedPolygonalComplex, IsVertexEdgePath], function(complex,path) - local edges, incidentFaces, e, foe; + local edges, incidentFaces, e, foe, edgeGraph, vertices, subdigr, i, lastV, vertex; + edges:=EdgesAsList(path); - incidentFaces:=[]; if ForAll(edges, e->IsInnerEdge(complex,e)) and IsClosedPath(path) then # check if the edges are not incident to the same faces @@ -965,6 +965,21 @@ InstallMethod(IsWaist, "for a complex and a vertex-edge path", return false; fi; od; + + # check distance-faithful + if Length(edges)>3 then + edgeGraph:=EdgeDigraphsGraph(complex); + vertices:=ShallowCopy(VerticesAsList(path)); + Remove(vertices); + subdigr:=InducedSubdigraph(edgeGraph,vertices); + lastV:=Position(DigraphVertexLabels(subdigr),Last(vertices)); + for i in [1..Length(vertices)-1] do + vertex:=Position(DigraphVertexLabels(subdigr),vertices[i]); + if DigraphShortestDistance(edgeGraph,vertices[i],Last(vertices))<>DigraphShortestDistance(subdigr,vertex,lastV) then + return false; + fi; + od; + fi; else return false; fi; @@ -1007,14 +1022,18 @@ end InstallMethod(AllWaistsOfComplex, "for a twisted polygonal complex", [IsTwistedPolygonalComplex], function(complex) - local cycles, waists, c, edges, incident, incidentFaces, e, foe; - - cycles:=AllClosedVertexEdgePaths(complex); + local threeWaists, cycles, waists, c, edges, incident, incidentFaces, e, foe; + + threeWaists:=AllThreeWaistsOfComplex(complex); + if threeWaists<>[] then + return Concatenation(threeWaists,AllTwoWaistsOfComplex(complex)); + fi; + cycles:=AllClosedVertexEdgePaths(complex); waists:=[]; for c in cycles do - if IsWaist(complex,c) then - Add(waists,c); + if IsWaist(complex,c) then + Add(waists,c); fi; od; return waists; From 2a4599d2977a2feead640d5638b3f109b1f7e40f Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Meike=20Wei=C3=9F?= Date: Wed, 14 Feb 2024 16:09:46 +0100 Subject: [PATCH 11/44] added example --- gap/Paths/paths.gd | 3 +++ 1 file changed, 3 insertions(+) diff --git a/gap/Paths/paths.gd b/gap/Paths/paths.gd index 112ec37b..e8cfd924 100644 --- a/gap/Paths/paths.gd +++ b/gap/Paths/paths.gd @@ -1309,6 +1309,9 @@ DeclareAttribute( "AllThreeWaistsOfComplex", IsTwistedPolygonalComplex); #! @BeginExampleSession #! gap> AllWaistsOfComplex(doubleTetra); #! [ ( v4, E7, v3, E8, v5, E10, v4 ), ( v5, E8, v3, E9, v6, E12, v5 ) ] +#! gap> AllWaistsOfComplex(Octahedron()); +#! [ ( v1, E1, v2, E7, v6, E11, v4, E3, v1 ), ( v3, E2, v1, E4, v5, E12, v6, E9, v3 ), +#! ( v3, E5, v2, E6, v5, E10, v4, E8, v3 ) ] #! @EndExampleSession #! #! @Returns a set of closed vertex-edge-paths From 289b0f31699e70a59d83725b622432b661bd7f66 Mon Sep 17 00:00:00 2001 From: Flynn Fehre Date: Fri, 23 Feb 2024 14:08:45 +0100 Subject: [PATCH 12/44] Added the functions ButterflyFaithfulMonomorphismIntoSimplicialSurface and AllButterflyFaithfulMonomorphismsIntoSimplicialSurface as well as their documentation --- ...utterfly_Faithful_Monomorphism_Hexagon.tex | 51 ++ gap/Morphisms/morphisms.gd | 77 ++- gap/Morphisms/morphisms.gi | 515 ++++++++++++++++++ 3 files changed, 641 insertions(+), 2 deletions(-) create mode 100644 doc/Image_Butterfly_Faithful_Monomorphism_Hexagon.tex diff --git a/doc/Image_Butterfly_Faithful_Monomorphism_Hexagon.tex b/doc/Image_Butterfly_Faithful_Monomorphism_Hexagon.tex new file mode 100644 index 00000000..cac13053 --- /dev/null +++ b/doc/Image_Butterfly_Faithful_Monomorphism_Hexagon.tex @@ -0,0 +1,51 @@ + +\newcommand{\setupCoord}{ + \coordinate (Z) at (0,0); + \foreach \i in {1,...,6}{ + \coordinate (A\i) at (180-60*\i:2.5); + } +} + + +\begin{scope}[shift={(3.5,0)}] + \setupCoord + + \draw[edge,face] + (Z) -- (A1) -- node[edgeLabel]{1} (A2) -- cycle + (Z) -- node[edgeLabel]{9} (A2) -- node[edgeLabel]{2} (A3) -- cycle + (Z) -- node[edgeLabel]{10} (A3) -- node[edgeLabel]{3} (A4) -- cycle + (Z) -- node[edgeLabel]{11} (A4) -- node[edgeLabel]{4} (A5) -- cycle + (Z) -- node[edgeLabel]{12} (A5) -- node[edgeLabel]{5} (A6) -- cycle + (Z) -- node[edgeLabel]{13} (A6) -- node[edgeLabel]{6} (A1) -- node[edgeLabel]{8} (Z); + + \foreach \p/\r/\n in {1/above left/1, 2/above right/2, 3/right/3, 4/below right/4, 5/below left/5, 6/left/6}{ + \vertexLabelR{A\p}{\r}{\n} + } + \vertexLabelR{Z}{above}{8} + + \foreach \i/\j/\n in {1/2/I, 2/3/II, 3/4/III, 4/5/IV, 5/6/V, 6/1/VI}{ + \node[faceLabel] at (barycentric cs:A\i=1,A\j=1,Z=1) {$\n$}; + } +\end{scope} + + +\node at (0,0) {$\rightarrow$}; + + +\begin{scope}[shift={(-3.5,0)}] + \setupCoord + + \draw[edge,face] + (Z) -- node[edgeLabel]{5} (A1) -- node[edgeLabel]{1} (A2) -- cycle + (Z) -- node[edgeLabel]{6} (A2) -- node[edgeLabel]{2} (A3) -- cycle + (Z) -- node[edgeLabel]{7} (A3) -- node[edgeLabel]{3} (A4) -- node[edgeLabel]{4} (Z); + + \foreach \p/\r/\n in {1/above left/1, 2/above right/2, 3/right/3, 4/below right/4}{ + \vertexLabelR{A\p}{\r}{\n} + } + \vertexLabelR{Z}{below left}{5} + + \foreach \i/\j/\n in {1/2/I, 2/3/II, 3/4/III}{ + \node[faceLabel] at (barycentric cs:A\i=1,A\j=1,Z=1) {$\n$}; + } +\end{scope} diff --git a/gap/Morphisms/morphisms.gd b/gap/Morphisms/morphisms.gd index 2e53ea2c..1bbb7a8f 100644 --- a/gap/Morphisms/morphisms.gd +++ b/gap/Morphisms/morphisms.gd @@ -376,6 +376,81 @@ DeclareOperation( "PolygonalIdentityMorphism", [IsPolygonalComplex] ); DeclareAttribute( "InversePolygonalMorphism", IsPolygonalMorphism and IsBijective ); +#! +#! +#! A polygonal morphism or fail +#! +#! Given two simplicial surfaces surf1 and surf2, return a butterfly-faithful +#! monomorphism from surf1 to surf2 if it exists. Otherwise return fail. +#! A homomorphism of simplicial surfaces is called butterfly-faithful if the homomorphism +#! when restricted to a butterfly, i.e. restricted to two incident faces of an inner edge, +#! becomes a bijection onto another butterfly. In other words, every butterfly of +#! surf1 is being preserved and does not degenerate in surf2. +#! As an example, consider the 3-half-umbrella and 6-umbrella. +#! +#! \begin{tikzpicture}[vertexStyle, edgeStyle, faceStyle] +#! \input{Image_Butterfly_Faithful_Monomorphism_Hexagon.tex} +#! \end{tikzpicture} +#! +#! @ExampleSession +#! gap> six := SimplicialSurfaceByDownwardIncidence( +#! > [[1,2],[2,3],[3,4],[4,5],[5,6],[6,1],,[1,8],[2,8],[3,8],[4,8],[5,8],[6,8]], +#! > [[1,8,9],[2,9,10],[3,10,11],[4,11,12],[5,12,13],[6,13,8]]);; +#! gap> three := SimplicialSurfaceByDownwardIncidence( +#! > [[1,2],[2,3],[3,4],[5,4],[1,5],[2,5],[3,5]], [[1,5,6],[2,6,7],[3,7,4]]);; +#! gap> mor_3_to_6 := ButterflyFaithfulMonomorphismIntoSimplicialSurface(three, +#! > six);; +#! gap> VertexMapAsImageList(mor_3_to_6); +#! [ 1, 2, 3, 4, 8 ] +#! gap> EdgeMapAsImageList(mor_3_to_6); +#! [ 1, 2, 3, 11, 8, 9, 10 ] +#! gap> FaceMapAsImageList(mor_3_to_6); +#! [ 1, 2, 3 ] +#! @EndExampleSession +#! +#! +# +DeclareOperation( "ButterflyFaithfulMonomorphismIntoSimplicialSurface", [IsSimplicialSurface, IsSimplicialSurface]); + +#! +#! +#! A list of polygonal morphisms +#! +#! Given two simplicial surfaces surf1 and surf2, return a list of all +#! butterfly-faithful monomorphisms from surf1 to surf2. +#! A homomorphism of simplicial surfaces is called butterfly-faithful if the homomorphism +#! when restricted to a butterfly, i.e. restricted to two incident faces of an inner edge, +#! becomes a bijection onto another butterfly. In other words, every butterfly of +#! surf1 is being preserved and does not degenerate in surf2. +#! As an example, consider the 3-half-umbrella and 6-umbrella. We would expect 12 +#! butterfly-faithful monomorphisms, namely by aligning the 3-half umbrella with 3 +#! consecutive faces of the 6-umbrella. There are 6 ways to do this and another 6 if +#! we flip the 3-half-umbrella first. +#! +#! \begin{tikzpicture}[vertexStyle, edgeStyle, faceStyle] +#! \input{Image_Butterfly_Faithful_Monomorphism_Hexagon.tex} +#! \end{tikzpicture} +#! +#! @ExampleSession +#! gap> six := SimplicialSurfaceByDownwardIncidence( +#! > [[1,2],[2,3],[3,4],[4,5],[5,6],[6,1],,[1,8],[2,8],[3,8],[4,8],[5,8],[6,8]], +#! > [[1,8,9],[2,9,10],[3,10,11],[4,11,12],[5,12,13],[6,13,8]]);; +#! gap> three := SimplicialSurfaceByDownwardIncidence( +#! > [[1,2],[2,3],[3,4],[5,4],[1,5],[2,5],[3,5]], [[1,5,6],[2,6,7],[3,7,4]]);; +#! gap> all_mor_3_to_6 := AllButterflyFaithfulMonomorphismsIntoSimplicialSurface( +#! > three, six);; +#! gap> Length(all_mor_3_to_6); +#! 12 +#! @EndExampleSession +#! +#! +# +DeclareOperation( "AllButterflyFaithfulMonomorphismsIntoSimplicialSurface", [IsSimplicialSurface, IsSimplicialSurface]); + #! @Section Images and pre-images #! @SectionLabel Morphisms_Images #! @@ -1095,5 +1170,3 @@ DeclareAttribute( "VEFLabelMapAsImageList", IsPolygonalMorphism ); # attribute VertexMapping # attribute EdgeMapping # attribute FaceMapping - - diff --git a/gap/Morphisms/morphisms.gi b/gap/Morphisms/morphisms.gi index 521168f0..e98c202f 100644 --- a/gap/Morphisms/morphisms.gi +++ b/gap/Morphisms/morphisms.gi @@ -478,8 +478,523 @@ InstallMethod( InverseGeneralMapping, "for a polygonal morphism", return InversePolygonalMorphism(polMor); end +); + +InstallMethod(ButterflyFaithfulMonomorphismIntoSimplicialSurface, "for two simplicial surfaces", + [IsSimplicialSurface, IsSimplicialSurface], + function(surface1, surface2) + local PermuteList, AllBijections, AllOneFaceIsomorphisms, MyImage, MyPreImage, MyImageCat, + MyPreImages, MyPreImagesCat, MyUpdateMap, SurfaceIdentityMap, RemoveElement, MyLess, + VertexDegreesOfFace, MyIsInjective, MonomorphismIntoSimplicialSurface; + PermuteList := function(list, perm) + return List(list, x -> x^perm); + end; + + AllBijections := function(list1, list2) + local res, AllPermutations, i, bijection, g, tmp; + res := []; + if not (Length(list1) = Length(list2)) then + return []; + else + AllPermutations := []; + for g in SymmetricGroup(list2) do + Add(AllPermutations, PermuteList(list2, g)); + od; + for bijection in AllPermutations do + tmp := []; + for i in [1..Length(list1)] do + tmp[list1[i]] := bijection[i]; + od; + Add(res, tmp); + od; + # res := List(AllPermutations, x -> IndexInducedMap(list1, x)); + return res; + fi; + end; + + MyImage := function(map, x) + return map[x]; + end; + + MyImageCat := function(map, x_list) + local res, i; + res := []; + for i in x_list do + if IsBound(map[i]) then + Add(res, map[i]); + fi; + od; + return res; + end; + + MyPreImage := function(map, y) + local res, i; + res := []; + for i in [1..Length(map)] do + if IsBound(map[i]) and map[i] = y then + Add(res, i); + fi; + od; + return res; + end; + + MyPreImagesCat := function(map, y_list) + return Concatenation(List(y_list, y -> MyPreImage(map, y))); + end; + + MyPreImages := function(map) + return MyPreImagesCat(map, Compacted(map)); + end; + + AllOneFaceIsomorphisms := function(face1, surface1, face2, surface2) + local res, e, vertex_maps, vertex_map, mapped_e, i, edge, edge_map, face_map; + res := []; + vertex_maps := AllBijections(VerticesOfFace(surface1, face1), + VerticesOfFace(surface2, face2)); + # edge_map := []; + for vertex_map in vertex_maps do + edge_map := []; + e := List([1,2,3], i -> Set(VerticesOfEdge(surface1, EdgesOfFace(surface1, face1)[i]))); + mapped_e := List(e, e_i -> Set(List(e_i, v -> vertex_map[v]))); + # Error(); + for i in [1..3] do + for edge in EdgesOfFace(surface2, face2) do + # Error(); + if Set(VerticesOfEdge(surface2, edge)) = Set(mapped_e[i]) then + # Error(); + # mapped_e[i] := edge; + edge_map[EdgesOfFace(surface1, face1)[i]]:= edge; + break; + fi; + od; + od; + face_map := []; + face_map[face1] := face2; + Add(res, [vertex_map, edge_map, face_map]); + od; + return res; + end; + + MyUpdateMap := function(map, element, image_of_element) # is used to update maps with new images, also updates when used in if-clauses ! + if not IsBound(map[element]) then + map[element] := image_of_element; + return true; + elif map[element] = image_of_element then + return true; + else + return false; + fi; + end; + + SurfaceIdentityMap := function(surface) + return [[1..NumberOfVertices(surface)], [1..NumberOfEdges(surface)], [1..NumberOfFaces(surface)]]; + end; + + RemoveElement := function(list, element) + if not element in list then + return fail; + else + Remove(list, Position(list, element)); + fi; + end; + + MyLess := function(fdeg1, fdeg2) + return fdeg1 < fdeg2; + end; + + VertexDegreesOfFace := function(surface, face) + return Set(List(VerticesOfFace(surface, face), v -> DegreeOfVertex(surface, v))); + end; + + MyIsInjective := function(map) + return IsDuplicateFree(Compacted(map)); + end; + MonomorphismIntoSimplicialSurface := function(surface1, surface2) + local possible_vertex_maps, possible_monomorphisms, starting_face, image_starting_face, mapped_edges, mapped_faces, + remaining_faces, cur_edges, cur_edge, mapped_vertices, monomorphism, cur_face, face_map, edge_map, + vertex_map, i, new_face, new_image_face, is_correct_morphism, new_vertex, new_image_vertex, new_edges, new_image_edges, + cur_new_edge, cur_new_image_edge, finished_cur_edges, faces1, faces2, face_counter1, face_counter2, face_degrees1, face_degrees2, + min_degrees, min_pos, possible_image_faces; + + faces1 := Filtered(Faces(surface1), face -> ForAll(VerticesOfFace(surface1, face), v -> IsInnerVertex(surface1, v))); + faces2 := Filtered(Faces(surface2), face -> ForAll(VerticesOfFace(surface2, face), v -> IsInnerVertex(surface2, v))); + possible_image_faces := Faces(surface2); + if not faces1 = [] then # inner vertex degrees heuristic + face_counter1 := List(faces1, face -> Set(List(VerticesOfFace(surface1, face), v -> DegreeOfVertex(surface1, v)))); + face_counter2 := List(faces1, face -> Set(List(VerticesOfFace(surface2, face), v -> DegreeOfVertex(surface2, v)))); + # face_counter1 := ListCounter(CounterOfFaces(surface1)); + # face_counter2 := ListCounter(CounterOfFaces(surface2)); + # face_degrees1 := List(face_counter1, fdegs1 -> Set(fdegs1[1])); + # face_degrees2 := List(face_counter2, fdegs2 -> Set(fdegs2[1])); + if ForAny(face_counter2, fdegs2 -> not fdegs2 in face_counter1) then + # Error("heuristic"); + return fail; + else + min_pos := PositionMinimum(List(Collected(face_counter2), fdeg2 -> fdeg2[2])); + min_degrees := Collected(face_counter2)[min_pos][1]; + starting_face := Filtered(faces1, face -> min_degrees = Set(List(VerticesOfFace(surface1, face), v -> DegreeOfVertex(surface1, v))))[1]; + possible_image_faces := Filtered(faces2, face -> min_degrees = Set(List(VerticesOfFace(surface2, face), v -> DegreeOfVertex(surface2, v)))); + fi; + else + starting_face := Faces(surface1)[1]; + fi; + + for image_starting_face in possible_image_faces do + possible_monomorphisms := AllOneFaceIsomorphisms(starting_face, surface1, + image_starting_face, surface2); + for i in [1..Length(possible_monomorphisms)] do + is_correct_morphism := true; + monomorphism := possible_monomorphisms[i]; + vertex_map := monomorphism[1]; + edge_map := monomorphism[2]; + face_map := monomorphism[3]; + + cur_edges := Filtered(EdgesOfFace(surface1, starting_face), e -> IsInnerEdge(surface1, e)); + finished_cur_edges := []; + remaining_faces := Difference(Faces(surface1), [starting_face]); + mapped_faces := MyPreImages(face_map); + while not IsEmpty(remaining_faces) do + cur_edge := cur_edges[1]; + # Error("Mono"); + # update face_map + if Length(Difference(FacesOfEdge(surface2, edge_map[cur_edge]), face_map)) = 1 then + # Error("Mono"); + new_image_face := Difference(FacesOfEdge(surface2, edge_map[cur_edge]), face_map)[1]; + else # QUESTION not sure if this case is correct + # Error("Mono"); + is_correct_morphism := false; + break; + fi; + new_face := Difference(FacesOfEdge(surface1, cur_edge), mapped_faces)[1]; + + if not new_face in remaining_faces then + # Error("Mono"); + is_correct_morphism := false; + break; + fi; + + if MyUpdateMap(face_map, new_face, new_image_face) = false or MyIsInjective(face_map) = false then + # Error("Mono"); + is_correct_morphism := false; + break; + fi; + mapped_faces := MyPreImages(face_map); + + # update vertex_map + # new_vertex := Difference(VerticesOfFace(surface1, new_face), + # Intersection(List(FacesOfEdge(surface1, cur_edge), F -> VerticesOfFace(surface1, F))))[1]; # QUESTION requires vertex-faithful + new_vertex := Difference(VerticesOfFace(surface1, new_face), VerticesOfEdge(surface1, cur_edge))[1]; + # new_image_vertex := Difference(VerticesOfFace(surface2, new_image_face), + # Intersection(List(FacesOfEdge(surface2, edge_map[cur_edge]), F -> VerticesOfFace(surface2, F))))[1]; # QUESTION requires vertex-faithful + new_image_vertex := Difference(VerticesOfFace(surface2, new_image_face), VerticesOfEdge(surface2, edge_map[cur_edge]))[1]; + if MyUpdateMap(vertex_map, new_vertex, new_image_vertex) = false or MyIsInjective(vertex_map) = false then + # Error("Mono"); + is_correct_morphism := false; + break; + fi; + + # update edge_map + new_edges := Difference(EdgesOfFace(surface1, new_face), [cur_edge]); + new_image_edges := Difference(EdgesOfFace(surface2, new_image_face), [edge_map[cur_edge]]); + for cur_new_edge in new_edges do + for cur_new_image_edge in new_image_edges do + # Error("MonoEdge"); + if Set(MyImageCat(vertex_map, VerticesOfEdge(surface1, cur_new_edge))) = Set(VerticesOfEdge(surface2, cur_new_image_edge)) then # QUESTION requires vertex-faithful + if MyUpdateMap(edge_map, cur_new_edge, cur_new_image_edge) = false or MyIsInjective(edge_map) = false then + # Error("Mono"); + is_correct_morphism := false; + fi; + if cur_new_edge in cur_edges then + Add(finished_cur_edges, cur_new_edge); + fi; + # Error("MonoEdge"); + fi; + od; + od; + if is_correct_morphism = false then + break; + fi; + + # update cur_edges + cur_edges := Union(cur_edges, Filtered(EdgesOfFace(surface1, new_face), e -> IsInnerEdge(surface1, e))); + Add(finished_cur_edges, cur_edge); + cur_edges := Difference(cur_edges, finished_cur_edges); + + # update remaining_faces + remaining_faces := Difference(remaining_faces, [new_face]); + # Error("Mono"); + od; + + if is_correct_morphism = true then + # return monomorphism; # uncomment for the lists that make the homomorphism FLAG(LISTS) + return PolygonalMorphismByLists(surface1, surface2, monomorphism[1], monomorphism[2], monomorphism[3]); #FLAG(MORPHISMS) + fi; + od; + od; + return fail; + end; + return MonomorphismIntoSimplicialSurface(surface1, surface2); + end ); +InstallMethod(AllButterflyFaithfulMonomorphismsIntoSimplicialSurface, "for two simplicial surfaces", + [IsSimplicialSurface, IsSimplicialSurface], + function(surface1, surface2) + local PermuteList, AllBijections, AllOneFaceIsomorphisms, MyImage, MyPreImage, MyImageCat, + MyPreImages, MyPreImagesCat, MyUpdateMap, SurfaceIdentityMap, RemoveElement, MyLess, + VertexDegreesOfFace, MyIsInjective, AllMonomorphismsIntoSimplicialSurface; + PermuteList := function(list, perm) + return List(list, x -> x^perm); + end; + + AllBijections := function(list1, list2) + local res, AllPermutations, i, bijection, g, tmp; + res := []; + if not (Length(list1) = Length(list2)) then + return []; + else + AllPermutations := []; + for g in SymmetricGroup(list2) do + Add(AllPermutations, PermuteList(list2, g)); + od; + for bijection in AllPermutations do + tmp := []; + for i in [1..Length(list1)] do + tmp[list1[i]] := bijection[i]; + od; + Add(res, tmp); + od; + # res := List(AllPermutations, x -> IndexInducedMap(list1, x)); + return res; + fi; + end; + + MyImage := function(map, x) + return map[x]; + end; + + MyImageCat := function(map, x_list) + local res, i; + res := []; + for i in x_list do + if IsBound(map[i]) then + Add(res, map[i]); + fi; + od; + return res; + end; + + MyPreImage := function(map, y) + local res, i; + res := []; + for i in [1..Length(map)] do + if IsBound(map[i]) and map[i] = y then + Add(res, i); + fi; + od; + return res; + end; + + MyPreImagesCat := function(map, y_list) + return Concatenation(List(y_list, y -> MyPreImage(map, y))); + end; + + MyPreImages := function(map) + return MyPreImagesCat(map, Compacted(map)); + end; + + AllOneFaceIsomorphisms := function(face1, surface1, face2, surface2) + local res, e, vertex_maps, vertex_map, mapped_e, i, edge, edge_map, face_map; + res := []; + vertex_maps := AllBijections(VerticesOfFace(surface1, face1), + VerticesOfFace(surface2, face2)); + # edge_map := []; + for vertex_map in vertex_maps do + edge_map := []; + e := List([1,2,3], i -> Set(VerticesOfEdge(surface1, EdgesOfFace(surface1, face1)[i]))); + mapped_e := List(e, e_i -> Set(List(e_i, v -> vertex_map[v]))); + # Error(); + for i in [1..3] do + for edge in EdgesOfFace(surface2, face2) do + # Error(); + if Set(VerticesOfEdge(surface2, edge)) = Set(mapped_e[i]) then + # Error(); + # mapped_e[i] := edge; + edge_map[EdgesOfFace(surface1, face1)[i]]:= edge; + break; + fi; + od; + od; + face_map := []; + face_map[face1] := face2; + Add(res, [vertex_map, edge_map, face_map]); + od; + return res; + end; + + MyUpdateMap := function(map, element, image_of_element) # is used to update maps with new images, also updates when used in if-clauses ! + if not IsBound(map[element]) then + map[element] := image_of_element; + return true; + elif map[element] = image_of_element then + return true; + else + return false; + fi; + end; + + SurfaceIdentityMap := function(surface) + return [[1..NumberOfVertices(surface)], [1..NumberOfEdges(surface)], [1..NumberOfFaces(surface)]]; + end; + + RemoveElement := function(list, element) + if not element in list then + return fail; + else + Remove(list, Position(list, element)); + fi; + end; + + MyLess := function(fdeg1, fdeg2) + return fdeg1 < fdeg2; + end; + + VertexDegreesOfFace := function(surface, face) + return Set(List(VerticesOfFace(surface, face), v -> DegreeOfVertex(surface, v))); + end; + + MyIsInjective := function(map) + return IsDuplicateFree(Compacted(map)); + end; + + AllMonomorphismsIntoSimplicialSurface := function(surface1, surface2) + local possible_vertex_maps, possible_monomorphisms, starting_face, image_starting_face, mapped_edges, mapped_faces, + remaining_faces, cur_edges, cur_edge, mapped_vertices, monomorphism, cur_face, face_map, edge_map, + vertex_map, i, new_face, new_image_face, is_correct_morphism, new_vertex, new_image_vertex, new_edges, new_image_edges, + cur_new_edge, cur_new_image_edge, finished_cur_edges, faces1, faces2, face_counter1, face_counter2, face_degrees1, face_degrees2, + min_degrees, min_pos, possible_image_faces, res; + + res := []; + faces1 := Filtered(Faces(surface1), face -> ForAll(VerticesOfFace(surface1, face), v -> IsInnerVertex(surface1, v))); + faces2 := Filtered(Faces(surface2), face -> ForAll(VerticesOfFace(surface2, face), v -> IsInnerVertex(surface2, v))); + possible_image_faces := Faces(surface2); + if not faces1 = [] then # inner vertex degrees heuristic + face_counter1 := List(faces1, face -> Set(List(VerticesOfFace(surface1, face), v -> DegreeOfVertex(surface1, v)))); + face_counter2 := List(faces1, face -> Set(List(VerticesOfFace(surface2, face), v -> DegreeOfVertex(surface2, v)))); + # face_counter1 := ListCounter(CounterOfFaces(surface1)); + # face_counter2 := ListCounter(CounterOfFaces(surface2)); + # face_degrees1 := List(face_counter1, fdegs1 -> Set(fdegs1[1])); + # face_degrees2 := List(face_counter2, fdegs2 -> Set(fdegs2[1])); + if ForAny(face_counter2, fdegs2 -> not fdegs2 in face_counter1) then + # Error("heuristic"); + return res; # empty list + else + min_pos := PositionMinimum(List(Collected(face_counter2), fdeg2 -> fdeg2[2])); + min_degrees := Collected(face_counter2)[min_pos][1]; + starting_face := Filtered(faces1, face -> min_degrees = Set(List(VerticesOfFace(surface1, face), v -> DegreeOfVertex(surface1, v))))[1]; + possible_image_faces := Filtered(faces2, face -> min_degrees = Set(List(VerticesOfFace(surface2, face), v -> DegreeOfVertex(surface2, v)))); + fi; + else + starting_face := Faces(surface1)[1]; + fi; + + for image_starting_face in possible_image_faces do + possible_monomorphisms := AllOneFaceIsomorphisms(starting_face, surface1, + image_starting_face, surface2); + for i in [1..Length(possible_monomorphisms)] do + is_correct_morphism := true; + monomorphism := possible_monomorphisms[i]; + vertex_map := monomorphism[1]; + edge_map := monomorphism[2]; + face_map := monomorphism[3]; + + cur_edges := Filtered(EdgesOfFace(surface1, starting_face), e -> IsInnerEdge(surface1, e)); + finished_cur_edges := []; + remaining_faces := Difference(Faces(surface1), [starting_face]); + mapped_faces := MyPreImages(face_map); + while not IsEmpty(remaining_faces) do + cur_edge := cur_edges[1]; + # Error("Mono"); + # update face_map + if Length(Difference(FacesOfEdge(surface2, edge_map[cur_edge]), face_map)) = 1 then + # Error("Mono"); + new_image_face := Difference(FacesOfEdge(surface2, edge_map[cur_edge]), face_map)[1]; + else # QUESTION not sure if this case is correct + # Error("Mono"); + is_correct_morphism := false; + break; + fi; + new_face := Difference(FacesOfEdge(surface1, cur_edge), mapped_faces)[1]; + + if not new_face in remaining_faces then + # Error("Mono"); + is_correct_morphism := false; + break; + fi; + + if MyUpdateMap(face_map, new_face, new_image_face) = false or MyIsInjective(face_map) = false then + # Error("Mono"); + is_correct_morphism := false; + break; + fi; + mapped_faces := MyPreImages(face_map); + + # update vertex_map + # new_vertex := Difference(VerticesOfFace(surface1, new_face), + # Intersection(List(FacesOfEdge(surface1, cur_edge), F -> VerticesOfFace(surface1, F))))[1]; # QUESTION requires vertex-faithful + new_vertex := Difference(VerticesOfFace(surface1, new_face), VerticesOfEdge(surface1, cur_edge))[1]; + # new_image_vertex := Difference(VerticesOfFace(surface2, new_image_face), + # Intersection(List(FacesOfEdge(surface2, edge_map[cur_edge]), F -> VerticesOfFace(surface2, F))))[1]; # QUESTION requires vertex-faithful + new_image_vertex := Difference(VerticesOfFace(surface2, new_image_face), VerticesOfEdge(surface2, edge_map[cur_edge]))[1]; + if MyUpdateMap(vertex_map, new_vertex, new_image_vertex) = false or MyIsInjective(vertex_map) = false then + # Error("Mono"); + is_correct_morphism := false; + break; + fi; + + # update edge_map + new_edges := Difference(EdgesOfFace(surface1, new_face), [cur_edge]); + new_image_edges := Difference(EdgesOfFace(surface2, new_image_face), [edge_map[cur_edge]]); + for cur_new_edge in new_edges do + for cur_new_image_edge in new_image_edges do + # Error("MonoEdge"); + if Set(MyImageCat(vertex_map, VerticesOfEdge(surface1, cur_new_edge))) = Set(VerticesOfEdge(surface2, cur_new_image_edge)) then # QUESTION requires vertex-faithful + if MyUpdateMap(edge_map, cur_new_edge, cur_new_image_edge) = false or MyIsInjective(edge_map) = false then + # Error("Mono"); + is_correct_morphism := false; + fi; + if cur_new_edge in cur_edges then + Add(finished_cur_edges, cur_new_edge); + fi; + # Error("MonoEdge"); + fi; + od; + od; + if is_correct_morphism = false then + break; + fi; + + # update cur_edges + cur_edges := Union(cur_edges, Filtered(EdgesOfFace(surface1, new_face), e -> IsInnerEdge(surface1, e))); + Add(finished_cur_edges, cur_edge); + cur_edges := Difference(cur_edges, finished_cur_edges); + + # update remaining_faces + remaining_faces := Difference(remaining_faces, [new_face]); + # Error("Mono"); + od; + + if is_correct_morphism = true then + # Add(res, monomorphism); # uncomment to add the list the monomorphism is made of FLAG(LISTS) + Add(res,PolygonalMorphismByLists(surface1, surface2, monomorphism[1], monomorphism[2], monomorphism[3])); # FLAG(MORPHISMS) + fi; + od; + od; + return res; + end; + return AllMonomorphismsIntoSimplicialSurface(surface1, surface2); + end +); ## ## End of constructions From 825093b20dc6c363dd57f14f69c3504874f19827 Mon Sep 17 00:00:00 2001 From: Flynn Fehre Date: Sun, 10 Mar 2024 19:01:25 +0100 Subject: [PATCH 13/44] removed everything related to DrawConvexFacegraphToTikz in order to split the monomorphism_function branch from the other changes --- gap/PolygonalComplexes/drawing.gd | 91 --------------- gap/PolygonalComplexes/drawing.gi | 185 ------------------------------ 2 files changed, 276 deletions(-) diff --git a/gap/PolygonalComplexes/drawing.gd b/gap/PolygonalComplexes/drawing.gd index 555dea13..b1e2b3d3 100644 --- a/gap/PolygonalComplexes/drawing.gd +++ b/gap/PolygonalComplexes/drawing.gd @@ -1299,10 +1299,6 @@ DrawFacegraphToTikz( tetra, "facegraph_oct_rescaled", pr);; #! * faceCoordinates2D: Modify the coordinates of the faces which are #! represented as vertices in the embedding. #! -#! * spread (Only available for DrawConvexFacegraphToTikz -#! ): Modify the spread of -#! the coordinates. -#! #! We will exemplify them with the tetrahedron to make clear how the parameters #! work: #! @@ -1350,75 +1346,6 @@ DrawFacegraphToTikz(tetra, #! #! -#! spread (Only available for DrawConvexFacegraphToTikz -#! ): Modifies the position of the -#! vertices representing the faces. The spread parameter can be chosen as a float in the -#! interval (0, 1). Choosing the parameter outside the interval results in -#! an error. Choosing a number close to 1 modifies the face coordinates such -#! that they tend torwards the outer ring of the face graph. Choosing a number -#! close to 0 modifies the face coordinates such that they tend torwards the -#! middle of the face graph. The default spread is set at 0.5. -#! -#! We will exemplify this parameter with the icosahedron. -#! @BeginLog -icosahedron := SimplicialSurfaceByVerticesInFaces([ [ 1, 2, 3 ], - [ 1, 2, 4 ], [ 1, 4, 5 ], [ 1, 5, 6 ], [ 1, 3, 6 ], [ 2, 3, 7 ], - [ 2, 4, 8 ], [ 4, 5, 9 ], [ 5, 6, 10 ], [ 3, 6, 11 ], - [ 2, 7, 8 ], [ 4, 8, 9 ], [ 5, 9, 10 ], [ 6, 10, 11 ], - [ 3, 7, 11 ], [ 7, 8, 12 ], [ 8, 9, 12 ], [ 9, 10, 12 ], - [ 10, 11, 12 ], [ 7, 11, 12 ] ]);; -DrawConvexFacegraphToTikz(icosahedron, -"convex_facegraph_icosahedron_default_spread");; -#! @EndLog - -#! -#! -#! spread (Only available for DrawConvexFacegraphToTikz -#! ): Modifies the position of the -#! vertices representing the faces. The spread parameter can be chosen as a float in the -#! interval (0, 1). Choosing the parameter outside the interval results in -#! an error. Choosing a number close to 1 modifies the face coordinates such -#! that they tend torwards the outer ring of the face graph. Choosing a number -#! close to 0 modifies the face coordinates such that they tend torwards the -#! middle of the face graph. The default spread is set at 0.5. -#! -#! We will exemplify this parameter with the icosahedron. -#! @BeginLog -icosahedron := SimplicialSurfaceByVerticesInFaces([ [ 1, 2, 3 ], - [ 1, 2, 4 ], [ 1, 4, 5 ], [ 1, 5, 6 ], [ 1, 3, 6 ], [ 2, 3, 7 ], - [ 2, 4, 8 ], [ 4, 5, 9 ], [ 5, 6, 10 ], [ 3, 6, 11 ], - [ 2, 7, 8 ], [ 4, 8, 9 ], [ 5, 9, 10 ], [ 6, 10, 11 ], - [ 3, 7, 11 ], [ 7, 8, 12 ], [ 8, 9, 12 ], [ 9, 10, 12 ], - [ 10, 11, 12 ], [ 7, 11, 12 ] ]);; -DrawConvexFacegraphToTikz(icosahedron, -"convex_facegraph_icosahedron_default_spread");; -#! @EndLog -#! -#! \input{_TIKZ_convex_facegraph_icosahedron_default_spread.tex} -#! -#! -#! @BeginLog -pr := rec(spread := 0.3);; -DrawConvexFacegraphToTikz(icosahedron, - "convex_facegraph_icosahedron_low_spread", pr);; -#! @EndLog -#! -#! \input{_TIKZ_convex_facegraph_icosahedron_low_spread.tex} -#! -#! -#! @BeginLog -pr := rec(spread := 0.7);; -DrawConvexFacegraphToTikz(icosahedron, - "convex_facegraph_icosahedron_high_spread", pr);; -#! @EndLog -#! -#! \input{_TIKZ_convex_facegraph_icosahedron_high_spread.tex} -#! -#! -#! -#! @EndChunk - - #! @BeginChunk DrawFacegraphToTikz_Geodesics #! This subsection covers the usage of the parameter that adds geodesics into #! the drawings of DrawFacegraphToTikz @@ -1498,22 +1425,4 @@ DrawFacegraphToTikz( oct, #! is false) the generated tex-file will only consist of a #! tikzpicture without header (it is not possible to compile it on #! its own). -#! @EndChunk - -#! @BeginChunk DrawConvexFacegraphToTikz_example -#! @BeginLog -double6Gon := SimplicialSurfaceByVerticesInFaces([[1,2,3],[1,3,4],[1,4,5], -[1,5,6],[1,6,7],[1,2,7],[2,3,8],[3,4,8],[4,5,8],[5,6,8],[6,7,8],[2,7,8]]);; -#! @EndLog -#! -#! -#! \input{Image_Double6gon.tex} -#! -#! @BeginLog -DrawConvexFacegraphToTikz( double6Gon, "convex_facegraph_Double6Gon.tex" );; -#! @EndLog -#! -#! -#! \input{Image_convex_facegraph_Double6Gon.tex} -#! #! @EndChunk \ No newline at end of file diff --git a/gap/PolygonalComplexes/drawing.gi b/gap/PolygonalComplexes/drawing.gi index 05cd943d..a7202043 100644 --- a/gap/PolygonalComplexes/drawing.gi +++ b/gap/PolygonalComplexes/drawing.gi @@ -2022,188 +2022,3 @@ InstallOtherMethod( DrawFacegraphToTikz, return DrawFacegraphToTikz(surface,file,rec()); end ); - - -InstallMethod( DrawConvexFacegraphToTikz, - "for a closed vertex-faithful simplicial sphere, a file name and a record", - [IsSimplicialSurface, IsString, IsRecord], - function(surf, name, record) - local graph, SplitListPosition, InFilterFunc, - IntersectionFilterFunc, CorrectFacesOfVertexFilter, WeightedCentricParameters, - TwoWeightedCentricParameters, MainHelp, RegularPolygon, DrawConvexFaceGraph, DrawGraph, q; - if not (IsClosedSurface(surf) and IsVertexFaithful(surf) and EulerCharacteristic(surf) = 2) and not IsBound(printRecord.faceCoordinates2D) then - return fail; - fi; - - SplitListPosition := function(list, v) # help function - local i, res1, res2; - res1:=[]; - res2:=[]; - for i in [2..v] do - Add(res1, list[i]); - od; - for i in [(v + 1)..Length(list)] do - Add(res2, list[i]); - od; - Add(res1, list[1]); - Add(res2, list[1]); - Add(res2, list[v]); - return [res1, res2]; - end; - - InFilterFunc := function(cur1, cur2, list) # help function - if cur1 in list and cur2 in list then - return true; - else - return false; - fi; - end; - - IntersectionFilterFunc := function(faceGraph, list) # help function - if not IsEmpty(Intersection(faceGraph, list)) then - return true; - else - return false; - fi; - end; - - CorrectFacesOfVertexFilter := function(cur1, cur2, faceGraph, list) # help function - return InFilterFunc(cur1, cur2, list) and IntersectionFilterFunc(faceGraph, list); - end; - - WeightedCentricParameters := function(list, p) # help function - return Float(p)*list[1] + Float((1-p)/2)*(list[2] + list[3]); - end; - - TwoWeightedCentricParameters := function(list, p, q) # help function - local res; - res := []; - Add(res, p*list[1] + (1-p)*q*list[2] + (1-p)*(1-q)*list[3]); - Add(res, p*list[1] + (1-p)*(1-q)*list[2] + (1-p)*q*list[3]); - return res; - end; - - RegularPolygon := function(list) #returns vertices of a regular polygon as a list of [vert, [x,y]] - local n, res, i; - res := []; - n := Length(list); - for i in [1..n] do - Add(res, [list[i], [Cos(2*3.14159265*((i-1)/n)), Sin(2*3.14159265*((i-1)/n))]]); - od; - return res; - end; - - MainHelp := function(surf, cur, faceGraph, spread, q) - local res, mainHelpi, curi, curLength, i, toSplitVertex, toSplitVertexPos, nodesOfFaceGraph, alreadyPositionedNeighbours, neighbours, v, newv, correctFacesOfVertex; - if Length(cur) >= 2 then # More than one convex drawing plane - res := []; - for i in [1..Length(cur)] do - mainHelpi := MainHelp(surf, [cur[i]], faceGraph, spread, q); - curi := mainHelpi[1]; - res := Concatenation(res, curi); - faceGraph := Set(Concatenation(faceGraph, mainHelpi[2])); - od; - return [res, faceGraph]; - else # Only one convex drawing plane - cur := cur[1]; # deabstracting the only current list - curLength := Length(cur); - if curLength < 2 then - return [[[]], faceGraph]; - else - neighbours := NeighbourFacesOfFace(surf, cur[1][1]); - nodesOfFaceGraph := List(faceGraph, x -> x[1]); - alreadyPositionedNeighbours := Difference(neighbours, [cur[2][1], cur[curLength][1]]); - if Length(Intersection(List(cur, x -> x[1]), alreadyPositionedNeighbours)) = 0 then # case 1: edge does not violate convex drawing plane - if Length(Intersection(nodesOfFaceGraph, neighbours)) = 1 then # Only one neighbour has been positioned already, so 2 more have to be added - correctFacesOfVertex := Filtered(FacesOfVertices(surf), x -> CorrectFacesOfVertexFilter(cur[1][1], cur[2][1], List(faceGraph, y -> y[1]), x)); - for v in Difference(Difference(neighbours, correctFacesOfVertex[1]), nodesOfFaceGraph) do - newv := [v, TwoWeightedCentricParameters([cur[1][2], cur[2][2], cur[curLength][2]], spread, q)[2]]; - Add(faceGraph, newv); - Add(cur, newv); - od; - for v in Difference(Intersection(neighbours, correctFacesOfVertex[1]), nodesOfFaceGraph) do - newv := [v, TwoWeightedCentricParameters([cur[1][2], cur[2][2], cur[curLength][2]], spread, q)[1]]; - Add(faceGraph, newv); - Add(cur, newv); - od; - Remove(cur, 1); - return [[cur], faceGraph]; - elif Length(Intersection(nodesOfFaceGraph, neighbours)) = 2 then # Only two neighbours have been positioned already, so 1 more has to be added - for v in neighbours do - if not v in nodesOfFaceGraph then # and (ForAny(VerticesOfFace(surf, v), faceVertex -> Length(Intersection(List(cur, x -> x[1]), FacesAsList(UmbrellaPathOfVertex(surf, faceVertex)))) >= 3)) - newv := [v, WeightedCentricParameters([cur[1][2], cur[2][2], cur[curLength][2]], spread)]; - Add(faceGraph, newv); - Remove(cur, 1); - Add(cur, newv); - fi; - od; - return [[cur], faceGraph]; - elif Length(Intersection(nodesOfFaceGraph, neighbours)) = 3 then # All three neighbours have been positioned already, so no more have to be added - Remove(cur, 1); - return [[cur], faceGraph]; - fi; - else # case 2: edge slices convex drawing plane in two and splits it - toSplitVertex := Intersection(List(cur, x -> x[1]), alreadyPositionedNeighbours)[1]; - toSplitVertexPos := Position(List(cur, x -> x[1]), toSplitVertex); - return [SplitListPosition(cur, toSplitVertexPos), faceGraph]; - fi; - fi; - fi; - end; - - RegularPolygon := function(list) #returns vertices of a regular polygon as a list of [vert, [x,y]] - local n, res, i; - res:=[]; - n:=Length(list); - for i in [1..n] do - Add(res,[list[i],[Cos(2*3.14159265*((i-1)/n)),Sin(2*3.14159265*((i-1)/n))]]); - od; - return res; - end; - - DrawConvexFaceGraph := function(surf, spread, q) - local cur, faceGraph, path, mainHelp, maxPathPos; - maxPathPos := PositionMaximum(List(UmbrellaPathsOfVertices(surf), x -> Length(FacesAsList(x)))); - path := UmbrellaPathOfVertex(surf, maxPathPos); # Start with the biggest UmbrellaPath - # path := UmbrellaPathOfVertex(surf, Vertices(surf)[1]); # Start with the UmbrellaPath of the vertex 1 - cur := [RegularPolygon(FacesAsList(path))]; - faceGraph := RegularPolygon(FacesAsList(path)); - while Length(faceGraph) < NumberOfFaces(surf) do - mainHelp := MainHelp(surf, cur, faceGraph, spread, q); - cur := mainHelp[1]; - faceGraph := mainHelp[2]; - od; - return faceGraph; - end; - - if not "spread" in RecNames(record) then - record.spread := Float(1/2); - elif record.spread >= Float(1) or record.spread <= Float(0) then - Error("The spread parameter has to be chosen in the interval (0, 1) !"); - fi; - q := Float(7/9); # another parameter that controls the spread but probably not important enough to let the user control it. q must be chosen in the interval ((1/2), 1). - graph := DrawConvexFaceGraph(surf, Float(record.spread), q); - SortBy(graph, x -> x[1]); - if "scale" in RecNames(record) and "faceCoordinates2D" in RecNames(record) then - return DrawFacegraphToTikz(surf, name, record); - elif (not "scale" in RecNames(record)) and "faceCoordinates2D" in RecNames(record) then - record.scale := 4; - elif "scale" in RecNames(record) and (not "faceCoordinates2D" in RecNames(record)) then - record.faceCoordinates2D := List(graph, x -> x[2]); - else - record.faceCoordinates2D := List(graph, x -> x[2]); - record.scale := 4; - fi; - - return DrawFacegraphToTikz(surf, name, record); - end -); - -InstallOtherMethod( DrawConvexFacegraphToTikz, - "for a simplicial surface and a file name", - [IsSimplicialSurface, IsString], - function(surf, name) - return DrawConvexFacegraphToTikz(surf, name, rec()); - end -); - From f22203d2bbf61dda2bae454717be7da4e5260eaf Mon Sep 17 00:00:00 2001 From: Flynn Fehre Date: Sun, 10 Mar 2024 19:22:38 +0100 Subject: [PATCH 14/44] removed everything related to ButterflyFaithfulMonomorphismIntoSimplicialSurface in order to split facegraph_function branch --- gap/Morphisms/morphisms.gd | 75 ------ gap/Morphisms/morphisms.gi | 516 ------------------------------------- 2 files changed, 591 deletions(-) diff --git a/gap/Morphisms/morphisms.gd b/gap/Morphisms/morphisms.gd index 8b01c12c..a494e951 100644 --- a/gap/Morphisms/morphisms.gd +++ b/gap/Morphisms/morphisms.gd @@ -422,81 +422,6 @@ DeclareOperation( "PolygonalIdentityMorphism", [IsPolygonalComplex] ); DeclareAttribute( "InversePolygonalMorphism", IsPolygonalMorphism and IsBijective ); -#! -#! -#! A polygonal morphism or fail -#! -#! Given two simplicial surfaces surf1 and surf2, return a butterfly-faithful -#! monomorphism from surf1 to surf2 if it exists. Otherwise return fail. -#! A homomorphism of simplicial surfaces is called butterfly-faithful if the homomorphism -#! when restricted to a butterfly, i.e. restricted to two incident faces of an inner edge, -#! becomes a bijection onto another butterfly. In other words, every butterfly of -#! surf1 is being preserved and does not degenerate in surf2. -#! As an example, consider the 3-half-umbrella and 6-umbrella. -#! -#! \begin{tikzpicture}[vertexStyle, edgeStyle, faceStyle] -#! \input{Image_Butterfly_Faithful_Monomorphism_Hexagon.tex} -#! \end{tikzpicture} -#! -#! @ExampleSession -#! gap> six := SimplicialSurfaceByDownwardIncidence( -#! > [[1,2],[2,3],[3,4],[4,5],[5,6],[6,1],,[1,8],[2,8],[3,8],[4,8],[5,8],[6,8]], -#! > [[1,8,9],[2,9,10],[3,10,11],[4,11,12],[5,12,13],[6,13,8]]);; -#! gap> three := SimplicialSurfaceByDownwardIncidence( -#! > [[1,2],[2,3],[3,4],[5,4],[1,5],[2,5],[3,5]], [[1,5,6],[2,6,7],[3,7,4]]);; -#! gap> mor_3_to_6 := ButterflyFaithfulMonomorphismIntoSimplicialSurface(three, -#! > six);; -#! gap> VertexMapAsImageList(mor_3_to_6); -#! [ 1, 2, 3, 4, 8 ] -#! gap> EdgeMapAsImageList(mor_3_to_6); -#! [ 1, 2, 3, 11, 8, 9, 10 ] -#! gap> FaceMapAsImageList(mor_3_to_6); -#! [ 1, 2, 3 ] -#! @EndExampleSession -#! -#! -# -DeclareOperation( "ButterflyFaithfulMonomorphismIntoSimplicialSurface", [IsSimplicialSurface, IsSimplicialSurface]); - -#! -#! -#! A list of polygonal morphisms -#! -#! Given two simplicial surfaces surf1 and surf2, return a list of all -#! butterfly-faithful monomorphisms from surf1 to surf2. -#! A homomorphism of simplicial surfaces is called butterfly-faithful if the homomorphism -#! when restricted to a butterfly, i.e. restricted to two incident faces of an inner edge, -#! becomes a bijection onto another butterfly. In other words, every butterfly of -#! surf1 is being preserved and does not degenerate in surf2. -#! As an example, consider the 3-half-umbrella and 6-umbrella. We would expect 12 -#! butterfly-faithful monomorphisms, namely by aligning the 3-half umbrella with 3 -#! consecutive faces of the 6-umbrella. There are 6 ways to do this and another 6 if -#! we flip the 3-half-umbrella first. -#! -#! \begin{tikzpicture}[vertexStyle, edgeStyle, faceStyle] -#! \input{Image_Butterfly_Faithful_Monomorphism_Hexagon.tex} -#! \end{tikzpicture} -#! -#! @ExampleSession -#! gap> six := SimplicialSurfaceByDownwardIncidence( -#! > [[1,2],[2,3],[3,4],[4,5],[5,6],[6,1],,[1,8],[2,8],[3,8],[4,8],[5,8],[6,8]], -#! > [[1,8,9],[2,9,10],[3,10,11],[4,11,12],[5,12,13],[6,13,8]]);; -#! gap> three := SimplicialSurfaceByDownwardIncidence( -#! > [[1,2],[2,3],[3,4],[5,4],[1,5],[2,5],[3,5]], [[1,5,6],[2,6,7],[3,7,4]]);; -#! gap> all_mor_3_to_6 := AllButterflyFaithfulMonomorphismsIntoSimplicialSurface( -#! > three, six);; -#! gap> Length(all_mor_3_to_6); -#! 12 -#! @EndExampleSession -#! -#! -# -DeclareOperation( "AllButterflyFaithfulMonomorphismsIntoSimplicialSurface", [IsSimplicialSurface, IsSimplicialSurface]); - #! @Section Images and pre-images #! @SectionLabel Morphisms_Images #! diff --git a/gap/Morphisms/morphisms.gi b/gap/Morphisms/morphisms.gi index e98c202f..b8726847 100644 --- a/gap/Morphisms/morphisms.gi +++ b/gap/Morphisms/morphisms.gi @@ -480,522 +480,6 @@ InstallMethod( InverseGeneralMapping, "for a polygonal morphism", end ); -InstallMethod(ButterflyFaithfulMonomorphismIntoSimplicialSurface, "for two simplicial surfaces", - [IsSimplicialSurface, IsSimplicialSurface], - function(surface1, surface2) - local PermuteList, AllBijections, AllOneFaceIsomorphisms, MyImage, MyPreImage, MyImageCat, - MyPreImages, MyPreImagesCat, MyUpdateMap, SurfaceIdentityMap, RemoveElement, MyLess, - VertexDegreesOfFace, MyIsInjective, MonomorphismIntoSimplicialSurface; - PermuteList := function(list, perm) - return List(list, x -> x^perm); - end; - - AllBijections := function(list1, list2) - local res, AllPermutations, i, bijection, g, tmp; - res := []; - if not (Length(list1) = Length(list2)) then - return []; - else - AllPermutations := []; - for g in SymmetricGroup(list2) do - Add(AllPermutations, PermuteList(list2, g)); - od; - for bijection in AllPermutations do - tmp := []; - for i in [1..Length(list1)] do - tmp[list1[i]] := bijection[i]; - od; - Add(res, tmp); - od; - # res := List(AllPermutations, x -> IndexInducedMap(list1, x)); - return res; - fi; - end; - - MyImage := function(map, x) - return map[x]; - end; - - MyImageCat := function(map, x_list) - local res, i; - res := []; - for i in x_list do - if IsBound(map[i]) then - Add(res, map[i]); - fi; - od; - return res; - end; - - MyPreImage := function(map, y) - local res, i; - res := []; - for i in [1..Length(map)] do - if IsBound(map[i]) and map[i] = y then - Add(res, i); - fi; - od; - return res; - end; - - MyPreImagesCat := function(map, y_list) - return Concatenation(List(y_list, y -> MyPreImage(map, y))); - end; - - MyPreImages := function(map) - return MyPreImagesCat(map, Compacted(map)); - end; - - AllOneFaceIsomorphisms := function(face1, surface1, face2, surface2) - local res, e, vertex_maps, vertex_map, mapped_e, i, edge, edge_map, face_map; - res := []; - vertex_maps := AllBijections(VerticesOfFace(surface1, face1), - VerticesOfFace(surface2, face2)); - # edge_map := []; - for vertex_map in vertex_maps do - edge_map := []; - e := List([1,2,3], i -> Set(VerticesOfEdge(surface1, EdgesOfFace(surface1, face1)[i]))); - mapped_e := List(e, e_i -> Set(List(e_i, v -> vertex_map[v]))); - # Error(); - for i in [1..3] do - for edge in EdgesOfFace(surface2, face2) do - # Error(); - if Set(VerticesOfEdge(surface2, edge)) = Set(mapped_e[i]) then - # Error(); - # mapped_e[i] := edge; - edge_map[EdgesOfFace(surface1, face1)[i]]:= edge; - break; - fi; - od; - od; - face_map := []; - face_map[face1] := face2; - Add(res, [vertex_map, edge_map, face_map]); - od; - return res; - end; - - MyUpdateMap := function(map, element, image_of_element) # is used to update maps with new images, also updates when used in if-clauses ! - if not IsBound(map[element]) then - map[element] := image_of_element; - return true; - elif map[element] = image_of_element then - return true; - else - return false; - fi; - end; - - SurfaceIdentityMap := function(surface) - return [[1..NumberOfVertices(surface)], [1..NumberOfEdges(surface)], [1..NumberOfFaces(surface)]]; - end; - - RemoveElement := function(list, element) - if not element in list then - return fail; - else - Remove(list, Position(list, element)); - fi; - end; - - MyLess := function(fdeg1, fdeg2) - return fdeg1 < fdeg2; - end; - - VertexDegreesOfFace := function(surface, face) - return Set(List(VerticesOfFace(surface, face), v -> DegreeOfVertex(surface, v))); - end; - - MyIsInjective := function(map) - return IsDuplicateFree(Compacted(map)); - end; - MonomorphismIntoSimplicialSurface := function(surface1, surface2) - local possible_vertex_maps, possible_monomorphisms, starting_face, image_starting_face, mapped_edges, mapped_faces, - remaining_faces, cur_edges, cur_edge, mapped_vertices, monomorphism, cur_face, face_map, edge_map, - vertex_map, i, new_face, new_image_face, is_correct_morphism, new_vertex, new_image_vertex, new_edges, new_image_edges, - cur_new_edge, cur_new_image_edge, finished_cur_edges, faces1, faces2, face_counter1, face_counter2, face_degrees1, face_degrees2, - min_degrees, min_pos, possible_image_faces; - - faces1 := Filtered(Faces(surface1), face -> ForAll(VerticesOfFace(surface1, face), v -> IsInnerVertex(surface1, v))); - faces2 := Filtered(Faces(surface2), face -> ForAll(VerticesOfFace(surface2, face), v -> IsInnerVertex(surface2, v))); - possible_image_faces := Faces(surface2); - if not faces1 = [] then # inner vertex degrees heuristic - face_counter1 := List(faces1, face -> Set(List(VerticesOfFace(surface1, face), v -> DegreeOfVertex(surface1, v)))); - face_counter2 := List(faces1, face -> Set(List(VerticesOfFace(surface2, face), v -> DegreeOfVertex(surface2, v)))); - # face_counter1 := ListCounter(CounterOfFaces(surface1)); - # face_counter2 := ListCounter(CounterOfFaces(surface2)); - # face_degrees1 := List(face_counter1, fdegs1 -> Set(fdegs1[1])); - # face_degrees2 := List(face_counter2, fdegs2 -> Set(fdegs2[1])); - if ForAny(face_counter2, fdegs2 -> not fdegs2 in face_counter1) then - # Error("heuristic"); - return fail; - else - min_pos := PositionMinimum(List(Collected(face_counter2), fdeg2 -> fdeg2[2])); - min_degrees := Collected(face_counter2)[min_pos][1]; - starting_face := Filtered(faces1, face -> min_degrees = Set(List(VerticesOfFace(surface1, face), v -> DegreeOfVertex(surface1, v))))[1]; - possible_image_faces := Filtered(faces2, face -> min_degrees = Set(List(VerticesOfFace(surface2, face), v -> DegreeOfVertex(surface2, v)))); - fi; - else - starting_face := Faces(surface1)[1]; - fi; - - for image_starting_face in possible_image_faces do - possible_monomorphisms := AllOneFaceIsomorphisms(starting_face, surface1, - image_starting_face, surface2); - for i in [1..Length(possible_monomorphisms)] do - is_correct_morphism := true; - monomorphism := possible_monomorphisms[i]; - vertex_map := monomorphism[1]; - edge_map := monomorphism[2]; - face_map := monomorphism[3]; - - cur_edges := Filtered(EdgesOfFace(surface1, starting_face), e -> IsInnerEdge(surface1, e)); - finished_cur_edges := []; - remaining_faces := Difference(Faces(surface1), [starting_face]); - mapped_faces := MyPreImages(face_map); - while not IsEmpty(remaining_faces) do - cur_edge := cur_edges[1]; - # Error("Mono"); - # update face_map - if Length(Difference(FacesOfEdge(surface2, edge_map[cur_edge]), face_map)) = 1 then - # Error("Mono"); - new_image_face := Difference(FacesOfEdge(surface2, edge_map[cur_edge]), face_map)[1]; - else # QUESTION not sure if this case is correct - # Error("Mono"); - is_correct_morphism := false; - break; - fi; - new_face := Difference(FacesOfEdge(surface1, cur_edge), mapped_faces)[1]; - - if not new_face in remaining_faces then - # Error("Mono"); - is_correct_morphism := false; - break; - fi; - - if MyUpdateMap(face_map, new_face, new_image_face) = false or MyIsInjective(face_map) = false then - # Error("Mono"); - is_correct_morphism := false; - break; - fi; - mapped_faces := MyPreImages(face_map); - - # update vertex_map - # new_vertex := Difference(VerticesOfFace(surface1, new_face), - # Intersection(List(FacesOfEdge(surface1, cur_edge), F -> VerticesOfFace(surface1, F))))[1]; # QUESTION requires vertex-faithful - new_vertex := Difference(VerticesOfFace(surface1, new_face), VerticesOfEdge(surface1, cur_edge))[1]; - # new_image_vertex := Difference(VerticesOfFace(surface2, new_image_face), - # Intersection(List(FacesOfEdge(surface2, edge_map[cur_edge]), F -> VerticesOfFace(surface2, F))))[1]; # QUESTION requires vertex-faithful - new_image_vertex := Difference(VerticesOfFace(surface2, new_image_face), VerticesOfEdge(surface2, edge_map[cur_edge]))[1]; - if MyUpdateMap(vertex_map, new_vertex, new_image_vertex) = false or MyIsInjective(vertex_map) = false then - # Error("Mono"); - is_correct_morphism := false; - break; - fi; - - # update edge_map - new_edges := Difference(EdgesOfFace(surface1, new_face), [cur_edge]); - new_image_edges := Difference(EdgesOfFace(surface2, new_image_face), [edge_map[cur_edge]]); - for cur_new_edge in new_edges do - for cur_new_image_edge in new_image_edges do - # Error("MonoEdge"); - if Set(MyImageCat(vertex_map, VerticesOfEdge(surface1, cur_new_edge))) = Set(VerticesOfEdge(surface2, cur_new_image_edge)) then # QUESTION requires vertex-faithful - if MyUpdateMap(edge_map, cur_new_edge, cur_new_image_edge) = false or MyIsInjective(edge_map) = false then - # Error("Mono"); - is_correct_morphism := false; - fi; - if cur_new_edge in cur_edges then - Add(finished_cur_edges, cur_new_edge); - fi; - # Error("MonoEdge"); - fi; - od; - od; - if is_correct_morphism = false then - break; - fi; - - # update cur_edges - cur_edges := Union(cur_edges, Filtered(EdgesOfFace(surface1, new_face), e -> IsInnerEdge(surface1, e))); - Add(finished_cur_edges, cur_edge); - cur_edges := Difference(cur_edges, finished_cur_edges); - - # update remaining_faces - remaining_faces := Difference(remaining_faces, [new_face]); - # Error("Mono"); - od; - - if is_correct_morphism = true then - # return monomorphism; # uncomment for the lists that make the homomorphism FLAG(LISTS) - return PolygonalMorphismByLists(surface1, surface2, monomorphism[1], monomorphism[2], monomorphism[3]); #FLAG(MORPHISMS) - fi; - od; - od; - return fail; - end; - return MonomorphismIntoSimplicialSurface(surface1, surface2); - end -); - -InstallMethod(AllButterflyFaithfulMonomorphismsIntoSimplicialSurface, "for two simplicial surfaces", - [IsSimplicialSurface, IsSimplicialSurface], - function(surface1, surface2) - local PermuteList, AllBijections, AllOneFaceIsomorphisms, MyImage, MyPreImage, MyImageCat, - MyPreImages, MyPreImagesCat, MyUpdateMap, SurfaceIdentityMap, RemoveElement, MyLess, - VertexDegreesOfFace, MyIsInjective, AllMonomorphismsIntoSimplicialSurface; - PermuteList := function(list, perm) - return List(list, x -> x^perm); - end; - - AllBijections := function(list1, list2) - local res, AllPermutations, i, bijection, g, tmp; - res := []; - if not (Length(list1) = Length(list2)) then - return []; - else - AllPermutations := []; - for g in SymmetricGroup(list2) do - Add(AllPermutations, PermuteList(list2, g)); - od; - for bijection in AllPermutations do - tmp := []; - for i in [1..Length(list1)] do - tmp[list1[i]] := bijection[i]; - od; - Add(res, tmp); - od; - # res := List(AllPermutations, x -> IndexInducedMap(list1, x)); - return res; - fi; - end; - - MyImage := function(map, x) - return map[x]; - end; - - MyImageCat := function(map, x_list) - local res, i; - res := []; - for i in x_list do - if IsBound(map[i]) then - Add(res, map[i]); - fi; - od; - return res; - end; - - MyPreImage := function(map, y) - local res, i; - res := []; - for i in [1..Length(map)] do - if IsBound(map[i]) and map[i] = y then - Add(res, i); - fi; - od; - return res; - end; - - MyPreImagesCat := function(map, y_list) - return Concatenation(List(y_list, y -> MyPreImage(map, y))); - end; - - MyPreImages := function(map) - return MyPreImagesCat(map, Compacted(map)); - end; - - AllOneFaceIsomorphisms := function(face1, surface1, face2, surface2) - local res, e, vertex_maps, vertex_map, mapped_e, i, edge, edge_map, face_map; - res := []; - vertex_maps := AllBijections(VerticesOfFace(surface1, face1), - VerticesOfFace(surface2, face2)); - # edge_map := []; - for vertex_map in vertex_maps do - edge_map := []; - e := List([1,2,3], i -> Set(VerticesOfEdge(surface1, EdgesOfFace(surface1, face1)[i]))); - mapped_e := List(e, e_i -> Set(List(e_i, v -> vertex_map[v]))); - # Error(); - for i in [1..3] do - for edge in EdgesOfFace(surface2, face2) do - # Error(); - if Set(VerticesOfEdge(surface2, edge)) = Set(mapped_e[i]) then - # Error(); - # mapped_e[i] := edge; - edge_map[EdgesOfFace(surface1, face1)[i]]:= edge; - break; - fi; - od; - od; - face_map := []; - face_map[face1] := face2; - Add(res, [vertex_map, edge_map, face_map]); - od; - return res; - end; - - MyUpdateMap := function(map, element, image_of_element) # is used to update maps with new images, also updates when used in if-clauses ! - if not IsBound(map[element]) then - map[element] := image_of_element; - return true; - elif map[element] = image_of_element then - return true; - else - return false; - fi; - end; - - SurfaceIdentityMap := function(surface) - return [[1..NumberOfVertices(surface)], [1..NumberOfEdges(surface)], [1..NumberOfFaces(surface)]]; - end; - - RemoveElement := function(list, element) - if not element in list then - return fail; - else - Remove(list, Position(list, element)); - fi; - end; - - MyLess := function(fdeg1, fdeg2) - return fdeg1 < fdeg2; - end; - - VertexDegreesOfFace := function(surface, face) - return Set(List(VerticesOfFace(surface, face), v -> DegreeOfVertex(surface, v))); - end; - - MyIsInjective := function(map) - return IsDuplicateFree(Compacted(map)); - end; - - AllMonomorphismsIntoSimplicialSurface := function(surface1, surface2) - local possible_vertex_maps, possible_monomorphisms, starting_face, image_starting_face, mapped_edges, mapped_faces, - remaining_faces, cur_edges, cur_edge, mapped_vertices, monomorphism, cur_face, face_map, edge_map, - vertex_map, i, new_face, new_image_face, is_correct_morphism, new_vertex, new_image_vertex, new_edges, new_image_edges, - cur_new_edge, cur_new_image_edge, finished_cur_edges, faces1, faces2, face_counter1, face_counter2, face_degrees1, face_degrees2, - min_degrees, min_pos, possible_image_faces, res; - - res := []; - faces1 := Filtered(Faces(surface1), face -> ForAll(VerticesOfFace(surface1, face), v -> IsInnerVertex(surface1, v))); - faces2 := Filtered(Faces(surface2), face -> ForAll(VerticesOfFace(surface2, face), v -> IsInnerVertex(surface2, v))); - possible_image_faces := Faces(surface2); - if not faces1 = [] then # inner vertex degrees heuristic - face_counter1 := List(faces1, face -> Set(List(VerticesOfFace(surface1, face), v -> DegreeOfVertex(surface1, v)))); - face_counter2 := List(faces1, face -> Set(List(VerticesOfFace(surface2, face), v -> DegreeOfVertex(surface2, v)))); - # face_counter1 := ListCounter(CounterOfFaces(surface1)); - # face_counter2 := ListCounter(CounterOfFaces(surface2)); - # face_degrees1 := List(face_counter1, fdegs1 -> Set(fdegs1[1])); - # face_degrees2 := List(face_counter2, fdegs2 -> Set(fdegs2[1])); - if ForAny(face_counter2, fdegs2 -> not fdegs2 in face_counter1) then - # Error("heuristic"); - return res; # empty list - else - min_pos := PositionMinimum(List(Collected(face_counter2), fdeg2 -> fdeg2[2])); - min_degrees := Collected(face_counter2)[min_pos][1]; - starting_face := Filtered(faces1, face -> min_degrees = Set(List(VerticesOfFace(surface1, face), v -> DegreeOfVertex(surface1, v))))[1]; - possible_image_faces := Filtered(faces2, face -> min_degrees = Set(List(VerticesOfFace(surface2, face), v -> DegreeOfVertex(surface2, v)))); - fi; - else - starting_face := Faces(surface1)[1]; - fi; - - for image_starting_face in possible_image_faces do - possible_monomorphisms := AllOneFaceIsomorphisms(starting_face, surface1, - image_starting_face, surface2); - for i in [1..Length(possible_monomorphisms)] do - is_correct_morphism := true; - monomorphism := possible_monomorphisms[i]; - vertex_map := monomorphism[1]; - edge_map := monomorphism[2]; - face_map := monomorphism[3]; - - cur_edges := Filtered(EdgesOfFace(surface1, starting_face), e -> IsInnerEdge(surface1, e)); - finished_cur_edges := []; - remaining_faces := Difference(Faces(surface1), [starting_face]); - mapped_faces := MyPreImages(face_map); - while not IsEmpty(remaining_faces) do - cur_edge := cur_edges[1]; - # Error("Mono"); - # update face_map - if Length(Difference(FacesOfEdge(surface2, edge_map[cur_edge]), face_map)) = 1 then - # Error("Mono"); - new_image_face := Difference(FacesOfEdge(surface2, edge_map[cur_edge]), face_map)[1]; - else # QUESTION not sure if this case is correct - # Error("Mono"); - is_correct_morphism := false; - break; - fi; - new_face := Difference(FacesOfEdge(surface1, cur_edge), mapped_faces)[1]; - - if not new_face in remaining_faces then - # Error("Mono"); - is_correct_morphism := false; - break; - fi; - - if MyUpdateMap(face_map, new_face, new_image_face) = false or MyIsInjective(face_map) = false then - # Error("Mono"); - is_correct_morphism := false; - break; - fi; - mapped_faces := MyPreImages(face_map); - - # update vertex_map - # new_vertex := Difference(VerticesOfFace(surface1, new_face), - # Intersection(List(FacesOfEdge(surface1, cur_edge), F -> VerticesOfFace(surface1, F))))[1]; # QUESTION requires vertex-faithful - new_vertex := Difference(VerticesOfFace(surface1, new_face), VerticesOfEdge(surface1, cur_edge))[1]; - # new_image_vertex := Difference(VerticesOfFace(surface2, new_image_face), - # Intersection(List(FacesOfEdge(surface2, edge_map[cur_edge]), F -> VerticesOfFace(surface2, F))))[1]; # QUESTION requires vertex-faithful - new_image_vertex := Difference(VerticesOfFace(surface2, new_image_face), VerticesOfEdge(surface2, edge_map[cur_edge]))[1]; - if MyUpdateMap(vertex_map, new_vertex, new_image_vertex) = false or MyIsInjective(vertex_map) = false then - # Error("Mono"); - is_correct_morphism := false; - break; - fi; - - # update edge_map - new_edges := Difference(EdgesOfFace(surface1, new_face), [cur_edge]); - new_image_edges := Difference(EdgesOfFace(surface2, new_image_face), [edge_map[cur_edge]]); - for cur_new_edge in new_edges do - for cur_new_image_edge in new_image_edges do - # Error("MonoEdge"); - if Set(MyImageCat(vertex_map, VerticesOfEdge(surface1, cur_new_edge))) = Set(VerticesOfEdge(surface2, cur_new_image_edge)) then # QUESTION requires vertex-faithful - if MyUpdateMap(edge_map, cur_new_edge, cur_new_image_edge) = false or MyIsInjective(edge_map) = false then - # Error("Mono"); - is_correct_morphism := false; - fi; - if cur_new_edge in cur_edges then - Add(finished_cur_edges, cur_new_edge); - fi; - # Error("MonoEdge"); - fi; - od; - od; - if is_correct_morphism = false then - break; - fi; - - # update cur_edges - cur_edges := Union(cur_edges, Filtered(EdgesOfFace(surface1, new_face), e -> IsInnerEdge(surface1, e))); - Add(finished_cur_edges, cur_edge); - cur_edges := Difference(cur_edges, finished_cur_edges); - - # update remaining_faces - remaining_faces := Difference(remaining_faces, [new_face]); - # Error("Mono"); - od; - - if is_correct_morphism = true then - # Add(res, monomorphism); # uncomment to add the list the monomorphism is made of FLAG(LISTS) - Add(res,PolygonalMorphismByLists(surface1, surface2, monomorphism[1], monomorphism[2], monomorphism[3])); # FLAG(MORPHISMS) - fi; - od; - od; - return res; - end; - return AllMonomorphismsIntoSimplicialSurface(surface1, surface2); - end -); - ## ## End of constructions ## From 48e525d0cfd2f01def4cbc154a2d185a2455907b Mon Sep 17 00:00:00 2001 From: Flynn Fehre Date: Mon, 11 Mar 2024 17:57:18 +0100 Subject: [PATCH 15/44] pre-compiled old images for new image structure --- ...utterfly_Faithful_Monomorphism_Hexagon.tex | 51 - doc/Image_convex_facegraph_Double6Gon.tex | 47 - ...utterfly_Faithful_Monomorphism_Hexagon.pdf | Bin 0 -> 40202 bytes ...utterfly_Faithful_Monomorphism_Hexagon.svg | 428 ++++++ .../Image_convex_facegraph_Double6Gon.pdf | Bin 0 -> 13477 bytes .../Image_convex_facegraph_Double6Gon.svg | 822 ++++++++++ ...x_facegraph_icosahedron_default_spread.pdf | Bin 0 -> 15238 bytes ...x_facegraph_icosahedron_default_spread.svg | 1358 +++++++++++++++++ ...nvex_facegraph_icosahedron_high_spread.pdf | Bin 0 -> 15240 bytes ...nvex_facegraph_icosahedron_high_spread.svg | 1358 +++++++++++++++++ ...onvex_facegraph_icosahedron_low_spread.pdf | Bin 0 -> 15225 bytes ...onvex_facegraph_icosahedron_low_spread.svg | 1358 +++++++++++++++++ ...utterfly_Faithful_Monomorphism_Hexagon.tex | 319 ++++ .../Image_convex_facegraph_Double6Gon.tex | 312 ++++ ...x_facegraph_icosahedron_default_spread.tex | 340 +++++ ...nvex_facegraph_icosahedron_high_spread.tex | 341 +++++ ...onvex_facegraph_icosahedron_low_spread.tex | 341 +++++ gap/Morphisms/morphisms.gd | 32 +- gap/PolygonalComplexes/drawing.gd | 62 +- 19 files changed, 7049 insertions(+), 120 deletions(-) delete mode 100644 doc/Image_Butterfly_Faithful_Monomorphism_Hexagon.tex delete mode 100644 doc/Image_convex_facegraph_Double6Gon.tex create mode 100644 doc/images/Image_Butterfly_Faithful_Monomorphism_Hexagon.pdf create mode 100644 doc/images/Image_Butterfly_Faithful_Monomorphism_Hexagon.svg create mode 100644 doc/images/Image_convex_facegraph_Double6Gon.pdf create mode 100644 doc/images/Image_convex_facegraph_Double6Gon.svg create mode 100644 doc/images/_TIKZ_convex_facegraph_icosahedron_default_spread.pdf create mode 100644 doc/images/_TIKZ_convex_facegraph_icosahedron_default_spread.svg create mode 100644 doc/images/_TIKZ_convex_facegraph_icosahedron_high_spread.pdf create mode 100644 doc/images/_TIKZ_convex_facegraph_icosahedron_high_spread.svg create mode 100644 doc/images/_TIKZ_convex_facegraph_icosahedron_low_spread.pdf create mode 100644 doc/images/_TIKZ_convex_facegraph_icosahedron_low_spread.svg create mode 100644 doc/tikz-files/Image_Butterfly_Faithful_Monomorphism_Hexagon.tex create mode 100644 doc/tikz-files/Image_convex_facegraph_Double6Gon.tex create mode 100644 doc/tikz-files/_TIKZ_convex_facegraph_icosahedron_default_spread.tex create mode 100644 doc/tikz-files/_TIKZ_convex_facegraph_icosahedron_high_spread.tex create mode 100644 doc/tikz-files/_TIKZ_convex_facegraph_icosahedron_low_spread.tex diff --git a/doc/Image_Butterfly_Faithful_Monomorphism_Hexagon.tex b/doc/Image_Butterfly_Faithful_Monomorphism_Hexagon.tex deleted file mode 100644 index cac13053..00000000 --- a/doc/Image_Butterfly_Faithful_Monomorphism_Hexagon.tex +++ /dev/null @@ -1,51 +0,0 @@ - -\newcommand{\setupCoord}{ - \coordinate (Z) at (0,0); - \foreach \i in {1,...,6}{ - \coordinate (A\i) at (180-60*\i:2.5); - } -} - - -\begin{scope}[shift={(3.5,0)}] - \setupCoord - - \draw[edge,face] - (Z) -- (A1) -- node[edgeLabel]{1} (A2) -- cycle - (Z) -- node[edgeLabel]{9} (A2) -- node[edgeLabel]{2} (A3) -- cycle - (Z) -- node[edgeLabel]{10} (A3) -- node[edgeLabel]{3} (A4) -- cycle - (Z) -- node[edgeLabel]{11} (A4) -- node[edgeLabel]{4} (A5) -- cycle - (Z) -- node[edgeLabel]{12} (A5) -- node[edgeLabel]{5} (A6) -- cycle - (Z) -- node[edgeLabel]{13} (A6) -- node[edgeLabel]{6} (A1) -- node[edgeLabel]{8} (Z); - - \foreach \p/\r/\n in {1/above left/1, 2/above right/2, 3/right/3, 4/below right/4, 5/below left/5, 6/left/6}{ - \vertexLabelR{A\p}{\r}{\n} - } - \vertexLabelR{Z}{above}{8} - - \foreach \i/\j/\n in {1/2/I, 2/3/II, 3/4/III, 4/5/IV, 5/6/V, 6/1/VI}{ - \node[faceLabel] at (barycentric cs:A\i=1,A\j=1,Z=1) {$\n$}; - } -\end{scope} - - -\node at (0,0) {$\rightarrow$}; - - -\begin{scope}[shift={(-3.5,0)}] - \setupCoord - - \draw[edge,face] - (Z) -- node[edgeLabel]{5} (A1) -- node[edgeLabel]{1} (A2) -- cycle - (Z) -- node[edgeLabel]{6} (A2) -- node[edgeLabel]{2} (A3) -- cycle - (Z) -- node[edgeLabel]{7} (A3) -- node[edgeLabel]{3} (A4) -- node[edgeLabel]{4} (Z); - - \foreach \p/\r/\n in {1/above left/1, 2/above right/2, 3/right/3, 4/below right/4}{ - \vertexLabelR{A\p}{\r}{\n} - } - \vertexLabelR{Z}{below left}{5} - - \foreach \i/\j/\n in {1/2/I, 2/3/II, 3/4/III}{ - \node[faceLabel] at (barycentric cs:A\i=1,A\j=1,Z=1) {$\n$}; - } -\end{scope} diff --git a/doc/Image_convex_facegraph_Double6Gon.tex b/doc/Image_convex_facegraph_Double6Gon.tex deleted file mode 100644 index a919f0e3..00000000 --- a/doc/Image_convex_facegraph_Double6Gon.tex +++ /dev/null @@ -1,47 +0,0 @@ -\begin{tikzpicture}[vertexBall, edgeDouble=nolabels, faceStyle=nolabels, scale=4] - -\coordinate (V1) at (1. , 0.); -\coordinate (V2) at (0.5000000010362841 , 0.8660254031861397); -\coordinate (V3) at (-0.4999999979274318 , 0.8660254049810364); -\coordinate (V4) at (-1. , 3.589793029841612e-09); -\coordinate (V5) at (-0.5000000041451365 , -0.866025401391243); -\coordinate (V6) at (0.4999999948185802 , -0.8660254067759328); -\coordinate (V7) at (0.8333333326424773 , -5.982988363998724e-10); -\coordinate (V8) at (0.3888888898100303 , 0.7216878361878827); -\coordinate (V9) at (-0.4351851836499495 , 0.6976315766169703); -\coordinate (V10) at (-0.8225308646325142 , -0.02806563506918342); -\coordinate (V11) at (-0.3870884810657467 , -0.7263654412350147); -\coordinate (V12) at (0.4077074718085085 , -0.698411178156174); -\draw[edge] (V1) -- node[edgeLabel] {$1$} (V6); -\draw[edge] (V1) -- node[edgeLabel] {$2$} (V2); -\draw[edge] (V2) -- node[edgeLabel] {$3$} (V3); -\draw[edge] (V3) -- node[edgeLabel] {$4$} (V4); -\draw[edge] (V4) -- node[edgeLabel] {$5$} (V5); -\draw[edge] (V5) -- node[edgeLabel] {$6$} (V6); -\draw[edge] (V1) -- node[edgeLabel] {$7$} (V7); -\draw[edge] (V6) -- node[edgeLabel] {$8$} (V12); -\draw[edge] (V7) -- node[edgeLabel] {$9$} (V12); -\draw[edge] (V2) -- node[edgeLabel] {$10$} (V8); -\draw[edge] (V7) -- node[edgeLabel] {$11$} (V8); -\draw[edge] (V3) -- node[edgeLabel] {$12$} (V9); -\draw[edge] (V8) -- node[edgeLabel] {$13$} (V9); -\draw[edge] (V4) -- node[edgeLabel] {$14$} (V10); -\draw[edge] (V9) -- node[edgeLabel] {$15$} (V10); -\draw[edge] (V5) -- node[edgeLabel] {$16$} (V11); -\draw[edge] (V10) -- node[edgeLabel] {$17$} (V11); -\draw[edge] (V11) -- node[edgeLabel] {$18$} (V12); -% Draw the faces -\vertexLabelR{V1}{left}{$1$} -\vertexLabelR{V2}{left}{$2$} -\vertexLabelR{V3}{left}{$3$} -\vertexLabelR{V4}{left}{$4$} -\vertexLabelR{V5}{left}{$5$} -\vertexLabelR{V6}{left}{$6$} -\vertexLabelR{V7}{left}{$7$} -\vertexLabelR{V8}{left}{$8$} -\vertexLabelR{V9}{left}{$9$} -\vertexLabelR{V10}{left}{$10$} -\vertexLabelR{V11}{left}{$11$} -\vertexLabelR{V12}{left}{$12$} -\end{tikzpicture} - diff --git a/doc/images/Image_Butterfly_Faithful_Monomorphism_Hexagon.pdf b/doc/images/Image_Butterfly_Faithful_Monomorphism_Hexagon.pdf 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+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/doc/tikz-files/Image_Butterfly_Faithful_Monomorphism_Hexagon.tex b/doc/tikz-files/Image_Butterfly_Faithful_Monomorphism_Hexagon.tex new file mode 100644 index 00000000..db621e50 --- /dev/null +++ b/doc/tikz-files/Image_Butterfly_Faithful_Monomorphism_Hexagon.tex @@ -0,0 +1,319 @@ +\documentclass{standalone} + +\pagestyle{empty} +% This document contains the TikZ-header for all our LaTeX-computations. +% It especially contains all global graphic parameters. + +\usepackage{amsmath, amssymb, amsfonts} % Standard Math-stuff + +\usepackage{ifthen} + +\usepackage{tikz} +\usetikzlibrary{calc} +\usetikzlibrary{positioning} +\usetikzlibrary{shapes} +\usetikzlibrary{patterns} + + +% Sometimes we want to implement different behaviour for the generated +% HTML-pictures (for example, shading is not supported in HTML). +% For that we define a macro to check whether we run the code with +% htlatex. The code comes from +% https://tex.stackexchange.com/questions/93852/what-is-the-correct-way-to-check-for-latex-pdflatex-and-html-in-the-same-latex +\makeatletter +\edef\texforht{TT\noexpand\fi + \@ifpackageloaded{tex4ht} + {\noexpand\iftrue} + {\noexpand\iffalse}} +\makeatother + + +% Define a text=none option for nodes that ignores the given text, from +% https://tex.stackexchange.com/questions/59354/no-text-none-in-tikz +\makeatletter +\newif\iftikz@node@phantom +\tikzset{ + phantom/.is if=tikz@node@phantom, + text/.code=% + \edef\tikz@temp{#1}% + \ifx\tikz@temp\tikz@nonetext + \tikz@node@phantomtrue + \else + \tikz@node@phantomfalse + \let\tikz@textcolor\tikz@temp + \fi +} +\usepackage{etoolbox} +\patchcmd\tikz@fig@continue{\tikz@node@transformations}{% + \iftikz@node@phantom + \setbox\pgfnodeparttextbox\hbox{} + \fi\tikz@node@transformations}{}{} +\makeatother + +% Find the angle of a given line (within TikZ) +\newcommand{\tikzAngleOfLine}{\tikz@AngleOfLine} +\def\tikz@AngleOfLine(#1)(#2)#3{% + \pgfmathanglebetweenpoints{% + \pgfpointanchor{#1}{center}}{% + \pgfpointanchor{#2}{center}} + \pgfmathsetmacro{#3}{\pgfmathresult}% +} + +% Now we define the global styles +% The global styles are defined nestedly. You have to give your tikzpicture +% the global options [vertexStyle, edgeStyle, faceStyle] to activate them. +% +% You can disable labels by using the option nolabels, i.e. +% vertexStyle=nolabels to deactivate vertex labels. +% +% If you want to have a specific style for your picture, you can also use +% this specific meta-style instead of the general style. For example if you +% want to use double edges in one single picture - no matter the style of +% the rest of the document - you can use edgeDouble instead of edgeStyle. +% +% To set the default style, modify the vertexStyle/.default entry. + +% Vertex styles +\tikzset{ + vertexNodePlain/.style = {fill=#1, shape=circle, inner sep=0pt, minimum size=2pt, text=none}, + vertexNodePlain/.default=gray, + vertexPlain/labels/.style = { + vertexNode/.style={vertexNodePlain=##1}, + vertexLabel/.style={gray} + }, + vertexPlain/nolabels/.style = { + vertexNode/.style={vertexNodePlain=##1}, + vertexLabel/.style={text=none} + }, + vertexPlain/.style = vertexPlain/#1, + vertexPlain/.default=labels +} +\tikzset{ + vertexNodeNormal/.style = {fill=#1, shape=circle, inner sep=0pt, minimum size=4pt, text=none}, + vertexNodeNormal/.default = blue, + vertexNormal/labels/.style = { + vertexNode/.style={vertexNodeNormal=##1}, + vertexLabel/.style={blue} + }, + vertexNormal/nolabels/.style = { + vertexNode/.style={vertexNodeNormal=##1}, + vertexLabel/.style={text=none} + }, + vertexNormal/.style = vertexNormal/#1, + vertexNormal/.default=labels +} +\tikzset{ + vertexNodeBallShading/pdf/.style = {ball color=#1}, + vertexNodeBallShading/svg/.style = {fill=#1}, + vertexNodeBallShading/.code = {% Conditional shading depending whether we want pdf or svg output + \if\texforht + \tikzset{vertexNodeBallShading/svg=#1!90!black} + \else + \tikzset{vertexNodeBallShading/pdf=#1} + \fi + }, + vertexNodeBall/.style = {shape=circle, vertexNodeBallShading=#1, inner sep=2pt, outer sep=0pt, minimum size=3pt, font=\tiny}, + vertexNodeBall/.default = white, + vertexBall/labels/.style = { + vertexNode/.style={vertexNodeBall=##1, text=black}, + vertexLabel/.style={text=none} + }, + vertexBall/nolabels/.style = { + vertexNode/.style={vertexNodeBall=##1, text=none}, + vertexLabel/.style={text=none} + }, + vertexBall/.style = vertexBall/#1, + vertexBall/.default=labels +} +\tikzset{ + vertexStyle/.style={vertexNormal=#1}, + vertexStyle/.default = labels +} + + +% 1) optional: colour of vertex +% 2) position of the vertex +% 3) relative position of the node +% 4) name of the vertex +\newcommand{\vertexLabelR}[4][]{ + \ifthenelse{ \equal{#1}{} } + { \node[vertexNode] (#2 name) at (#2) {#4}; } + { \node[vertexNode=#1] (#2 name) at (#2) {#4}; } + \node[vertexLabel, #3] at (#2) {#4}; +} +% 1) optional: colour of vertex +% 2) position of the vertex +% 3) absolute position of the node +% 4) name of the vertex +\newcommand{\vertexLabelA}[4][]{ + \ifthenelse{ \equal{#1}{} } + { \node[vertexNode] (#2 name) at (#2) {#4}; } + { \node[vertexNode=#1] (#2 name) at (#2) {#4}; } + \node[vertexLabel] at (#3) {#4}; +} + + +% Edge styles +% If you have trouble with the double-lines overlapping, this might (?) help: +% https://tex.stackexchange.com/questions/288159/closing-the-ends-of-double-line-in-tikz +\newcommand{\edgeLabelColor}{blue!20!white} +\tikzset{ + edgeLineNone/.style = {draw=none}, + edgeLineNone/.default=black, + edgeNone/labels/.style = { + edge/.style = {edgeLineNone=##1}, + edgeLabel/.style = {fill=\edgeLabelColor,font=\small} + }, + edgeNone/nolabels/.style = { + edge/.style = {edgeLineNone=##1}, + edgeLabel/.style = {text=none} + }, + edgeNone/.style = edgeNone/#1, + edgeNone/.default = labels +} +\tikzset{ + edgeLinePlain/.style={line join=round, draw=#1}, + edgeLinePlain/.default=black, + edgePlain/labels/.style = { + edge/.style={edgeLinePlain=##1}, + edgeLabel/.style={fill=\edgeLabelColor,font=\small} + }, + edgePlain/nolabels/.style = { + edge/.style={edgeLinePlain=##1}, + edgeLabel/.style={text=none} + }, + edgePlain/.style = edgePlain/#1, + edgePlain/.default = labels +} +\tikzset{ + edgeLineDouble/.style = {very thin, double=#1, double distance=.8pt, line join=round}, + edgeLineDouble/.default=gray!90!white, + edgeDouble/labels/.style = { + edge/.style = {edgeLineDouble=##1}, + edgeLabel/.style = {fill=\edgeLabelColor,font=\small} + }, + edgeDouble/nolabels/.style = { + edge/.style = {edgeLineDouble=##1}, + edgeLabel/.style = {text=none} + }, + edgeDouble/.style = edgeDouble/#1, + edgeDouble/.default = labels +} +\tikzset{ + edgeStyle/.style = {edgePlain=#1}, + edgeStyle/.default = labels +} + +% Face styles +% Here we have an exception - the style face is always defined. +% +\newcommand{\faceColorY}{yellow!60!white} % yellow +\newcommand{\faceColorB}{blue!60!white} % blue +\newcommand{\faceColorC}{cyan!60} % cyan +\newcommand{\faceColorR}{red!60!white} % red +\newcommand{\faceColorG}{green!60!white} % green +\newcommand{\faceColorO}{orange!50!yellow!70!white} % orange + +% define default face colour (and default swap colour) +\newcommand{\faceColor}{\faceColorY} +\newcommand{\faceColorSwap}{\faceColorC} + +% define secondary default colours (to use in a single section) +\newcommand{\faceColorFirst}{green!40!white} +\newcommand{\faceColorSecond}{gray!15!white} +\newcommand{\faceColorThird}{red!17!white} +\newcommand{\faceColorFourth}{olive!20!white} + +\tikzset{ + face/.style = {fill=#1}, + face/.default = \faceColor, + faceY/.style = {face=\faceColorY}, + faceB/.style = {face=\faceColorB}, + faceC/.style = {face=\faceColorC}, + faceR/.style = {face=\faceColorR}, + faceG/.style = {face=\faceColorG}, + faceO/.style = {face=\faceColorO} +} +\tikzset{ + faceStyle/labels/.style = { + faceLabel/.style = {} + }, + faceStyle/nolabels/.style = { + faceLabel/.style = {text=none} + }, + faceStyle/.style = faceStyle/#1, + faceStyle/.default = labels +} +\tikzset{ face/.style={fill=#1} } +\tikzset{ faceSwap/.code= + \ifdefined\swapColors + \tikzset{face=\faceColorSwap} + \else + \tikzset{face=\faceColor} + \fi +} + + + +\usepackage{hyperref} + + +\begin{document} + + + +\begin{tikzpicture}[vertexStyle, edgeStyle, faceStyle] + + \newcommand{\setupCoord}{ + \coordinate (Z) at (0,0); + \foreach \i in {1,...,6}{ + \coordinate (A\i) at (180-60*\i:2.5); + } + } + + + \begin{scope}[shift={(3.5,0)}] + \setupCoord + + \draw[edge,face] + (Z) -- (A1) -- node[edgeLabel]{1} (A2) -- cycle + (Z) -- node[edgeLabel]{9} (A2) -- node[edgeLabel]{2} (A3) -- cycle + (Z) -- node[edgeLabel]{10} (A3) -- node[edgeLabel]{3} (A4) -- cycle + (Z) -- node[edgeLabel]{11} (A4) -- node[edgeLabel]{4} (A5) -- cycle + (Z) -- node[edgeLabel]{12} (A5) -- node[edgeLabel]{5} (A6) -- cycle + (Z) -- node[edgeLabel]{13} (A6) -- node[edgeLabel]{6} (A1) -- node[edgeLabel]{8} (Z); + + \foreach \p/\r/\n in {1/above left/1, 2/above right/2, 3/right/3, 4/below right/4, 5/below left/5, 6/left/6}{ + \vertexLabelR{A\p}{\r}{\n} + } + \vertexLabelR{Z}{above}{8} + + \foreach \i/\j/\n in {1/2/I, 2/3/II, 3/4/III, 4/5/IV, 5/6/V, 6/1/VI}{ + \node[faceLabel] at (barycentric cs:A\i=1,A\j=1,Z=1) {$\n$}; + } + \end{scope} + + + \node at (0,0) {$\rightarrow$}; + + + \begin{scope}[shift={(-3.5,0)}] + \setupCoord + + \draw[edge,face] + (Z) -- node[edgeLabel]{5} (A1) -- node[edgeLabel]{1} (A2) -- cycle + (Z) -- node[edgeLabel]{6} (A2) -- node[edgeLabel]{2} (A3) -- cycle + (Z) -- node[edgeLabel]{7} (A3) -- node[edgeLabel]{3} (A4) -- node[edgeLabel]{4} (Z); + + \foreach \p/\r/\n in {1/above left/1, 2/above right/2, 3/right/3, 4/below right/4}{ + \vertexLabelR{A\p}{\r}{\n} + } + \vertexLabelR{Z}{below left}{5} + + \foreach \i/\j/\n in {1/2/I, 2/3/II, 3/4/III}{ + \node[faceLabel] at (barycentric cs:A\i=1,A\j=1,Z=1) {$\n$}; + } + \end{scope} +\end{tikzpicture} + +\end{document} diff --git a/doc/tikz-files/Image_convex_facegraph_Double6Gon.tex b/doc/tikz-files/Image_convex_facegraph_Double6Gon.tex new file mode 100644 index 00000000..3e6fd2b7 --- /dev/null +++ b/doc/tikz-files/Image_convex_facegraph_Double6Gon.tex @@ -0,0 +1,312 @@ +\documentclass{standalone} + +\pagestyle{empty} +% This document contains the TikZ-header for all our LaTeX-computations. +% It especially contains all global graphic parameters. + +\usepackage{amsmath, amssymb, amsfonts} % Standard Math-stuff + +\usepackage{ifthen} + +\usepackage{tikz} +\usetikzlibrary{calc} +\usetikzlibrary{positioning} +\usetikzlibrary{shapes} +\usetikzlibrary{patterns} + + +% Sometimes we want to implement different behaviour for the generated +% HTML-pictures (for example, shading is not supported in HTML). +% For that we define a macro to check whether we run the code with +% htlatex. The code comes from +% https://tex.stackexchange.com/questions/93852/what-is-the-correct-way-to-check-for-latex-pdflatex-and-html-in-the-same-latex +\makeatletter +\edef\texforht{TT\noexpand\fi + \@ifpackageloaded{tex4ht} + {\noexpand\iftrue} + {\noexpand\iffalse}} +\makeatother + + +% Define a text=none option for nodes that ignores the given text, from +% https://tex.stackexchange.com/questions/59354/no-text-none-in-tikz +\makeatletter +\newif\iftikz@node@phantom +\tikzset{ + phantom/.is if=tikz@node@phantom, + text/.code=% + \edef\tikz@temp{#1}% + \ifx\tikz@temp\tikz@nonetext + \tikz@node@phantomtrue + \else + \tikz@node@phantomfalse + \let\tikz@textcolor\tikz@temp + \fi +} +\usepackage{etoolbox} +\patchcmd\tikz@fig@continue{\tikz@node@transformations}{% + \iftikz@node@phantom + \setbox\pgfnodeparttextbox\hbox{} + \fi\tikz@node@transformations}{}{} +\makeatother + +% Find the angle of a given line (within TikZ) +\newcommand{\tikzAngleOfLine}{\tikz@AngleOfLine} +\def\tikz@AngleOfLine(#1)(#2)#3{% + \pgfmathanglebetweenpoints{% + \pgfpointanchor{#1}{center}}{% + \pgfpointanchor{#2}{center}} + \pgfmathsetmacro{#3}{\pgfmathresult}% +} + +% Now we define the global styles +% The global styles are defined nestedly. You have to give your tikzpicture +% the global options [vertexStyle, edgeStyle, faceStyle] to activate them. +% +% You can disable labels by using the option nolabels, i.e. +% vertexStyle=nolabels to deactivate vertex labels. +% +% If you want to have a specific style for your picture, you can also use +% this specific meta-style instead of the general style. For example if you +% want to use double edges in one single picture - no matter the style of +% the rest of the document - you can use edgeDouble instead of edgeStyle. +% +% To set the default style, modify the vertexStyle/.default entry. + +% Vertex styles +\tikzset{ + vertexNodePlain/.style = {fill=#1, shape=circle, inner sep=0pt, minimum size=2pt, text=none}, + vertexNodePlain/.default=gray, + vertexPlain/labels/.style = { + vertexNode/.style={vertexNodePlain=##1}, + vertexLabel/.style={gray} + }, + vertexPlain/nolabels/.style = { + vertexNode/.style={vertexNodePlain=##1}, + vertexLabel/.style={text=none} + }, + vertexPlain/.style = vertexPlain/#1, + vertexPlain/.default=labels +} +\tikzset{ + vertexNodeNormal/.style = {fill=#1, shape=circle, inner sep=0pt, minimum size=4pt, text=none}, + vertexNodeNormal/.default = blue, + vertexNormal/labels/.style = { + vertexNode/.style={vertexNodeNormal=##1}, + vertexLabel/.style={blue} + }, + vertexNormal/nolabels/.style = { + vertexNode/.style={vertexNodeNormal=##1}, + vertexLabel/.style={text=none} + }, + vertexNormal/.style = vertexNormal/#1, + vertexNormal/.default=labels +} +\tikzset{ + vertexNodeBallShading/pdf/.style = {ball color=#1}, + vertexNodeBallShading/svg/.style = {fill=#1}, + vertexNodeBallShading/.code = {% Conditional shading depending whether we want pdf or svg output + \if\texforht + \tikzset{vertexNodeBallShading/svg=#1!90!black} + \else + \tikzset{vertexNodeBallShading/pdf=#1} + \fi + }, + vertexNodeBall/.style = {shape=circle, vertexNodeBallShading=#1, inner sep=2pt, outer sep=0pt, minimum size=3pt, font=\tiny}, + vertexNodeBall/.default = white, + vertexBall/labels/.style = { + vertexNode/.style={vertexNodeBall=##1, text=black}, + vertexLabel/.style={text=none} + }, + vertexBall/nolabels/.style = { + vertexNode/.style={vertexNodeBall=##1, text=none}, + vertexLabel/.style={text=none} + }, + vertexBall/.style = vertexBall/#1, + vertexBall/.default=labels +} +\tikzset{ + vertexStyle/.style={vertexNormal=#1}, + vertexStyle/.default = labels +} + + +% 1) optional: colour of vertex +% 2) position of the vertex +% 3) relative position of the node +% 4) name of the vertex +\newcommand{\vertexLabelR}[4][]{ + \ifthenelse{ \equal{#1}{} } + { \node[vertexNode] (#2 name) at (#2) {#4}; } + { \node[vertexNode=#1] (#2 name) at (#2) {#4}; } + \node[vertexLabel, #3] at (#2) {#4}; +} +% 1) optional: colour of vertex +% 2) position of the vertex +% 3) absolute position of the node +% 4) name of the vertex +\newcommand{\vertexLabelA}[4][]{ + \ifthenelse{ \equal{#1}{} } + { \node[vertexNode] (#2 name) at (#2) {#4}; } + { \node[vertexNode=#1] (#2 name) at (#2) {#4}; } + \node[vertexLabel] at (#3) {#4}; +} + + +% Edge styles +% If you have trouble with the double-lines overlapping, this might (?) help: +% https://tex.stackexchange.com/questions/288159/closing-the-ends-of-double-line-in-tikz +\newcommand{\edgeLabelColor}{blue!20!white} +\tikzset{ + edgeLineNone/.style = {draw=none}, + edgeLineNone/.default=black, + edgeNone/labels/.style = { + edge/.style = {edgeLineNone=##1}, + edgeLabel/.style = {fill=\edgeLabelColor,font=\small} + }, + edgeNone/nolabels/.style = { + edge/.style = {edgeLineNone=##1}, + edgeLabel/.style = {text=none} + }, + edgeNone/.style = edgeNone/#1, + edgeNone/.default = labels +} +\tikzset{ + edgeLinePlain/.style={line join=round, draw=#1}, + edgeLinePlain/.default=black, + edgePlain/labels/.style = { + edge/.style={edgeLinePlain=##1}, + edgeLabel/.style={fill=\edgeLabelColor,font=\small} + }, + edgePlain/nolabels/.style = { + edge/.style={edgeLinePlain=##1}, + edgeLabel/.style={text=none} + }, + edgePlain/.style = edgePlain/#1, + edgePlain/.default = labels +} +\tikzset{ + edgeLineDouble/.style = {very thin, double=#1, double distance=.8pt, line join=round}, + edgeLineDouble/.default=gray!90!white, + edgeDouble/labels/.style = { + edge/.style = {edgeLineDouble=##1}, + edgeLabel/.style = {fill=\edgeLabelColor,font=\small} + }, + edgeDouble/nolabels/.style = { + edge/.style = {edgeLineDouble=##1}, + edgeLabel/.style = {text=none} + }, + edgeDouble/.style = edgeDouble/#1, + edgeDouble/.default = labels +} +\tikzset{ + edgeStyle/.style = {edgePlain=#1}, + edgeStyle/.default = labels +} + +% Face styles +% Here we have an exception - the style face is always defined. +% +\newcommand{\faceColorY}{yellow!60!white} % yellow +\newcommand{\faceColorB}{blue!60!white} % blue +\newcommand{\faceColorC}{cyan!60} % cyan +\newcommand{\faceColorR}{red!60!white} % red +\newcommand{\faceColorG}{green!60!white} % green +\newcommand{\faceColorO}{orange!50!yellow!70!white} % orange + +% define default face colour (and default swap colour) +\newcommand{\faceColor}{\faceColorY} +\newcommand{\faceColorSwap}{\faceColorC} + +% define secondary default colours (to use in a single section) +\newcommand{\faceColorFirst}{green!40!white} +\newcommand{\faceColorSecond}{gray!15!white} +\newcommand{\faceColorThird}{red!17!white} +\newcommand{\faceColorFourth}{olive!20!white} + +\tikzset{ + face/.style = {fill=#1}, + face/.default = \faceColor, + faceY/.style = {face=\faceColorY}, + faceB/.style = {face=\faceColorB}, + faceC/.style = {face=\faceColorC}, + faceR/.style = {face=\faceColorR}, + faceG/.style = {face=\faceColorG}, + faceO/.style = {face=\faceColorO} +} +\tikzset{ + faceStyle/labels/.style = { + faceLabel/.style = {} + }, + faceStyle/nolabels/.style = { + faceLabel/.style = {text=none} + }, + faceStyle/.style = faceStyle/#1, + faceStyle/.default = labels +} +\tikzset{ face/.style={fill=#1} } +\tikzset{ faceSwap/.code= + \ifdefined\swapColors + \tikzset{face=\faceColorSwap} + \else + \tikzset{face=\faceColor} + \fi +} + + + +\usepackage{hyperref} + + +\begin{document} + +\begin{tikzpicture}[vertexBall, edgeDouble=nolabels, faceStyle=nolabels, scale=4] + + \coordinate (V1) at (1. , 0.); + \coordinate (V2) at (0.5000000010362841 , 0.8660254031861397); + \coordinate (V3) at (-0.4999999979274318 , 0.8660254049810364); + \coordinate (V4) at (-1. , 3.589793029841612e-09); + \coordinate (V5) at (-0.5000000041451365 , -0.866025401391243); + \coordinate (V6) at (0.4999999948185802 , -0.8660254067759328); + \coordinate (V7) at (0.8333333326424773 , -5.982988363998724e-10); + \coordinate (V8) at (0.3888888898100303 , 0.7216878361878827); + \coordinate (V9) at (-0.4351851836499495 , 0.6976315766169703); + \coordinate (V10) at (-0.8225308646325142 , -0.02806563506918342); + \coordinate (V11) at (-0.3870884810657467 , -0.7263654412350147); + \coordinate (V12) at (0.4077074718085085 , -0.698411178156174); + \draw[edge] (V1) -- node[edgeLabel] {$1$} (V6); + \draw[edge] (V1) -- node[edgeLabel] {$2$} (V2); + \draw[edge] (V2) -- node[edgeLabel] {$3$} (V3); + \draw[edge] (V3) -- node[edgeLabel] {$4$} (V4); + \draw[edge] (V4) -- node[edgeLabel] {$5$} (V5); + \draw[edge] (V5) -- node[edgeLabel] {$6$} (V6); + \draw[edge] (V1) -- node[edgeLabel] {$7$} (V7); + \draw[edge] (V6) -- node[edgeLabel] {$8$} (V12); + \draw[edge] (V7) -- node[edgeLabel] {$9$} (V12); + \draw[edge] (V2) -- node[edgeLabel] {$10$} (V8); + \draw[edge] (V7) -- node[edgeLabel] {$11$} (V8); + \draw[edge] (V3) -- node[edgeLabel] {$12$} (V9); + \draw[edge] (V8) -- node[edgeLabel] {$13$} (V9); + \draw[edge] (V4) -- node[edgeLabel] {$14$} (V10); + \draw[edge] (V9) -- node[edgeLabel] {$15$} (V10); + \draw[edge] (V5) -- node[edgeLabel] {$16$} (V11); + \draw[edge] (V10) -- node[edgeLabel] {$17$} (V11); + \draw[edge] (V11) -- node[edgeLabel] {$18$} (V12); + % Draw the faces + \vertexLabelR{V1}{left}{$1$} + \vertexLabelR{V2}{left}{$2$} + \vertexLabelR{V3}{left}{$3$} + \vertexLabelR{V4}{left}{$4$} + \vertexLabelR{V5}{left}{$5$} + \vertexLabelR{V6}{left}{$6$} + \vertexLabelR{V7}{left}{$7$} + \vertexLabelR{V8}{left}{$8$} + \vertexLabelR{V9}{left}{$9$} + \vertexLabelR{V10}{left}{$10$} + \vertexLabelR{V11}{left}{$11$} + \vertexLabelR{V12}{left}{$12$} + \end{tikzpicture} + +\end{document} + + diff --git a/doc/tikz-files/_TIKZ_convex_facegraph_icosahedron_default_spread.tex b/doc/tikz-files/_TIKZ_convex_facegraph_icosahedron_default_spread.tex new file mode 100644 index 00000000..e527e1bc --- /dev/null +++ b/doc/tikz-files/_TIKZ_convex_facegraph_icosahedron_default_spread.tex @@ -0,0 +1,340 @@ +\documentclass{standalone} + +\pagestyle{empty} +% This document contains the TikZ-header for all our LaTeX-computations. +% It especially contains all global graphic parameters. + +\usepackage{amsmath, amssymb, amsfonts} % Standard Math-stuff + +\usepackage{ifthen} + +\usepackage{tikz} +\usetikzlibrary{calc} +\usetikzlibrary{positioning} +\usetikzlibrary{shapes} +\usetikzlibrary{patterns} + + +% Sometimes we want to implement different behaviour for the generated +% HTML-pictures (for example, shading is not supported in HTML). +% For that we define a macro to check whether we run the code with +% htlatex. The code comes from +% https://tex.stackexchange.com/questions/93852/what-is-the-correct-way-to-check-for-latex-pdflatex-and-html-in-the-same-latex +\makeatletter +\edef\texforht{TT\noexpand\fi + \@ifpackageloaded{tex4ht} + {\noexpand\iftrue} + {\noexpand\iffalse}} +\makeatother + + +% Define a text=none option for nodes that ignores the given text, from +% https://tex.stackexchange.com/questions/59354/no-text-none-in-tikz +\makeatletter +\newif\iftikz@node@phantom +\tikzset{ + phantom/.is if=tikz@node@phantom, + text/.code=% + \edef\tikz@temp{#1}% + \ifx\tikz@temp\tikz@nonetext + \tikz@node@phantomtrue + \else + \tikz@node@phantomfalse + \let\tikz@textcolor\tikz@temp + \fi +} +\usepackage{etoolbox} +\patchcmd\tikz@fig@continue{\tikz@node@transformations}{% + \iftikz@node@phantom + \setbox\pgfnodeparttextbox\hbox{} + \fi\tikz@node@transformations}{}{} +\makeatother + +% Find the angle of a given line (within TikZ) +\newcommand{\tikzAngleOfLine}{\tikz@AngleOfLine} +\def\tikz@AngleOfLine(#1)(#2)#3{% + \pgfmathanglebetweenpoints{% + \pgfpointanchor{#1}{center}}{% + \pgfpointanchor{#2}{center}} + \pgfmathsetmacro{#3}{\pgfmathresult}% +} + +% Now we define the global styles +% The global styles are defined nestedly. You have to give your tikzpicture +% the global options [vertexStyle, edgeStyle, faceStyle] to activate them. +% +% You can disable labels by using the option nolabels, i.e. +% vertexStyle=nolabels to deactivate vertex labels. +% +% If you want to have a specific style for your picture, you can also use +% this specific meta-style instead of the general style. For example if you +% want to use double edges in one single picture - no matter the style of +% the rest of the document - you can use edgeDouble instead of edgeStyle. +% +% To set the default style, modify the vertexStyle/.default entry. + +% Vertex styles +\tikzset{ + vertexNodePlain/.style = {fill=#1, shape=circle, inner sep=0pt, minimum size=2pt, text=none}, + vertexNodePlain/.default=gray, + vertexPlain/labels/.style = { + vertexNode/.style={vertexNodePlain=##1}, + vertexLabel/.style={gray} + }, + vertexPlain/nolabels/.style = { + vertexNode/.style={vertexNodePlain=##1}, + vertexLabel/.style={text=none} + }, + vertexPlain/.style = vertexPlain/#1, + vertexPlain/.default=labels +} +\tikzset{ + vertexNodeNormal/.style = {fill=#1, shape=circle, inner sep=0pt, minimum size=4pt, text=none}, + vertexNodeNormal/.default = blue, + vertexNormal/labels/.style = { + vertexNode/.style={vertexNodeNormal=##1}, + vertexLabel/.style={blue} + }, + vertexNormal/nolabels/.style = { + vertexNode/.style={vertexNodeNormal=##1}, + vertexLabel/.style={text=none} + }, + vertexNormal/.style = vertexNormal/#1, + vertexNormal/.default=labels +} +\tikzset{ + vertexNodeBallShading/pdf/.style = {ball color=#1}, + vertexNodeBallShading/svg/.style = {fill=#1}, + vertexNodeBallShading/.code = {% Conditional shading depending whether we want pdf or svg output + \if\texforht + \tikzset{vertexNodeBallShading/svg=#1!90!black} + \else + \tikzset{vertexNodeBallShading/pdf=#1} + \fi + }, + vertexNodeBall/.style = {shape=circle, vertexNodeBallShading=#1, inner sep=2pt, outer sep=0pt, minimum size=3pt, font=\tiny}, + vertexNodeBall/.default = white, + vertexBall/labels/.style = { + vertexNode/.style={vertexNodeBall=##1, text=black}, + vertexLabel/.style={text=none} + }, + vertexBall/nolabels/.style = { + vertexNode/.style={vertexNodeBall=##1, text=none}, + vertexLabel/.style={text=none} + }, + vertexBall/.style = vertexBall/#1, + vertexBall/.default=labels +} +\tikzset{ + vertexStyle/.style={vertexNormal=#1}, + vertexStyle/.default = labels +} + + +% 1) optional: colour of vertex +% 2) position of the vertex +% 3) relative position of the node +% 4) name of the vertex +\newcommand{\vertexLabelR}[4][]{ + \ifthenelse{ \equal{#1}{} } + { \node[vertexNode] (#2 name) at (#2) {#4}; } + { \node[vertexNode=#1] (#2 name) at (#2) {#4}; } + \node[vertexLabel, #3] at (#2) {#4}; +} +% 1) optional: colour of vertex +% 2) position of the vertex +% 3) absolute position of the node +% 4) name of the vertex +\newcommand{\vertexLabelA}[4][]{ + \ifthenelse{ \equal{#1}{} } + { \node[vertexNode] (#2 name) at (#2) {#4}; } + { \node[vertexNode=#1] (#2 name) at (#2) {#4}; } + \node[vertexLabel] at (#3) {#4}; +} + + +% Edge styles +% If you have trouble with the double-lines overlapping, this might (?) help: +% https://tex.stackexchange.com/questions/288159/closing-the-ends-of-double-line-in-tikz +\newcommand{\edgeLabelColor}{blue!20!white} +\tikzset{ + edgeLineNone/.style = {draw=none}, + edgeLineNone/.default=black, + edgeNone/labels/.style = { + edge/.style = {edgeLineNone=##1}, + edgeLabel/.style = {fill=\edgeLabelColor,font=\small} + }, + edgeNone/nolabels/.style = { + edge/.style = {edgeLineNone=##1}, + edgeLabel/.style = {text=none} + }, + edgeNone/.style = edgeNone/#1, + edgeNone/.default = labels +} +\tikzset{ + edgeLinePlain/.style={line join=round, draw=#1}, + edgeLinePlain/.default=black, + edgePlain/labels/.style = { + edge/.style={edgeLinePlain=##1}, + edgeLabel/.style={fill=\edgeLabelColor,font=\small} + }, + edgePlain/nolabels/.style = { + edge/.style={edgeLinePlain=##1}, + edgeLabel/.style={text=none} + }, + edgePlain/.style = edgePlain/#1, + edgePlain/.default = labels +} +\tikzset{ + edgeLineDouble/.style = {very thin, double=#1, double distance=.8pt, line join=round}, + edgeLineDouble/.default=gray!90!white, + edgeDouble/labels/.style = { + edge/.style = {edgeLineDouble=##1}, + edgeLabel/.style = {fill=\edgeLabelColor,font=\small} + }, + edgeDouble/nolabels/.style = { + edge/.style = {edgeLineDouble=##1}, + edgeLabel/.style = {text=none} + }, + edgeDouble/.style = edgeDouble/#1, + edgeDouble/.default = labels +} +\tikzset{ + edgeStyle/.style = {edgePlain=#1}, + edgeStyle/.default = labels +} + +% Face styles +% Here we have an exception - the style face is always defined. +% +\newcommand{\faceColorY}{yellow!60!white} % yellow +\newcommand{\faceColorB}{blue!60!white} % blue +\newcommand{\faceColorC}{cyan!60} % cyan +\newcommand{\faceColorR}{red!60!white} % red +\newcommand{\faceColorG}{green!60!white} % green +\newcommand{\faceColorO}{orange!50!yellow!70!white} % orange + +% define default face colour (and default swap colour) +\newcommand{\faceColor}{\faceColorY} +\newcommand{\faceColorSwap}{\faceColorC} + +% define secondary default colours (to use in a single section) +\newcommand{\faceColorFirst}{green!40!white} +\newcommand{\faceColorSecond}{gray!15!white} +\newcommand{\faceColorThird}{red!17!white} +\newcommand{\faceColorFourth}{olive!20!white} + +\tikzset{ + face/.style = {fill=#1}, + face/.default = \faceColor, + faceY/.style = {face=\faceColorY}, + faceB/.style = {face=\faceColorB}, + faceC/.style = {face=\faceColorC}, + faceR/.style = {face=\faceColorR}, + faceG/.style = {face=\faceColorG}, + faceO/.style = {face=\faceColorO} +} +\tikzset{ + faceStyle/labels/.style = { + faceLabel/.style = {} + }, + faceStyle/nolabels/.style = { + faceLabel/.style = {text=none} + }, + faceStyle/.style = faceStyle/#1, + faceStyle/.default = labels +} +\tikzset{ face/.style={fill=#1} } +\tikzset{ faceSwap/.code= + \ifdefined\swapColors + \tikzset{face=\faceColorSwap} + \else + \tikzset{face=\faceColor} + \fi +} + + + +\usepackage{hyperref} + + +\begin{document} + +\begin{tikzpicture}[vertexBall, edgeDouble=nolabels, faceStyle=nolabels, scale=4] + + \coordinate (V1) at (1. , 0.); + \coordinate (V2) at (0.3090169889123937 , -0.9510565180700449); + \coordinate (V3) at (-0.8090169969069803 , -0.5877852488074289); + \coordinate (V4) at (-0.8090169926869255 , 0.587785254615836); + \coordinate (V5) at (0.3090169957405858 , 0.9510565158514307); + \coordinate (V6) at (0.6545084961632449 , -5.546535453149204e-10); + \coordinate (V7) at (0.2002100305571999 , -0.5895321377810976); + \coordinate (V8) at (-0.4717023517592329 , -0.4560155144296473); + \coordinate (V9) at (-0.5777924021353646 , 0.3025649579663135); + \coordinate (V10) at (0.1158813737393728 , 0.6224745714410109); + \coordinate (V11) at (0.417989412602686 , -0.1600986570320857); + \coordinate (V12) at (-0.2867457540694981 , -0.3391323294699786); + \coordinate (V13) at (-0.4037883433167264 , 0.1450338487604777); + \coordinate (V14) at (0.01213378276305652 , 0.4310209935389311); + \coordinate (V15) at (0.3945647857088452 , 0.1765698733073889); + \coordinate (V16) at (0.2359494642111798 , -0.1206899425566903); + \coordinate (V17) at (-0.1546590631070234 , -0.1844779471328884); + \coordinate (V18) at (-0.2810942085002772 , 0.06104281296509385); + \coordinate (V19) at (-0.03005439329815793 , 0.2932358838093986); + \coordinate (V20) at (0.2593032045979817 , 0.1658676993992546); + \draw[edge] (V1) -- node[edgeLabel] {$1$} (V2); + \draw[edge] (V1) -- node[edgeLabel] {$2$} (V5); + \draw[edge] (V2) -- node[edgeLabel] {$3$} (V3); + \draw[edge] (V3) -- node[edgeLabel] {$4$} (V4); + \draw[edge] (V4) -- node[edgeLabel] {$5$} (V5); + \draw[edge] (V1) -- node[edgeLabel] {$6$} (V6); + \draw[edge] (V2) -- node[edgeLabel] {$7$} (V7); + \draw[edge] (V6) -- node[edgeLabel] {$8$} (V11); + \draw[edge] (V7) -- node[edgeLabel] {$9$} (V11); + \draw[edge] (V5) -- node[edgeLabel] {$10$} (V10); + \draw[edge] (V6) -- node[edgeLabel] {$11$} (V15); + \draw[edge] (V10) -- node[edgeLabel] {$12$} (V15); + \draw[edge] (V3) -- node[edgeLabel] {$13$} (V8); + \draw[edge] (V7) -- node[edgeLabel] {$14$} (V12); + \draw[edge] (V8) -- node[edgeLabel] {$15$} (V12); + \draw[edge] (V4) -- node[edgeLabel] {$16$} (V9); + \draw[edge] (V8) -- node[edgeLabel] {$17$} (V13); + \draw[edge] (V9) -- node[edgeLabel] {$18$} (V13); + \draw[edge] (V9) -- node[edgeLabel] {$19$} (V14); + \draw[edge] (V10) -- node[edgeLabel] {$20$} (V14); + \draw[edge] (V11) -- node[edgeLabel] {$21$} (V16); + \draw[edge] (V15) -- node[edgeLabel] {$22$} (V20); + \draw[edge] (V16) -- node[edgeLabel] {$23$} (V20); + \draw[edge] (V12) -- node[edgeLabel] {$24$} (V17); + \draw[edge] (V16) -- node[edgeLabel] {$25$} (V17); + \draw[edge] (V13) -- node[edgeLabel] {$26$} (V18); + \draw[edge] (V17) -- node[edgeLabel] {$27$} (V18); + \draw[edge] (V14) -- node[edgeLabel] {$28$} (V19); + \draw[edge] (V18) -- node[edgeLabel] {$29$} (V19); + \draw[edge] (V19) -- node[edgeLabel] {$30$} (V20); + % Draw the faces + \vertexLabelR{V1}{left}{$1$} + \vertexLabelR{V2}{left}{$2$} + \vertexLabelR{V3}{left}{$3$} + \vertexLabelR{V4}{left}{$4$} + \vertexLabelR{V5}{left}{$5$} + \vertexLabelR{V6}{left}{$6$} + \vertexLabelR{V7}{left}{$7$} + \vertexLabelR{V8}{left}{$8$} + \vertexLabelR{V9}{left}{$9$} + \vertexLabelR{V10}{left}{$10$} + \vertexLabelR{V11}{left}{$11$} + \vertexLabelR{V12}{left}{$12$} + \vertexLabelR{V13}{left}{$13$} + \vertexLabelR{V14}{left}{$14$} + \vertexLabelR{V15}{left}{$15$} + \vertexLabelR{V16}{left}{$16$} + \vertexLabelR{V17}{left}{$17$} + \vertexLabelR{V18}{left}{$18$} + \vertexLabelR{V19}{left}{$19$} + \vertexLabelR{V20}{left}{$20$} + \end{tikzpicture} + +\end{document} + + diff --git a/doc/tikz-files/_TIKZ_convex_facegraph_icosahedron_high_spread.tex b/doc/tikz-files/_TIKZ_convex_facegraph_icosahedron_high_spread.tex new file mode 100644 index 00000000..4783561d --- /dev/null +++ b/doc/tikz-files/_TIKZ_convex_facegraph_icosahedron_high_spread.tex @@ -0,0 +1,341 @@ +\documentclass{standalone} + +\pagestyle{empty} +% This document contains the TikZ-header for all our LaTeX-computations. +% It especially contains all global graphic parameters. + +\usepackage{amsmath, amssymb, amsfonts} % Standard Math-stuff + +\usepackage{ifthen} + +\usepackage{tikz} +\usetikzlibrary{calc} +\usetikzlibrary{positioning} +\usetikzlibrary{shapes} +\usetikzlibrary{patterns} + + +% Sometimes we want to implement different behaviour for the generated +% HTML-pictures (for example, shading is not supported in HTML). +% For that we define a macro to check whether we run the code with +% htlatex. The code comes from +% https://tex.stackexchange.com/questions/93852/what-is-the-correct-way-to-check-for-latex-pdflatex-and-html-in-the-same-latex +\makeatletter +\edef\texforht{TT\noexpand\fi + \@ifpackageloaded{tex4ht} + {\noexpand\iftrue} + {\noexpand\iffalse}} +\makeatother + + +% Define a text=none option for nodes that ignores the given text, from +% https://tex.stackexchange.com/questions/59354/no-text-none-in-tikz +\makeatletter +\newif\iftikz@node@phantom +\tikzset{ + phantom/.is if=tikz@node@phantom, + text/.code=% + \edef\tikz@temp{#1}% + \ifx\tikz@temp\tikz@nonetext + \tikz@node@phantomtrue + \else + \tikz@node@phantomfalse + \let\tikz@textcolor\tikz@temp + \fi +} +\usepackage{etoolbox} +\patchcmd\tikz@fig@continue{\tikz@node@transformations}{% + \iftikz@node@phantom + \setbox\pgfnodeparttextbox\hbox{} + \fi\tikz@node@transformations}{}{} +\makeatother + +% Find the angle of a given line (within TikZ) +\newcommand{\tikzAngleOfLine}{\tikz@AngleOfLine} +\def\tikz@AngleOfLine(#1)(#2)#3{% + \pgfmathanglebetweenpoints{% + \pgfpointanchor{#1}{center}}{% + \pgfpointanchor{#2}{center}} + \pgfmathsetmacro{#3}{\pgfmathresult}% +} + +% Now we define the global styles +% The global styles are defined nestedly. You have to give your tikzpicture +% the global options [vertexStyle, edgeStyle, faceStyle] to activate them. +% +% You can disable labels by using the option nolabels, i.e. +% vertexStyle=nolabels to deactivate vertex labels. +% +% If you want to have a specific style for your picture, you can also use +% this specific meta-style instead of the general style. For example if you +% want to use double edges in one single picture - no matter the style of +% the rest of the document - you can use edgeDouble instead of edgeStyle. +% +% To set the default style, modify the vertexStyle/.default entry. + +% Vertex styles +\tikzset{ + vertexNodePlain/.style = {fill=#1, shape=circle, inner sep=0pt, minimum size=2pt, text=none}, + vertexNodePlain/.default=gray, + vertexPlain/labels/.style = { + vertexNode/.style={vertexNodePlain=##1}, + vertexLabel/.style={gray} + }, + vertexPlain/nolabels/.style = { + vertexNode/.style={vertexNodePlain=##1}, + vertexLabel/.style={text=none} + }, + vertexPlain/.style = vertexPlain/#1, + vertexPlain/.default=labels +} +\tikzset{ + vertexNodeNormal/.style = {fill=#1, shape=circle, inner sep=0pt, minimum size=4pt, text=none}, + vertexNodeNormal/.default = blue, + vertexNormal/labels/.style = { + vertexNode/.style={vertexNodeNormal=##1}, + vertexLabel/.style={blue} + }, + vertexNormal/nolabels/.style = { + vertexNode/.style={vertexNodeNormal=##1}, + vertexLabel/.style={text=none} + }, + vertexNormal/.style = vertexNormal/#1, + vertexNormal/.default=labels +} +\tikzset{ + vertexNodeBallShading/pdf/.style = {ball color=#1}, + vertexNodeBallShading/svg/.style = {fill=#1}, + vertexNodeBallShading/.code = {% Conditional shading depending whether we want pdf or svg output + \if\texforht + \tikzset{vertexNodeBallShading/svg=#1!90!black} + \else + \tikzset{vertexNodeBallShading/pdf=#1} + \fi + }, + vertexNodeBall/.style = {shape=circle, vertexNodeBallShading=#1, inner sep=2pt, outer sep=0pt, minimum size=3pt, font=\tiny}, + vertexNodeBall/.default = white, + vertexBall/labels/.style = { + vertexNode/.style={vertexNodeBall=##1, text=black}, + vertexLabel/.style={text=none} + }, + vertexBall/nolabels/.style = { + vertexNode/.style={vertexNodeBall=##1, text=none}, + vertexLabel/.style={text=none} + }, + vertexBall/.style = vertexBall/#1, + vertexBall/.default=labels +} +\tikzset{ + vertexStyle/.style={vertexNormal=#1}, + vertexStyle/.default = labels +} + + +% 1) optional: colour of vertex +% 2) position of the vertex +% 3) relative position of the node +% 4) name of the vertex +\newcommand{\vertexLabelR}[4][]{ + \ifthenelse{ \equal{#1}{} } + { \node[vertexNode] (#2 name) at (#2) {#4}; } + { \node[vertexNode=#1] (#2 name) at (#2) {#4}; } + \node[vertexLabel, #3] at (#2) {#4}; +} +% 1) optional: colour of vertex +% 2) position of the vertex +% 3) absolute position of the node +% 4) name of the vertex +\newcommand{\vertexLabelA}[4][]{ + \ifthenelse{ \equal{#1}{} } + { \node[vertexNode] (#2 name) at (#2) {#4}; } + { \node[vertexNode=#1] (#2 name) at (#2) {#4}; } + \node[vertexLabel] at (#3) {#4}; +} + + +% Edge styles +% If you have trouble with the double-lines overlapping, this might (?) help: +% https://tex.stackexchange.com/questions/288159/closing-the-ends-of-double-line-in-tikz +\newcommand{\edgeLabelColor}{blue!20!white} +\tikzset{ + edgeLineNone/.style = {draw=none}, + edgeLineNone/.default=black, + edgeNone/labels/.style = { + edge/.style = {edgeLineNone=##1}, + edgeLabel/.style = {fill=\edgeLabelColor,font=\small} + }, + edgeNone/nolabels/.style = { + edge/.style = {edgeLineNone=##1}, + edgeLabel/.style = {text=none} + }, + edgeNone/.style = edgeNone/#1, + edgeNone/.default = labels +} +\tikzset{ + edgeLinePlain/.style={line join=round, draw=#1}, + edgeLinePlain/.default=black, + edgePlain/labels/.style = { + edge/.style={edgeLinePlain=##1}, + edgeLabel/.style={fill=\edgeLabelColor,font=\small} + }, + edgePlain/nolabels/.style = { + edge/.style={edgeLinePlain=##1}, + edgeLabel/.style={text=none} + }, + edgePlain/.style = edgePlain/#1, + edgePlain/.default = labels +} +\tikzset{ + edgeLineDouble/.style = {very thin, double=#1, double distance=.8pt, line join=round}, + edgeLineDouble/.default=gray!90!white, + edgeDouble/labels/.style = { + edge/.style = {edgeLineDouble=##1}, + edgeLabel/.style = {fill=\edgeLabelColor,font=\small} + }, + edgeDouble/nolabels/.style = { + edge/.style = {edgeLineDouble=##1}, + edgeLabel/.style = {text=none} + }, + edgeDouble/.style = edgeDouble/#1, + edgeDouble/.default = labels +} +\tikzset{ + edgeStyle/.style = {edgePlain=#1}, + edgeStyle/.default = labels +} + +% Face styles +% Here we have an exception - the style face is always defined. +% +\newcommand{\faceColorY}{yellow!60!white} % yellow +\newcommand{\faceColorB}{blue!60!white} % blue +\newcommand{\faceColorC}{cyan!60} % cyan +\newcommand{\faceColorR}{red!60!white} % red +\newcommand{\faceColorG}{green!60!white} % green +\newcommand{\faceColorO}{orange!50!yellow!70!white} % orange + +% define default face colour (and default swap colour) +\newcommand{\faceColor}{\faceColorY} +\newcommand{\faceColorSwap}{\faceColorC} + +% define secondary default colours (to use in a single section) +\newcommand{\faceColorFirst}{green!40!white} +\newcommand{\faceColorSecond}{gray!15!white} +\newcommand{\faceColorThird}{red!17!white} +\newcommand{\faceColorFourth}{olive!20!white} + +\tikzset{ + face/.style = {fill=#1}, + face/.default = \faceColor, + faceY/.style = {face=\faceColorY}, + faceB/.style = {face=\faceColorB}, + faceC/.style = {face=\faceColorC}, + faceR/.style = {face=\faceColorR}, + faceG/.style = {face=\faceColorG}, + faceO/.style = {face=\faceColorO} +} +\tikzset{ + faceStyle/labels/.style = { + faceLabel/.style = {} + }, + faceStyle/nolabels/.style = { + faceLabel/.style = {text=none} + }, + faceStyle/.style = faceStyle/#1, + faceStyle/.default = labels +} +\tikzset{ face/.style={fill=#1} } +\tikzset{ faceSwap/.code= + \ifdefined\swapColors + \tikzset{face=\faceColorSwap} + \else + \tikzset{face=\faceColor} + \fi +} + + + +\usepackage{hyperref} + + +\begin{document} + +\begin{tikzpicture}[vertexBall, edgeDouble=nolabels, faceStyle=nolabels, scale=4] + + \coordinate (V1) at (1. , 0.); + \coordinate (V2) at (0.3090169889123937 , -0.9510565180700449); + \coordinate (V3) at (-0.8090169969069803 , -0.5877852488074289); + \coordinate (V4) at (-0.8090169926869255 , 0.587785254615836); + \coordinate (V5) at (0.3090169957405858 , 0.9510565158514307); + \coordinate (V6) at (0.7927050976979469 , -3.327921271889523e-10); + \coordinate (V7) at (0.2424730992248824 , -0.7390375056311521); + \coordinate (V8) at (-0.6182970511232349 , -0.488652952881346); + \coordinate (V9) at (-0.6555846775013854 , 0.4363679932957395); + \coordinate (V10) at (0.2138651127700633 , 0.753907349238458); + \coordinate (V11) at (0.6257282990590397 , -0.1221815949309928); + \coordinate (V12) at (-0.4759335274339455 , -0.4043145436795418); + \coordinate (V13) at (-0.5299770435427567 , 0.3239876612138216); + \coordinate (V14) at (0.1445119225113219 , 0.6121867255933728); + \coordinate (V15) at (0.6209603013165698 , 0.1266425475472756); + \coordinate (V16) at (0.4597638254237214 , -0.1271779158715349); + \coordinate (V17) at (-0.3282846657626078 , -0.2658951127485535); + \coordinate (V18) at (-0.4273051358160279 , 0.2413450347190398); + \coordinate (V19) at (0.1004588251932902 , 0.5013390228086395); + \coordinate (V20) at (0.5253135731118553 , 0.1614011047413686); + \draw[edge] (V1) -- node[edgeLabel] {$1$} (V2); + \draw[edge] (V1) -- node[edgeLabel] {$2$} (V5); + \draw[edge] (V2) -- node[edgeLabel] {$3$} (V3); + \draw[edge] (V3) -- node[edgeLabel] {$4$} (V4); + \draw[edge] (V4) -- node[edgeLabel] {$5$} (V5); + \draw[edge] (V1) -- node[edgeLabel] {$6$} (V6); + \draw[edge] (V2) -- node[edgeLabel] {$7$} (V7); + \draw[edge] (V6) -- node[edgeLabel] {$8$} (V11); + \draw[edge] (V7) -- node[edgeLabel] {$9$} (V11); + \draw[edge] (V5) -- node[edgeLabel] {$10$} (V10); + \draw[edge] (V6) -- node[edgeLabel] {$11$} (V15); + \draw[edge] (V10) -- node[edgeLabel] {$12$} (V15); + \draw[edge] (V3) -- node[edgeLabel] {$13$} (V8); + \draw[edge] (V7) -- node[edgeLabel] {$14$} (V12); + \draw[edge] (V8) -- node[edgeLabel] {$15$} (V12); + \draw[edge] (V4) -- node[edgeLabel] {$16$} (V9); + \draw[edge] (V8) -- node[edgeLabel] {$17$} (V13); + \draw[edge] (V9) -- node[edgeLabel] {$18$} (V13); + \draw[edge] (V9) -- node[edgeLabel] {$19$} (V14); + \draw[edge] (V10) -- node[edgeLabel] {$20$} (V14); + \draw[edge] (V11) -- node[edgeLabel] {$21$} (V16); + \draw[edge] (V15) -- node[edgeLabel] {$22$} (V20); + \draw[edge] (V16) -- node[edgeLabel] {$23$} (V20); + \draw[edge] (V12) -- node[edgeLabel] {$24$} (V17); + \draw[edge] (V16) -- node[edgeLabel] {$25$} (V17); + \draw[edge] (V13) -- node[edgeLabel] {$26$} (V18); + \draw[edge] (V17) -- node[edgeLabel] {$27$} (V18); + \draw[edge] (V14) -- node[edgeLabel] {$28$} (V19); + \draw[edge] (V18) -- node[edgeLabel] {$29$} (V19); + \draw[edge] (V19) -- node[edgeLabel] {$30$} (V20); + % Draw the faces + \vertexLabelR{V1}{left}{$1$} + \vertexLabelR{V2}{left}{$2$} + \vertexLabelR{V3}{left}{$3$} + \vertexLabelR{V4}{left}{$4$} + \vertexLabelR{V5}{left}{$5$} + \vertexLabelR{V6}{left}{$6$} + \vertexLabelR{V7}{left}{$7$} + \vertexLabelR{V8}{left}{$8$} + \vertexLabelR{V9}{left}{$9$} + \vertexLabelR{V10}{left}{$10$} + \vertexLabelR{V11}{left}{$11$} + \vertexLabelR{V12}{left}{$12$} + \vertexLabelR{V13}{left}{$13$} + \vertexLabelR{V14}{left}{$14$} + \vertexLabelR{V15}{left}{$15$} + \vertexLabelR{V16}{left}{$16$} + \vertexLabelR{V17}{left}{$17$} + \vertexLabelR{V18}{left}{$18$} + \vertexLabelR{V19}{left}{$19$} + \vertexLabelR{V20}{left}{$20$} + \end{tikzpicture} + +\end{document} + + + diff --git a/doc/tikz-files/_TIKZ_convex_facegraph_icosahedron_low_spread.tex b/doc/tikz-files/_TIKZ_convex_facegraph_icosahedron_low_spread.tex new file mode 100644 index 00000000..15ae0fe6 --- /dev/null +++ b/doc/tikz-files/_TIKZ_convex_facegraph_icosahedron_low_spread.tex @@ -0,0 +1,341 @@ +\documentclass{standalone} + +\pagestyle{empty} +% This document contains the TikZ-header for all our LaTeX-computations. +% It especially contains all global graphic parameters. + +\usepackage{amsmath, amssymb, amsfonts} % Standard Math-stuff + +\usepackage{ifthen} + +\usepackage{tikz} +\usetikzlibrary{calc} +\usetikzlibrary{positioning} +\usetikzlibrary{shapes} +\usetikzlibrary{patterns} + + +% Sometimes we want to implement different behaviour for the generated +% HTML-pictures (for example, shading is not supported in HTML). +% For that we define a macro to check whether we run the code with +% htlatex. The code comes from +% https://tex.stackexchange.com/questions/93852/what-is-the-correct-way-to-check-for-latex-pdflatex-and-html-in-the-same-latex +\makeatletter +\edef\texforht{TT\noexpand\fi + \@ifpackageloaded{tex4ht} + {\noexpand\iftrue} + {\noexpand\iffalse}} +\makeatother + + +% Define a text=none option for nodes that ignores the given text, from +% https://tex.stackexchange.com/questions/59354/no-text-none-in-tikz +\makeatletter +\newif\iftikz@node@phantom +\tikzset{ + phantom/.is if=tikz@node@phantom, + text/.code=% + \edef\tikz@temp{#1}% + \ifx\tikz@temp\tikz@nonetext + \tikz@node@phantomtrue + \else + \tikz@node@phantomfalse + \let\tikz@textcolor\tikz@temp + \fi +} +\usepackage{etoolbox} +\patchcmd\tikz@fig@continue{\tikz@node@transformations}{% + \iftikz@node@phantom + \setbox\pgfnodeparttextbox\hbox{} + \fi\tikz@node@transformations}{}{} +\makeatother + +% Find the angle of a given line (within TikZ) +\newcommand{\tikzAngleOfLine}{\tikz@AngleOfLine} +\def\tikz@AngleOfLine(#1)(#2)#3{% + \pgfmathanglebetweenpoints{% + \pgfpointanchor{#1}{center}}{% + \pgfpointanchor{#2}{center}} + \pgfmathsetmacro{#3}{\pgfmathresult}% +} + +% Now we define the global styles +% The global styles are defined nestedly. You have to give your tikzpicture +% the global options [vertexStyle, edgeStyle, faceStyle] to activate them. +% +% You can disable labels by using the option nolabels, i.e. +% vertexStyle=nolabels to deactivate vertex labels. +% +% If you want to have a specific style for your picture, you can also use +% this specific meta-style instead of the general style. For example if you +% want to use double edges in one single picture - no matter the style of +% the rest of the document - you can use edgeDouble instead of edgeStyle. +% +% To set the default style, modify the vertexStyle/.default entry. + +% Vertex styles +\tikzset{ + vertexNodePlain/.style = {fill=#1, shape=circle, inner sep=0pt, minimum size=2pt, text=none}, + vertexNodePlain/.default=gray, + vertexPlain/labels/.style = { + vertexNode/.style={vertexNodePlain=##1}, + vertexLabel/.style={gray} + }, + vertexPlain/nolabels/.style = { + vertexNode/.style={vertexNodePlain=##1}, + vertexLabel/.style={text=none} + }, + vertexPlain/.style = vertexPlain/#1, + vertexPlain/.default=labels +} +\tikzset{ + vertexNodeNormal/.style = {fill=#1, shape=circle, inner sep=0pt, minimum size=4pt, text=none}, + vertexNodeNormal/.default = blue, + vertexNormal/labels/.style = { + vertexNode/.style={vertexNodeNormal=##1}, + vertexLabel/.style={blue} + }, + vertexNormal/nolabels/.style = { + vertexNode/.style={vertexNodeNormal=##1}, + vertexLabel/.style={text=none} + }, + vertexNormal/.style = vertexNormal/#1, + vertexNormal/.default=labels +} +\tikzset{ + vertexNodeBallShading/pdf/.style = {ball color=#1}, + vertexNodeBallShading/svg/.style = {fill=#1}, + vertexNodeBallShading/.code = {% Conditional shading depending whether we want pdf or svg output + \if\texforht + \tikzset{vertexNodeBallShading/svg=#1!90!black} + \else + \tikzset{vertexNodeBallShading/pdf=#1} + \fi + }, + vertexNodeBall/.style = {shape=circle, vertexNodeBallShading=#1, inner sep=2pt, outer sep=0pt, minimum size=3pt, font=\tiny}, + vertexNodeBall/.default = white, + vertexBall/labels/.style = { + vertexNode/.style={vertexNodeBall=##1, text=black}, + vertexLabel/.style={text=none} + }, + vertexBall/nolabels/.style = { + vertexNode/.style={vertexNodeBall=##1, text=none}, + vertexLabel/.style={text=none} + }, + vertexBall/.style = vertexBall/#1, + vertexBall/.default=labels +} +\tikzset{ + vertexStyle/.style={vertexNormal=#1}, + vertexStyle/.default = labels +} + + +% 1) optional: colour of vertex +% 2) position of the vertex +% 3) relative position of the node +% 4) name of the vertex +\newcommand{\vertexLabelR}[4][]{ + \ifthenelse{ \equal{#1}{} } + { \node[vertexNode] (#2 name) at (#2) {#4}; } + { \node[vertexNode=#1] (#2 name) at (#2) {#4}; } + \node[vertexLabel, #3] at (#2) {#4}; +} +% 1) optional: colour of vertex +% 2) position of the vertex +% 3) absolute position of the node +% 4) name of the vertex +\newcommand{\vertexLabelA}[4][]{ + \ifthenelse{ \equal{#1}{} } + { \node[vertexNode] (#2 name) at (#2) {#4}; } + { \node[vertexNode=#1] (#2 name) at (#2) {#4}; } + \node[vertexLabel] at (#3) {#4}; +} + + +% Edge styles +% If you have trouble with the double-lines overlapping, this might (?) help: +% https://tex.stackexchange.com/questions/288159/closing-the-ends-of-double-line-in-tikz +\newcommand{\edgeLabelColor}{blue!20!white} +\tikzset{ + edgeLineNone/.style = {draw=none}, + edgeLineNone/.default=black, + edgeNone/labels/.style = { + edge/.style = {edgeLineNone=##1}, + edgeLabel/.style = {fill=\edgeLabelColor,font=\small} + }, + edgeNone/nolabels/.style = { + edge/.style = {edgeLineNone=##1}, + edgeLabel/.style = {text=none} + }, + edgeNone/.style = edgeNone/#1, + edgeNone/.default = labels +} +\tikzset{ + edgeLinePlain/.style={line join=round, draw=#1}, + edgeLinePlain/.default=black, + edgePlain/labels/.style = { + edge/.style={edgeLinePlain=##1}, + edgeLabel/.style={fill=\edgeLabelColor,font=\small} + }, + edgePlain/nolabels/.style = { + edge/.style={edgeLinePlain=##1}, + edgeLabel/.style={text=none} + }, + edgePlain/.style = edgePlain/#1, + edgePlain/.default = labels +} +\tikzset{ + edgeLineDouble/.style = {very thin, double=#1, double distance=.8pt, line join=round}, + edgeLineDouble/.default=gray!90!white, + edgeDouble/labels/.style = { + edge/.style = {edgeLineDouble=##1}, + edgeLabel/.style = {fill=\edgeLabelColor,font=\small} + }, + edgeDouble/nolabels/.style = { + edge/.style = {edgeLineDouble=##1}, + edgeLabel/.style = {text=none} + }, + edgeDouble/.style = edgeDouble/#1, + edgeDouble/.default = labels +} +\tikzset{ + edgeStyle/.style = {edgePlain=#1}, + edgeStyle/.default = labels +} + +% Face styles +% Here we have an exception - the style face is always defined. +% +\newcommand{\faceColorY}{yellow!60!white} % yellow +\newcommand{\faceColorB}{blue!60!white} % blue +\newcommand{\faceColorC}{cyan!60} % cyan +\newcommand{\faceColorR}{red!60!white} % red +\newcommand{\faceColorG}{green!60!white} % green +\newcommand{\faceColorO}{orange!50!yellow!70!white} % orange + +% define default face colour (and default swap colour) +\newcommand{\faceColor}{\faceColorY} +\newcommand{\faceColorSwap}{\faceColorC} + +% define secondary default colours (to use in a single section) +\newcommand{\faceColorFirst}{green!40!white} +\newcommand{\faceColorSecond}{gray!15!white} +\newcommand{\faceColorThird}{red!17!white} +\newcommand{\faceColorFourth}{olive!20!white} + +\tikzset{ + face/.style = {fill=#1}, + face/.default = \faceColor, + faceY/.style = {face=\faceColorY}, + faceB/.style = {face=\faceColorB}, + faceC/.style = {face=\faceColorC}, + faceR/.style = {face=\faceColorR}, + faceG/.style = {face=\faceColorG}, + faceO/.style = {face=\faceColorO} +} +\tikzset{ + faceStyle/labels/.style = { + faceLabel/.style = {} + }, + faceStyle/nolabels/.style = { + faceLabel/.style = {text=none} + }, + faceStyle/.style = faceStyle/#1, + faceStyle/.default = labels +} +\tikzset{ face/.style={fill=#1} } +\tikzset{ faceSwap/.code= + \ifdefined\swapColors + \tikzset{face=\faceColorSwap} + \else + \tikzset{face=\faceColor} + \fi +} + + + +\usepackage{hyperref} + + +\begin{document} + +\begin{tikzpicture}[vertexBall, edgeDouble=nolabels, faceStyle=nolabels, scale=4] + + \coordinate (V1) at (1. , 0.); + \coordinate (V2) at (0.3090169889123937 , -0.9510565180700449); + \coordinate (V3) at (-0.8090169969069803 , -0.5877852488074289); + \coordinate (V4) at (-0.8090169926869255 , 0.587785254615836); + \coordinate (V5) at (0.3090169957405858 , 0.9510565158514307); + \coordinate (V6) at (0.5163118946285428 , -7.765149634408886e-10); + \coordinate (V7) at (0.1614864032665868 , -0.4460855978160754); + \coordinate (V8) at (-0.3197938757917752 , -0.4593389774950907); + \coordinate (V9) at (-0.5292706366829111 , 0.1424753670618677); + \coordinate (V10) at (-0.009741685598258207 , 0.4910417935991915); + \coordinate (V11) at (0.2412985701850865 , -0.1664845467062768); + \coordinate (V12) at (-0.1497258880922867 , -0.3025990736622617); + \coordinate (V13) at (-0.3151656185658844 , -0.02476406050888025); + \coordinate (V14) at (-0.1270187743825422 , 0.2664627757024033); + \coordinate (V15) at (0.1747098689598691 , 0.1979538832885492); + \coordinate (V16) at (0.08113396435917979 , -0.08657118064268243); + \coordinate (V17) at (-0.08457670923818356 , -0.1467718202157678); + \coordinate (V18) at (-0.1944452295320299 , -0.07340624254900144); + \coordinate (V19) at (-0.1356899517998978 , 0.1140932896727264); + \coordinate (V20) at (0.03635327717978389 , 0.1223482232574671); + \draw[edge] (V1) -- node[edgeLabel] {$1$} (V2); + \draw[edge] (V1) -- node[edgeLabel] {$2$} (V5); + \draw[edge] (V2) -- node[edgeLabel] {$3$} (V3); + \draw[edge] (V3) -- node[edgeLabel] {$4$} (V4); + \draw[edge] (V4) -- node[edgeLabel] {$5$} (V5); + \draw[edge] (V1) -- node[edgeLabel] {$6$} (V6); + \draw[edge] (V2) -- node[edgeLabel] {$7$} (V7); + \draw[edge] (V6) -- node[edgeLabel] {$8$} (V11); + \draw[edge] (V7) -- node[edgeLabel] {$9$} (V11); + \draw[edge] (V5) -- node[edgeLabel] {$10$} (V10); + \draw[edge] (V6) -- node[edgeLabel] {$11$} (V15); + \draw[edge] (V10) -- node[edgeLabel] {$12$} (V15); + \draw[edge] (V3) -- node[edgeLabel] {$13$} (V8); + \draw[edge] (V7) -- node[edgeLabel] {$14$} (V12); + \draw[edge] (V8) -- node[edgeLabel] {$15$} (V12); + \draw[edge] (V4) -- node[edgeLabel] {$16$} (V9); + \draw[edge] (V8) -- node[edgeLabel] {$17$} (V13); + \draw[edge] (V9) -- node[edgeLabel] {$18$} (V13); + \draw[edge] (V9) -- node[edgeLabel] {$19$} (V14); + \draw[edge] (V10) -- node[edgeLabel] {$20$} (V14); + \draw[edge] (V11) -- node[edgeLabel] {$21$} (V16); + \draw[edge] (V15) -- node[edgeLabel] {$22$} (V20); + \draw[edge] (V16) -- node[edgeLabel] {$23$} (V20); + \draw[edge] (V12) -- node[edgeLabel] {$24$} (V17); + \draw[edge] (V16) -- node[edgeLabel] {$25$} (V17); + \draw[edge] (V13) -- node[edgeLabel] {$26$} (V18); + \draw[edge] (V17) -- node[edgeLabel] {$27$} (V18); + \draw[edge] (V14) -- node[edgeLabel] {$28$} (V19); + \draw[edge] (V18) -- node[edgeLabel] {$29$} (V19); + \draw[edge] (V19) -- node[edgeLabel] {$30$} (V20); + % Draw the faces + \vertexLabelR{V1}{left}{$1$} + \vertexLabelR{V2}{left}{$2$} + \vertexLabelR{V3}{left}{$3$} + \vertexLabelR{V4}{left}{$4$} + \vertexLabelR{V5}{left}{$5$} + \vertexLabelR{V6}{left}{$6$} + \vertexLabelR{V7}{left}{$7$} + \vertexLabelR{V8}{left}{$8$} + \vertexLabelR{V9}{left}{$9$} + \vertexLabelR{V10}{left}{$10$} + \vertexLabelR{V11}{left}{$11$} + \vertexLabelR{V12}{left}{$12$} + \vertexLabelR{V13}{left}{$13$} + \vertexLabelR{V14}{left}{$14$} + \vertexLabelR{V15}{left}{$15$} + \vertexLabelR{V16}{left}{$16$} + \vertexLabelR{V17}{left}{$17$} + \vertexLabelR{V18}{left}{$18$} + \vertexLabelR{V19}{left}{$19$} + \vertexLabelR{V20}{left}{$20$} +\end{tikzpicture} + +\end{document} + + + diff --git a/gap/Morphisms/morphisms.gd b/gap/Morphisms/morphisms.gd index 8b01c12c..62f3f9e1 100644 --- a/gap/Morphisms/morphisms.gd +++ b/gap/Morphisms/morphisms.gd @@ -435,11 +435,17 @@ DeclareAttribute( "InversePolygonalMorphism", IsPolygonalMorphism and IsBijectiv #! becomes a bijection onto another butterfly. In other words, every butterfly of #! surf1 is being preserved and does not degenerate in surf2. #! As an example, consider the 3-half-umbrella and 6-umbrella. -#! -#! \begin{tikzpicture}[vertexStyle, edgeStyle, faceStyle] -#! \input{Image_Butterfly_Faithful_Monomorphism_Hexagon.tex} -#! \end{tikzpicture} -#! +#! +#! <br><img src="./images/Image_Butterfly_Faithful_Monomorphism_Hexagon.svg"> </img> <br> +#! +#! +#! \begin{center} +#! \includegraphics{images/Image_Butterfly_Faithful_Monomorphism_Hexagon.pdf} +#! \end{center} +#! +#! +#! Image omitted in terminal text +#! #! @ExampleSession #! gap> six := SimplicialSurfaceByDownwardIncidence( #! > [[1,2],[2,3],[3,4],[4,5],[5,6],[6,1],,[1,8],[2,8],[3,8],[4,8],[5,8],[6,8]], @@ -476,11 +482,17 @@ DeclareOperation( "ButterflyFaithfulMonomorphismIntoSimplicialSurface", [IsSimpl #! butterfly-faithful monomorphisms, namely by aligning the 3-half umbrella with 3 #! consecutive faces of the 6-umbrella. There are 6 ways to do this and another 6 if #! we flip the 3-half-umbrella first. -#! -#! \begin{tikzpicture}[vertexStyle, edgeStyle, faceStyle] -#! \input{Image_Butterfly_Faithful_Monomorphism_Hexagon.tex} -#! \end{tikzpicture} -#! +#! +#! <br><img src="./images/Image_Butterfly_Faithful_Monomorphism_Hexagon.svg"> </img> <br> +#! +#! +#! \begin{center} +#! \includegraphics{images/Image_Butterfly_Faithful_Monomorphism_Hexagon.pdf} +#! \end{center} +#! +#! +#! Image omitted in terminal text +#! #! @ExampleSession #! gap> six := SimplicialSurfaceByDownwardIncidence( #! > [[1,2],[2,3],[3,4],[4,5],[5,6],[6,1],,[1,8],[2,8],[3,8],[4,8],[5,8],[6,8]], diff --git a/gap/PolygonalComplexes/drawing.gd b/gap/PolygonalComplexes/drawing.gd index 555dea13..aa864a77 100644 --- a/gap/PolygonalComplexes/drawing.gd +++ b/gap/PolygonalComplexes/drawing.gd @@ -1393,26 +1393,48 @@ icosahedron := SimplicialSurfaceByVerticesInFaces([ [ 1, 2, 3 ], DrawConvexFacegraphToTikz(icosahedron, "convex_facegraph_icosahedron_default_spread");; #! @EndLog -#! -#! \input{_TIKZ_convex_facegraph_icosahedron_default_spread.tex} +#! +#! <br><img src="./images/_TIKZ_convex_facegraph_icosahedron_default_spread.svg"> </img> <br> +#! +#! +#! \begin{center} +#! \includegraphics{images/_TIKZ_convex_facegraph_icosahedron_default_spread.pdf} +#! \end{center} +#! +#! +#! Image omitted in terminal text #! -#! #! @BeginLog pr := rec(spread := 0.3);; DrawConvexFacegraphToTikz(icosahedron, "convex_facegraph_icosahedron_low_spread", pr);; #! @EndLog -#! -#! \input{_TIKZ_convex_facegraph_icosahedron_low_spread.tex} +#! +#! <br><img src="./images/_TIKZ_convex_facegraph_icosahedron_low_spread.svg"> </img> <br> +#! +#! +#! \begin{center} +#! \includegraphics{images/_TIKZ_convex_facegraph_icosahedron_low_spread.pdf} +#! \end{center} +#! +#! +#! Image omitted in terminal text #! -#! #! @BeginLog pr := rec(spread := 0.7);; DrawConvexFacegraphToTikz(icosahedron, "convex_facegraph_icosahedron_high_spread", pr);; #! @EndLog -#! -#! \input{_TIKZ_convex_facegraph_icosahedron_high_spread.tex} +#! +#! <br><img src="./images/_TIKZ_convex_facegraph_icosahedron_high_spread.svg"> </img> <br> +#! +#! +#! \begin{center} +#! \includegraphics{images/_TIKZ_convex_facegraph_icosahedron_high_spread.pdf} +#! \end{center} +#! +#! +#! Image omitted in terminal text #! #! #! @@ -1506,14 +1528,30 @@ double6Gon := SimplicialSurfaceByVerticesInFaces([[1,2,3],[1,3,4],[1,4,5], [1,5,6],[1,6,7],[1,2,7],[2,3,8],[3,4,8],[4,5,8],[5,6,8],[6,7,8],[2,7,8]]);; #! @EndLog #! -#! -#! \input{Image_Double6gon.tex} +#! +#! <br><img src="./images/_Wrapper_Image_Double6gon.svg"> </img> <br> +#! +#! +#! \begin{center} +#! \includegraphics{images/_Wrapper_Image_Double6gon.pdf} +#! \end{center} +#! +#! +#! Image omitted in terminal text #! #! @BeginLog DrawConvexFacegraphToTikz( double6Gon, "convex_facegraph_Double6Gon.tex" );; #! @EndLog #! -#! -#! \input{Image_convex_facegraph_Double6Gon.tex} +#! +#! <br><img src="./images/Image_convex_facegraph_Double6Gon.svg"> </img> <br> +#! +#! +#! \begin{center} +#! \includegraphics{images/Image_convex_facegraph_Double6Gon.pdf} +#! \end{center} +#! +#! +#! 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- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - From 2c7a2821335300be8ef9e90215932d7961754d4d Mon Sep 17 00:00:00 2001 From: Flynn Fehre Date: Tue, 12 Mar 2024 11:27:52 +0100 Subject: [PATCH 18/44] fixing the documentation --- gap/PolygonalComplexes/drawing.gd | 2 + gap/PolygonalComplexes/embedding.gd | 66 +---------------------------- 2 files changed, 3 insertions(+), 65 deletions(-) diff --git a/gap/PolygonalComplexes/drawing.gd b/gap/PolygonalComplexes/drawing.gd index b1e2b3d3..662dae41 100644 --- a/gap/PolygonalComplexes/drawing.gd +++ b/gap/PolygonalComplexes/drawing.gd @@ -1345,6 +1345,8 @@ DrawFacegraphToTikz(tetra, #! Image omitted in terminal text #! #! +#! +#! @EndChunk #! @BeginChunk DrawFacegraphToTikz_Geodesics #! This subsection covers the usage of the parameter that adds geodesics into diff --git a/gap/PolygonalComplexes/embedding.gd b/gap/PolygonalComplexes/embedding.gd index 9c85cdc4..1fe18f8f 100644 --- a/gap/PolygonalComplexes/embedding.gd +++ b/gap/PolygonalComplexes/embedding.gd @@ -382,68 +382,4 @@ DeclareOperation( "DrawFacegraphToTikz", [IsSimplicialSurface ,IsString,IsRecord #! @Subsection Output control #! @SubsectionLabel DrawFacegraphToTikz_Output -#! @InsertChunk DrawFacegraphToTikz_Output -#! -#! @BeginGroup DrawConvexFacegraphToTikz -#! @Description -#! Draw the face graph of the given surface into a tex-file (using TikZ). -#! An introduction to the use of this method (along with several examples) -#! can be found at the start of section . -#! If surface is a simplicial vertex faithful sphere and the function -#! is used without the argument printRecord, then the drawing printed -#! into file is a planar embedding of the face graph of surface, -#! where the vertices of the surface are identified by the faces of the -#! embedding. DrawConvexFacegraphToTikz differs from DrawFacegraphToTikz -#! () by constructing the face graph -#! by successively manipulating a convex drawing plane and calculating new face coordinates. -#! The new coordinates are then drawn with DrawFacegraphToTikz. -#! This results in an embedding which maps the faces -#! of one of the largest umbrella paths on the outer ring as a -#! regular polygon. Trying to use the function for a surface that is not a -#! vertex-faithful sphere results in returning fail. -#! -#! * If the given file does not end in .tex the ending -#! .tex will be added to it. -#! * The given file will be overwritten without asking if it already exists. -#! If you don't have permission to write in that file, this method will -#! throw an error. -#! * The particulars of the drawing are determined by the -#! given printRecord. If this is not given and surface is a -#! simplicial sphere, the default settings are used. -#! * The printRecord will be modified and returned by this method. -#! It contains the data to recreate the drawing of the surface. -#! -#! -#! There are several parameters to change the output of this method. -#! Since the design of the parameters is the design of the parameters -#! of DrawFacegraphToTikz(), -#! one can also refer to the corresponding subsections for a better -#! understanding. -#! There are the following classes of parameters: -#! * Colours -#! (): Change the -#! colours of edges and faces represented as vertices. -#! * Labels -#! (): Modify the labels -#! of vertices, edges and faces. -#! * Scale -#! (): These -#! parameters control the size of the drawing. -#! * faceCoordinates2D -#! (): -#! Modify the 2D-coordinates of the faces. -#! * Geodesics -#! (): Draw the -#! geodesics of the simplicial surface into the file. -#! * Output control -#! (): Modify how the -#! &LaTeX;-output behaves and how much information is printed to the -#! console. -#! -#! Consider the following example of the double-6-gon: -#! @InsertChunk DrawConvexFacegraphToTikz_example -#! -#! @Returns a record -#! @Arguments surface, file[, printRecord] -DeclareOperation( "DrawConvexFacegraphToTikz", [IsSimplicialSurface, IsString, IsRecord]); -#! @EndGroup \ No newline at end of file +#! @InsertChunk DrawFacegraphToTikz_Output \ No newline at end of file From 2323da88a4b13af543b1c09182f4a9ebfc14b595 Mon Sep 17 00:00:00 2001 From: Flynn Fehre Date: Wed, 13 Mar 2024 17:19:42 +0100 Subject: [PATCH 19/44] deleted unnecessary comments and functions from ButterflyFaithfulMonomorphismsIntoSimplicialSurface --- gap/Morphisms/morphisms.gi | 126 ++++--------------------------------- 1 file changed, 12 insertions(+), 114 deletions(-) diff --git a/gap/Morphisms/morphisms.gi b/gap/Morphisms/morphisms.gi index e98c202f..65df50bf 100644 --- a/gap/Morphisms/morphisms.gi +++ b/gap/Morphisms/morphisms.gi @@ -483,9 +483,9 @@ InstallMethod( InverseGeneralMapping, "for a polygonal morphism", InstallMethod(ButterflyFaithfulMonomorphismIntoSimplicialSurface, "for two simplicial surfaces", [IsSimplicialSurface, IsSimplicialSurface], function(surface1, surface2) - local PermuteList, AllBijections, AllOneFaceIsomorphisms, MyImage, MyPreImage, MyImageCat, - MyPreImages, MyPreImagesCat, MyUpdateMap, SurfaceIdentityMap, RemoveElement, MyLess, - VertexDegreesOfFace, MyIsInjective, MonomorphismIntoSimplicialSurface; + local PermuteList, AllBijections, AllOneFaceIsomorphisms, MyPreImage, MyImageCat, + MyPreImages, MyPreImagesCat, MyUpdateMap, + MyIsInjective, MonomorphismIntoSimplicialSurface; PermuteList := function(list, perm) return List(list, x -> x^perm); end; @@ -507,15 +507,10 @@ InstallMethod(ButterflyFaithfulMonomorphismIntoSimplicialSurface, "for two simpl od; Add(res, tmp); od; - # res := List(AllPermutations, x -> IndexInducedMap(list1, x)); return res; fi; end; - MyImage := function(map, x) - return map[x]; - end; - MyImageCat := function(map, x_list) local res, i; res := []; @@ -551,18 +546,13 @@ InstallMethod(ButterflyFaithfulMonomorphismIntoSimplicialSurface, "for two simpl res := []; vertex_maps := AllBijections(VerticesOfFace(surface1, face1), VerticesOfFace(surface2, face2)); - # edge_map := []; for vertex_map in vertex_maps do edge_map := []; e := List([1,2,3], i -> Set(VerticesOfEdge(surface1, EdgesOfFace(surface1, face1)[i]))); mapped_e := List(e, e_i -> Set(List(e_i, v -> vertex_map[v]))); - # Error(); for i in [1..3] do for edge in EdgesOfFace(surface2, face2) do - # Error(); if Set(VerticesOfEdge(surface2, edge)) = Set(mapped_e[i]) then - # Error(); - # mapped_e[i] := edge; edge_map[EdgesOfFace(surface1, face1)[i]]:= edge; break; fi; @@ -586,26 +576,6 @@ InstallMethod(ButterflyFaithfulMonomorphismIntoSimplicialSurface, "for two simpl fi; end; - SurfaceIdentityMap := function(surface) - return [[1..NumberOfVertices(surface)], [1..NumberOfEdges(surface)], [1..NumberOfFaces(surface)]]; - end; - - RemoveElement := function(list, element) - if not element in list then - return fail; - else - Remove(list, Position(list, element)); - fi; - end; - - MyLess := function(fdeg1, fdeg2) - return fdeg1 < fdeg2; - end; - - VertexDegreesOfFace := function(surface, face) - return Set(List(VerticesOfFace(surface, face), v -> DegreeOfVertex(surface, v))); - end; - MyIsInjective := function(map) return IsDuplicateFree(Compacted(map)); end; @@ -622,12 +592,7 @@ InstallMethod(ButterflyFaithfulMonomorphismIntoSimplicialSurface, "for two simpl if not faces1 = [] then # inner vertex degrees heuristic face_counter1 := List(faces1, face -> Set(List(VerticesOfFace(surface1, face), v -> DegreeOfVertex(surface1, v)))); face_counter2 := List(faces1, face -> Set(List(VerticesOfFace(surface2, face), v -> DegreeOfVertex(surface2, v)))); - # face_counter1 := ListCounter(CounterOfFaces(surface1)); - # face_counter2 := ListCounter(CounterOfFaces(surface2)); - # face_degrees1 := List(face_counter1, fdegs1 -> Set(fdegs1[1])); - # face_degrees2 := List(face_counter2, fdegs2 -> Set(fdegs2[1])); if ForAny(face_counter2, fdegs2 -> not fdegs2 in face_counter1) then - # Error("heuristic"); return fail; else min_pos := PositionMinimum(List(Collected(face_counter2), fdeg2 -> fdeg2[2])); @@ -655,40 +620,30 @@ InstallMethod(ButterflyFaithfulMonomorphismIntoSimplicialSurface, "for two simpl mapped_faces := MyPreImages(face_map); while not IsEmpty(remaining_faces) do cur_edge := cur_edges[1]; - # Error("Mono"); # update face_map if Length(Difference(FacesOfEdge(surface2, edge_map[cur_edge]), face_map)) = 1 then - # Error("Mono"); new_image_face := Difference(FacesOfEdge(surface2, edge_map[cur_edge]), face_map)[1]; - else # QUESTION not sure if this case is correct - # Error("Mono"); + else is_correct_morphism := false; break; fi; new_face := Difference(FacesOfEdge(surface1, cur_edge), mapped_faces)[1]; if not new_face in remaining_faces then - # Error("Mono"); is_correct_morphism := false; break; fi; if MyUpdateMap(face_map, new_face, new_image_face) = false or MyIsInjective(face_map) = false then - # Error("Mono"); is_correct_morphism := false; break; fi; mapped_faces := MyPreImages(face_map); # update vertex_map - # new_vertex := Difference(VerticesOfFace(surface1, new_face), - # Intersection(List(FacesOfEdge(surface1, cur_edge), F -> VerticesOfFace(surface1, F))))[1]; # QUESTION requires vertex-faithful new_vertex := Difference(VerticesOfFace(surface1, new_face), VerticesOfEdge(surface1, cur_edge))[1]; - # new_image_vertex := Difference(VerticesOfFace(surface2, new_image_face), - # Intersection(List(FacesOfEdge(surface2, edge_map[cur_edge]), F -> VerticesOfFace(surface2, F))))[1]; # QUESTION requires vertex-faithful new_image_vertex := Difference(VerticesOfFace(surface2, new_image_face), VerticesOfEdge(surface2, edge_map[cur_edge]))[1]; if MyUpdateMap(vertex_map, new_vertex, new_image_vertex) = false or MyIsInjective(vertex_map) = false then - # Error("Mono"); is_correct_morphism := false; break; fi; @@ -698,16 +653,13 @@ InstallMethod(ButterflyFaithfulMonomorphismIntoSimplicialSurface, "for two simpl new_image_edges := Difference(EdgesOfFace(surface2, new_image_face), [edge_map[cur_edge]]); for cur_new_edge in new_edges do for cur_new_image_edge in new_image_edges do - # Error("MonoEdge"); - if Set(MyImageCat(vertex_map, VerticesOfEdge(surface1, cur_new_edge))) = Set(VerticesOfEdge(surface2, cur_new_image_edge)) then # QUESTION requires vertex-faithful + if Set(MyImageCat(vertex_map, VerticesOfEdge(surface1, cur_new_edge))) = Set(VerticesOfEdge(surface2, cur_new_image_edge)) then if MyUpdateMap(edge_map, cur_new_edge, cur_new_image_edge) = false or MyIsInjective(edge_map) = false then - # Error("Mono"); is_correct_morphism := false; fi; if cur_new_edge in cur_edges then Add(finished_cur_edges, cur_new_edge); fi; - # Error("MonoEdge"); fi; od; od; @@ -722,12 +674,10 @@ InstallMethod(ButterflyFaithfulMonomorphismIntoSimplicialSurface, "for two simpl # update remaining_faces remaining_faces := Difference(remaining_faces, [new_face]); - # Error("Mono"); od; if is_correct_morphism = true then - # return monomorphism; # uncomment for the lists that make the homomorphism FLAG(LISTS) - return PolygonalMorphismByLists(surface1, surface2, monomorphism[1], monomorphism[2], monomorphism[3]); #FLAG(MORPHISMS) + return PolygonalMorphismByLists(surface1, surface2, monomorphism[1], monomorphism[2], monomorphism[3]); fi; od; od; @@ -740,9 +690,9 @@ InstallMethod(ButterflyFaithfulMonomorphismIntoSimplicialSurface, "for two simpl InstallMethod(AllButterflyFaithfulMonomorphismsIntoSimplicialSurface, "for two simplicial surfaces", [IsSimplicialSurface, IsSimplicialSurface], function(surface1, surface2) - local PermuteList, AllBijections, AllOneFaceIsomorphisms, MyImage, MyPreImage, MyImageCat, - MyPreImages, MyPreImagesCat, MyUpdateMap, SurfaceIdentityMap, RemoveElement, MyLess, - VertexDegreesOfFace, MyIsInjective, AllMonomorphismsIntoSimplicialSurface; + local PermuteList, AllBijections, AllOneFaceIsomorphisms, MyPreImage, MyImageCat, + MyPreImages, MyPreImagesCat, MyUpdateMap, + MyIsInjective, AllMonomorphismsIntoSimplicialSurface; PermuteList := function(list, perm) return List(list, x -> x^perm); end; @@ -764,15 +714,10 @@ InstallMethod(AllButterflyFaithfulMonomorphismsIntoSimplicialSurface, "for two s od; Add(res, tmp); od; - # res := List(AllPermutations, x -> IndexInducedMap(list1, x)); return res; fi; end; - MyImage := function(map, x) - return map[x]; - end; - MyImageCat := function(map, x_list) local res, i; res := []; @@ -808,18 +753,13 @@ InstallMethod(AllButterflyFaithfulMonomorphismsIntoSimplicialSurface, "for two s res := []; vertex_maps := AllBijections(VerticesOfFace(surface1, face1), VerticesOfFace(surface2, face2)); - # edge_map := []; for vertex_map in vertex_maps do edge_map := []; e := List([1,2,3], i -> Set(VerticesOfEdge(surface1, EdgesOfFace(surface1, face1)[i]))); mapped_e := List(e, e_i -> Set(List(e_i, v -> vertex_map[v]))); - # Error(); for i in [1..3] do for edge in EdgesOfFace(surface2, face2) do - # Error(); if Set(VerticesOfEdge(surface2, edge)) = Set(mapped_e[i]) then - # Error(); - # mapped_e[i] := edge; edge_map[EdgesOfFace(surface1, face1)[i]]:= edge; break; fi; @@ -843,26 +783,6 @@ InstallMethod(AllButterflyFaithfulMonomorphismsIntoSimplicialSurface, "for two s fi; end; - SurfaceIdentityMap := function(surface) - return [[1..NumberOfVertices(surface)], [1..NumberOfEdges(surface)], [1..NumberOfFaces(surface)]]; - end; - - RemoveElement := function(list, element) - if not element in list then - return fail; - else - Remove(list, Position(list, element)); - fi; - end; - - MyLess := function(fdeg1, fdeg2) - return fdeg1 < fdeg2; - end; - - VertexDegreesOfFace := function(surface, face) - return Set(List(VerticesOfFace(surface, face), v -> DegreeOfVertex(surface, v))); - end; - MyIsInjective := function(map) return IsDuplicateFree(Compacted(map)); end; @@ -881,12 +801,7 @@ InstallMethod(AllButterflyFaithfulMonomorphismsIntoSimplicialSurface, "for two s if not faces1 = [] then # inner vertex degrees heuristic face_counter1 := List(faces1, face -> Set(List(VerticesOfFace(surface1, face), v -> DegreeOfVertex(surface1, v)))); face_counter2 := List(faces1, face -> Set(List(VerticesOfFace(surface2, face), v -> DegreeOfVertex(surface2, v)))); - # face_counter1 := ListCounter(CounterOfFaces(surface1)); - # face_counter2 := ListCounter(CounterOfFaces(surface2)); - # face_degrees1 := List(face_counter1, fdegs1 -> Set(fdegs1[1])); - # face_degrees2 := List(face_counter2, fdegs2 -> Set(fdegs2[1])); if ForAny(face_counter2, fdegs2 -> not fdegs2 in face_counter1) then - # Error("heuristic"); return res; # empty list else min_pos := PositionMinimum(List(Collected(face_counter2), fdeg2 -> fdeg2[2])); @@ -914,40 +829,28 @@ InstallMethod(AllButterflyFaithfulMonomorphismsIntoSimplicialSurface, "for two s mapped_faces := MyPreImages(face_map); while not IsEmpty(remaining_faces) do cur_edge := cur_edges[1]; - # Error("Mono"); - # update face_map if Length(Difference(FacesOfEdge(surface2, edge_map[cur_edge]), face_map)) = 1 then - # Error("Mono"); new_image_face := Difference(FacesOfEdge(surface2, edge_map[cur_edge]), face_map)[1]; - else # QUESTION not sure if this case is correct - # Error("Mono"); + else is_correct_morphism := false; break; fi; new_face := Difference(FacesOfEdge(surface1, cur_edge), mapped_faces)[1]; if not new_face in remaining_faces then - # Error("Mono"); is_correct_morphism := false; break; fi; if MyUpdateMap(face_map, new_face, new_image_face) = false or MyIsInjective(face_map) = false then - # Error("Mono"); is_correct_morphism := false; break; fi; mapped_faces := MyPreImages(face_map); - # update vertex_map - # new_vertex := Difference(VerticesOfFace(surface1, new_face), - # Intersection(List(FacesOfEdge(surface1, cur_edge), F -> VerticesOfFace(surface1, F))))[1]; # QUESTION requires vertex-faithful new_vertex := Difference(VerticesOfFace(surface1, new_face), VerticesOfEdge(surface1, cur_edge))[1]; - # new_image_vertex := Difference(VerticesOfFace(surface2, new_image_face), - # Intersection(List(FacesOfEdge(surface2, edge_map[cur_edge]), F -> VerticesOfFace(surface2, F))))[1]; # QUESTION requires vertex-faithful new_image_vertex := Difference(VerticesOfFace(surface2, new_image_face), VerticesOfEdge(surface2, edge_map[cur_edge]))[1]; if MyUpdateMap(vertex_map, new_vertex, new_image_vertex) = false or MyIsInjective(vertex_map) = false then - # Error("Mono"); is_correct_morphism := false; break; fi; @@ -957,16 +860,13 @@ InstallMethod(AllButterflyFaithfulMonomorphismsIntoSimplicialSurface, "for two s new_image_edges := Difference(EdgesOfFace(surface2, new_image_face), [edge_map[cur_edge]]); for cur_new_edge in new_edges do for cur_new_image_edge in new_image_edges do - # Error("MonoEdge"); - if Set(MyImageCat(vertex_map, VerticesOfEdge(surface1, cur_new_edge))) = Set(VerticesOfEdge(surface2, cur_new_image_edge)) then # QUESTION requires vertex-faithful + if Set(MyImageCat(vertex_map, VerticesOfEdge(surface1, cur_new_edge))) = Set(VerticesOfEdge(surface2, cur_new_image_edge)) then if MyUpdateMap(edge_map, cur_new_edge, cur_new_image_edge) = false or MyIsInjective(edge_map) = false then - # Error("Mono"); is_correct_morphism := false; fi; if cur_new_edge in cur_edges then Add(finished_cur_edges, cur_new_edge); fi; - # Error("MonoEdge"); fi; od; od; @@ -981,12 +881,10 @@ InstallMethod(AllButterflyFaithfulMonomorphismsIntoSimplicialSurface, "for two s # update remaining_faces remaining_faces := Difference(remaining_faces, [new_face]); - # Error("Mono"); od; if is_correct_morphism = true then - # Add(res, monomorphism); # uncomment to add the list the monomorphism is made of FLAG(LISTS) - Add(res,PolygonalMorphismByLists(surface1, surface2, monomorphism[1], monomorphism[2], monomorphism[3])); # FLAG(MORPHISMS) + Add(res,PolygonalMorphismByLists(surface1, surface2, monomorphism[1], monomorphism[2], monomorphism[3])); fi; od; od; From 4f40180bc750e6af4a0fb4daaf4707f64c21a8b2 Mon Sep 17 00:00:00 2001 From: Max Horn Date: Sat, 23 Mar 2024 22:55:14 +0100 Subject: [PATCH 20/44] CI: test with GAP 4.13; test with mininimal set of packages loaded --- .github/workflows/CI.yml | 10 +++++++--- 1 file changed, 7 insertions(+), 3 deletions(-) diff --git a/.github/workflows/CI.yml b/.github/workflows/CI.yml index 5c6ffe49..2641e351 100644 --- a/.github/workflows/CI.yml +++ b/.github/workflows/CI.yml @@ -25,11 +25,12 @@ jobs: matrix: gap-branch: - master + - stable-4.13 - stable-4.12 - stable-4.11 steps: - - uses: actions/checkout@v3 + - uses: actions/checkout@v4 - uses: gap-actions/setup-gap@v2 with: GAP_PKGS_TO_BUILD: "io profiling AttributeScheduler grape datastructures orb digraphs NautyTracesInterface" @@ -38,6 +39,9 @@ jobs: - uses: gap-actions/build-pkg@v1 - uses: gap-actions/build-pkg-docs@v1 - uses: gap-actions/run-pkg-tests@v2 + - uses: gap-actions/run-pkg-tests@v2 + with: + only-needed: true - uses: gap-actions/process-coverage@v2 - uses: codecov/codecov-action@v3 @@ -49,7 +53,7 @@ jobs: steps: - run: sudo apt-get update - run: sudo apt-get install sed texlive-latex-base texlive-latex-recommended texlive-latex-extra texlive-extra-utils texlive-fonts-recommended texlive-fonts-extra tex4ht - - uses: actions/checkout@v3 + - uses: actions/checkout@v4 - uses: gap-actions/setup-gap@v2 with: GAP_PKGS_TO_BUILD: "io profiling AttributeScheduler grape datastructures orb digraphs NautyTracesInterface" @@ -60,7 +64,7 @@ jobs: with: use-latex: 'true' - name: 'Upload documentation' - uses: actions/upload-artifact@v3 + uses: actions/upload-artifact@v4 with: name: manual path: ./doc/manual.pdf From 68c1e13743e1602f537092bc6ffe4686a4e73aee Mon Sep 17 00:00:00 2001 From: Flynn Fehre Date: Fri, 29 Mar 2024 16:25:35 +0100 Subject: [PATCH 21/44] changed image names to _Wrapper_... and modularised help functions for ButterflyFaithfulMonomorphismIntoSimplicialSurface and AllButterflyFaithfulMonomorphismsIntoSimplicialSurface --- ...tterfly_Faithful_Monomorphism_Hexagon.pdf} | Bin ...tterfly_Faithful_Monomorphism_Hexagon.svg} | 0 gap/Morphisms/morphisms.gd | 8 +- gap/Morphisms/morphisms.gi | 677 ++++++++---------- 4 files changed, 299 insertions(+), 386 deletions(-) rename doc/images/{Image_Butterfly_Faithful_Monomorphism_Hexagon.pdf => _Wrapper_Butterfly_Faithful_Monomorphism_Hexagon.pdf} (100%) rename doc/images/{Image_Butterfly_Faithful_Monomorphism_Hexagon.svg => _Wrapper_Butterfly_Faithful_Monomorphism_Hexagon.svg} (100%) diff --git a/doc/images/Image_Butterfly_Faithful_Monomorphism_Hexagon.pdf b/doc/images/_Wrapper_Butterfly_Faithful_Monomorphism_Hexagon.pdf similarity index 100% rename from doc/images/Image_Butterfly_Faithful_Monomorphism_Hexagon.pdf rename to doc/images/_Wrapper_Butterfly_Faithful_Monomorphism_Hexagon.pdf diff --git a/doc/images/Image_Butterfly_Faithful_Monomorphism_Hexagon.svg b/doc/images/_Wrapper_Butterfly_Faithful_Monomorphism_Hexagon.svg similarity index 100% rename from doc/images/Image_Butterfly_Faithful_Monomorphism_Hexagon.svg rename to doc/images/_Wrapper_Butterfly_Faithful_Monomorphism_Hexagon.svg diff --git a/gap/Morphisms/morphisms.gd b/gap/Morphisms/morphisms.gd index 62f3f9e1..0294f658 100644 --- a/gap/Morphisms/morphisms.gd +++ b/gap/Morphisms/morphisms.gd @@ -436,11 +436,11 @@ DeclareAttribute( "InversePolygonalMorphism", IsPolygonalMorphism and IsBijectiv #! surf1 is being preserved and does not degenerate in surf2. #! As an example, consider the 3-half-umbrella and 6-umbrella. #! -#! <br><img src="./images/Image_Butterfly_Faithful_Monomorphism_Hexagon.svg"> </img> <br> +#! <br><img src="./images/_Wrapper_Butterfly_Faithful_Monomorphism_Hexagon.svg"> </img> <br> #! #! #! \begin{center} -#! \includegraphics{images/Image_Butterfly_Faithful_Monomorphism_Hexagon.pdf} +#! \includegraphics{images/_Wrapper_Butterfly_Faithful_Monomorphism_Hexagon.pdf} #! \end{center} #! #! @@ -483,11 +483,11 @@ DeclareOperation( "ButterflyFaithfulMonomorphismIntoSimplicialSurface", [IsSimpl #! consecutive faces of the 6-umbrella. There are 6 ways to do this and another 6 if #! we flip the 3-half-umbrella first. #! -#! <br><img src="./images/Image_Butterfly_Faithful_Monomorphism_Hexagon.svg"> </img> <br> +#! <br><img src="./images/_Wrapper_Butterfly_Faithful_Monomorphism_Hexagon.svg"> </img> <br> #! #! #! \begin{center} -#! \includegraphics{images/Image_Butterfly_Faithful_Monomorphism_Hexagon.pdf} +#! \includegraphics{images/_Wrapper_Butterfly_Faithful_Monomorphism_Hexagon.pdf} #! \end{center} #! #! diff --git a/gap/Morphisms/morphisms.gi b/gap/Morphisms/morphisms.gi index 65df50bf..2d88d3a5 100644 --- a/gap/Morphisms/morphisms.gi +++ b/gap/Morphisms/morphisms.gi @@ -480,417 +480,330 @@ InstallMethod( InverseGeneralMapping, "for a polygonal morphism", end ); -InstallMethod(ButterflyFaithfulMonomorphismIntoSimplicialSurface, "for two simplicial surfaces", - [IsSimplicialSurface, IsSimplicialSurface], - function(surface1, surface2) - local PermuteList, AllBijections, AllOneFaceIsomorphisms, MyPreImage, MyImageCat, - MyPreImages, MyPreImagesCat, MyUpdateMap, - MyIsInjective, MonomorphismIntoSimplicialSurface; - PermuteList := function(list, perm) - return List(list, x -> x^perm); - end; - - AllBijections := function(list1, list2) - local res, AllPermutations, i, bijection, g, tmp; - res := []; - if not (Length(list1) = Length(list2)) then - return []; - else - AllPermutations := []; - for g in SymmetricGroup(list2) do - Add(AllPermutations, PermuteList(list2, g)); - od; - for bijection in AllPermutations do - tmp := []; - for i in [1..Length(list1)] do - tmp[list1[i]] := bijection[i]; - od; - Add(res, tmp); - od; - return res; - fi; - end; - - MyImageCat := function(map, x_list) - local res, i; - res := []; - for i in x_list do - if IsBound(map[i]) then - Add(res, map[i]); - fi; - od; - return res; - end; - - MyPreImage := function(map, y) - local res, i; - res := []; - for i in [1..Length(map)] do - if IsBound(map[i]) and map[i] = y then - Add(res, i); - fi; +BindGlobal("__SIMPLICIAL_PermuteList", + function(list, perm) + return List(list, x -> x^perm); + end +); + +BindGlobal("__SIMPLICIAL_AllBijections", + function(list1, list2) + local res, AllPermutations, i, bijection, g, tmp; + res := []; + if not (Length(list1) = Length(list2)) then + return []; + else + AllPermutations := []; + for g in SymmetricGroup(list2) do + Add(AllPermutations, __SIMPLICIAL_PermuteList(list2, g)); od; - return res; - end; - - MyPreImagesCat := function(map, y_list) - return Concatenation(List(y_list, y -> MyPreImage(map, y))); - end; - - MyPreImages := function(map) - return MyPreImagesCat(map, Compacted(map)); - end; - - AllOneFaceIsomorphisms := function(face1, surface1, face2, surface2) - local res, e, vertex_maps, vertex_map, mapped_e, i, edge, edge_map, face_map; - res := []; - vertex_maps := AllBijections(VerticesOfFace(surface1, face1), - VerticesOfFace(surface2, face2)); - for vertex_map in vertex_maps do - edge_map := []; - e := List([1,2,3], i -> Set(VerticesOfEdge(surface1, EdgesOfFace(surface1, face1)[i]))); - mapped_e := List(e, e_i -> Set(List(e_i, v -> vertex_map[v]))); - for i in [1..3] do - for edge in EdgesOfFace(surface2, face2) do - if Set(VerticesOfEdge(surface2, edge)) = Set(mapped_e[i]) then - edge_map[EdgesOfFace(surface1, face1)[i]]:= edge; - break; - fi; - od; + for bijection in AllPermutations do + tmp := []; + for i in [1..Length(list1)] do + tmp[list1[i]] := bijection[i]; od; - face_map := []; - face_map[face1] := face2; - Add(res, [vertex_map, edge_map, face_map]); + Add(res, tmp); od; return res; - end; - - MyUpdateMap := function(map, element, image_of_element) # is used to update maps with new images, also updates when used in if-clauses ! - if not IsBound(map[element]) then - map[element] := image_of_element; - return true; - elif map[element] = image_of_element then - return true; - else - return false; - fi; - end; - - MyIsInjective := function(map) - return IsDuplicateFree(Compacted(map)); - end; - MonomorphismIntoSimplicialSurface := function(surface1, surface2) - local possible_vertex_maps, possible_monomorphisms, starting_face, image_starting_face, mapped_edges, mapped_faces, - remaining_faces, cur_edges, cur_edge, mapped_vertices, monomorphism, cur_face, face_map, edge_map, - vertex_map, i, new_face, new_image_face, is_correct_morphism, new_vertex, new_image_vertex, new_edges, new_image_edges, - cur_new_edge, cur_new_image_edge, finished_cur_edges, faces1, faces2, face_counter1, face_counter2, face_degrees1, face_degrees2, - min_degrees, min_pos, possible_image_faces; - - faces1 := Filtered(Faces(surface1), face -> ForAll(VerticesOfFace(surface1, face), v -> IsInnerVertex(surface1, v))); - faces2 := Filtered(Faces(surface2), face -> ForAll(VerticesOfFace(surface2, face), v -> IsInnerVertex(surface2, v))); - possible_image_faces := Faces(surface2); - if not faces1 = [] then # inner vertex degrees heuristic - face_counter1 := List(faces1, face -> Set(List(VerticesOfFace(surface1, face), v -> DegreeOfVertex(surface1, v)))); - face_counter2 := List(faces1, face -> Set(List(VerticesOfFace(surface2, face), v -> DegreeOfVertex(surface2, v)))); - if ForAny(face_counter2, fdegs2 -> not fdegs2 in face_counter1) then - return fail; - else - min_pos := PositionMinimum(List(Collected(face_counter2), fdeg2 -> fdeg2[2])); - min_degrees := Collected(face_counter2)[min_pos][1]; - starting_face := Filtered(faces1, face -> min_degrees = Set(List(VerticesOfFace(surface1, face), v -> DegreeOfVertex(surface1, v))))[1]; - possible_image_faces := Filtered(faces2, face -> min_degrees = Set(List(VerticesOfFace(surface2, face), v -> DegreeOfVertex(surface2, v)))); - fi; - else - starting_face := Faces(surface1)[1]; + fi; + end +); + +BindGlobal("__SIMPLICIAL_ImageCatFromListmap", + function(map, x_list) + local res, i; + res := []; + for i in x_list do + if IsBound(map[i]) then + Add(res, map[i]); fi; + od; + return res; + end +); - for image_starting_face in possible_image_faces do - possible_monomorphisms := AllOneFaceIsomorphisms(starting_face, surface1, - image_starting_face, surface2); - for i in [1..Length(possible_monomorphisms)] do - is_correct_morphism := true; - monomorphism := possible_monomorphisms[i]; - vertex_map := monomorphism[1]; - edge_map := monomorphism[2]; - face_map := monomorphism[3]; - - cur_edges := Filtered(EdgesOfFace(surface1, starting_face), e -> IsInnerEdge(surface1, e)); - finished_cur_edges := []; - remaining_faces := Difference(Faces(surface1), [starting_face]); - mapped_faces := MyPreImages(face_map); - while not IsEmpty(remaining_faces) do - cur_edge := cur_edges[1]; - # update face_map - if Length(Difference(FacesOfEdge(surface2, edge_map[cur_edge]), face_map)) = 1 then - new_image_face := Difference(FacesOfEdge(surface2, edge_map[cur_edge]), face_map)[1]; - else - is_correct_morphism := false; - break; - fi; - new_face := Difference(FacesOfEdge(surface1, cur_edge), mapped_faces)[1]; - - if not new_face in remaining_faces then - is_correct_morphism := false; - break; - fi; - - if MyUpdateMap(face_map, new_face, new_image_face) = false or MyIsInjective(face_map) = false then - is_correct_morphism := false; - break; - fi; - mapped_faces := MyPreImages(face_map); - - # update vertex_map - new_vertex := Difference(VerticesOfFace(surface1, new_face), VerticesOfEdge(surface1, cur_edge))[1]; - new_image_vertex := Difference(VerticesOfFace(surface2, new_image_face), VerticesOfEdge(surface2, edge_map[cur_edge]))[1]; - if MyUpdateMap(vertex_map, new_vertex, new_image_vertex) = false or MyIsInjective(vertex_map) = false then - is_correct_morphism := false; - break; - fi; - - # update edge_map - new_edges := Difference(EdgesOfFace(surface1, new_face), [cur_edge]); - new_image_edges := Difference(EdgesOfFace(surface2, new_image_face), [edge_map[cur_edge]]); - for cur_new_edge in new_edges do - for cur_new_image_edge in new_image_edges do - if Set(MyImageCat(vertex_map, VerticesOfEdge(surface1, cur_new_edge))) = Set(VerticesOfEdge(surface2, cur_new_image_edge)) then - if MyUpdateMap(edge_map, cur_new_edge, cur_new_image_edge) = false or MyIsInjective(edge_map) = false then - is_correct_morphism := false; - fi; - if cur_new_edge in cur_edges then - Add(finished_cur_edges, cur_new_edge); - fi; - fi; - od; - od; - if is_correct_morphism = false then - break; - fi; +BindGlobal("__SIMPLICIAL_PreImageFromListmap", + function(map, y) + local res, i; + res := []; + for i in [1..Length(map)] do + if IsBound(map[i]) and map[i] = y then + Add(res, i); + fi; + od; + return res; + end +); - # update cur_edges - cur_edges := Union(cur_edges, Filtered(EdgesOfFace(surface1, new_face), e -> IsInnerEdge(surface1, e))); - Add(finished_cur_edges, cur_edge); - cur_edges := Difference(cur_edges, finished_cur_edges); +BindGlobal("__SIMPLICIAL_PreImagesCatFromListmap", + function(map, y_list) + return Concatenation(List(y_list, y -> __SIMPLICIAL_PreImageFromListmap(map, y))); + end +); - # update remaining_faces - remaining_faces := Difference(remaining_faces, [new_face]); - od; +BindGlobal("__SIMPLICIAL_PreImagesFromListmap", + function(map) + return __SIMPLICIAL_PreImagesCatFromListmap(map, Compacted(map)); + end +); - if is_correct_morphism = true then - return PolygonalMorphismByLists(surface1, surface2, monomorphism[1], monomorphism[2], monomorphism[3]); +BindGlobal("__SIMPLICIAL_AllOneFaceIsomorphisms", + function(face1, surface1, face2, surface2) + local res, e, vertex_maps, vertex_map, mapped_e, i, edge, edge_map, face_map; + res := []; + vertex_maps := __SIMPLICIAL_AllBijections(VerticesOfFace(surface1, face1), + VerticesOfFace(surface2, face2)); + for vertex_map in vertex_maps do + edge_map := []; + e := List([1,2,3], i -> Set(VerticesOfEdge(surface1, EdgesOfFace(surface1, face1)[i]))); + mapped_e := List(e, e_i -> Set(List(e_i, v -> vertex_map[v]))); + for i in [1..3] do + for edge in EdgesOfFace(surface2, face2) do + if Set(VerticesOfEdge(surface2, edge)) = Set(mapped_e[i]) then + edge_map[EdgesOfFace(surface1, face1)[i]]:= edge; + break; fi; od; od; - return fail; - end; - return MonomorphismIntoSimplicialSurface(surface1, surface2); + face_map := []; + face_map[face1] := face2; + Add(res, [vertex_map, edge_map, face_map]); + od; + return res; end ); -InstallMethod(AllButterflyFaithfulMonomorphismsIntoSimplicialSurface, "for two simplicial surfaces", +BindGlobal("__SIMPLICIAL_UpdateListmap", + function(map, element, image_of_element) # is used to update maps with new images, also updates when used in if-clauses ! + if not IsBound(map[element]) then + map[element] := image_of_element; + return true; + elif map[element] = image_of_element then + return true; + else + return false; + fi; + end +); + +BindGlobal("__SIMPLICIAL_IsInjectiveListmap", + function(map) + return IsDuplicateFree(Compacted(map)); + end +); + +InstallMethod(ButterflyFaithfulMonomorphismIntoSimplicialSurface, "for two simplicial surfaces", [IsSimplicialSurface, IsSimplicialSurface], - function(surface1, surface2) - local PermuteList, AllBijections, AllOneFaceIsomorphisms, MyPreImage, MyImageCat, - MyPreImages, MyPreImagesCat, MyUpdateMap, - MyIsInjective, AllMonomorphismsIntoSimplicialSurface; - PermuteList := function(list, perm) - return List(list, x -> x^perm); - end; - - AllBijections := function(list1, list2) - local res, AllPermutations, i, bijection, g, tmp; - res := []; - if not (Length(list1) = Length(list2)) then - return []; - else - AllPermutations := []; - for g in SymmetricGroup(list2) do - Add(AllPermutations, PermuteList(list2, g)); - od; - for bijection in AllPermutations do - tmp := []; - for i in [1..Length(list1)] do - tmp[list1[i]] := bijection[i]; - od; - Add(res, tmp); - od; - return res; + function(surface1, surface2) + local possible_vertex_maps, possible_monomorphisms, starting_face, image_starting_face, mapped_edges, mapped_faces, + remaining_faces, cur_edges, cur_edge, mapped_vertices, monomorphism, cur_face, face_map, edge_map, + vertex_map, i, new_face, new_image_face, is_correct_morphism, new_vertex, new_image_vertex, new_edges, new_image_edges, + cur_new_edge, cur_new_image_edge, finished_cur_edges, faces1, faces2, face_counter1, face_counter2, face_degrees1, face_degrees2, + min_degrees, min_pos, possible_image_faces; + + faces1 := Filtered(Faces(surface1), face -> ForAll(VerticesOfFace(surface1, face), v -> IsInnerVertex(surface1, v))); + faces2 := Filtered(Faces(surface2), face -> ForAll(VerticesOfFace(surface2, face), v -> IsInnerVertex(surface2, v))); + possible_image_faces := Faces(surface2); + if not faces1 = [] then # inner vertex degrees heuristic + face_counter1 := List(faces1, face -> Set(List(VerticesOfFace(surface1, face), v -> DegreeOfVertex(surface1, v)))); + face_counter2 := List(faces1, face -> Set(List(VerticesOfFace(surface2, face), v -> DegreeOfVertex(surface2, v)))); + if ForAny(face_counter2, fdegs2 -> not fdegs2 in face_counter1) then + return fail; + else + min_pos := PositionMinimum(List(Collected(face_counter2), fdeg2 -> fdeg2[2])); + min_degrees := Collected(face_counter2)[min_pos][1]; + starting_face := Filtered(faces1, face -> min_degrees = Set(List(VerticesOfFace(surface1, face), v -> DegreeOfVertex(surface1, v))))[1]; + possible_image_faces := Filtered(faces2, face -> min_degrees = Set(List(VerticesOfFace(surface2, face), v -> DegreeOfVertex(surface2, v)))); fi; - end; - - MyImageCat := function(map, x_list) - local res, i; - res := []; - for i in x_list do - if IsBound(map[i]) then - Add(res, map[i]); - fi; - od; - return res; - end; - - MyPreImage := function(map, y) - local res, i; - res := []; - for i in [1..Length(map)] do - if IsBound(map[i]) and map[i] = y then - Add(res, i); - fi; - od; - return res; - end; - - MyPreImagesCat := function(map, y_list) - return Concatenation(List(y_list, y -> MyPreImage(map, y))); - end; - - MyPreImages := function(map) - return MyPreImagesCat(map, Compacted(map)); - end; - - AllOneFaceIsomorphisms := function(face1, surface1, face2, surface2) - local res, e, vertex_maps, vertex_map, mapped_e, i, edge, edge_map, face_map; - res := []; - vertex_maps := AllBijections(VerticesOfFace(surface1, face1), - VerticesOfFace(surface2, face2)); - for vertex_map in vertex_maps do - edge_map := []; - e := List([1,2,3], i -> Set(VerticesOfEdge(surface1, EdgesOfFace(surface1, face1)[i]))); - mapped_e := List(e, e_i -> Set(List(e_i, v -> vertex_map[v]))); - for i in [1..3] do - for edge in EdgesOfFace(surface2, face2) do - if Set(VerticesOfEdge(surface2, edge)) = Set(mapped_e[i]) then - edge_map[EdgesOfFace(surface1, face1)[i]]:= edge; - break; - fi; + else + starting_face := Faces(surface1)[1]; + fi; + + for image_starting_face in possible_image_faces do + possible_monomorphisms := __SIMPLICIAL_AllOneFaceIsomorphisms(starting_face, surface1, + image_starting_face, surface2); + for i in [1..Length(possible_monomorphisms)] do + is_correct_morphism := true; + monomorphism := possible_monomorphisms[i]; + vertex_map := monomorphism[1]; + edge_map := monomorphism[2]; + face_map := monomorphism[3]; + + cur_edges := Filtered(EdgesOfFace(surface1, starting_face), e -> IsInnerEdge(surface1, e)); + finished_cur_edges := []; + remaining_faces := Difference(Faces(surface1), [starting_face]); + mapped_faces := __SIMPLICIAL_PreImagesFromListmap(face_map); + while not IsEmpty(remaining_faces) do + cur_edge := cur_edges[1]; + # update face_map + if Length(Difference(FacesOfEdge(surface2, edge_map[cur_edge]), face_map)) = 1 then + new_image_face := Difference(FacesOfEdge(surface2, edge_map[cur_edge]), face_map)[1]; + else + is_correct_morphism := false; + break; + fi; + new_face := Difference(FacesOfEdge(surface1, cur_edge), mapped_faces)[1]; + + if not new_face in remaining_faces then + is_correct_morphism := false; + break; + fi; + + if __SIMPLICIAL_UpdateListmap(face_map, new_face, new_image_face) = false or __SIMPLICIAL_IsInjectiveListmap(face_map) = false then + is_correct_morphism := false; + break; + fi; + mapped_faces := __SIMPLICIAL_PreImagesFromListmap(face_map); + + # update vertex_map + new_vertex := Difference(VerticesOfFace(surface1, new_face), VerticesOfEdge(surface1, cur_edge))[1]; + new_image_vertex := Difference(VerticesOfFace(surface2, new_image_face), VerticesOfEdge(surface2, edge_map[cur_edge]))[1]; + if __SIMPLICIAL_UpdateListmap(vertex_map, new_vertex, new_image_vertex) = false or __SIMPLICIAL_IsInjectiveListmap(vertex_map) = false then + is_correct_morphism := false; + break; + fi; + + # update edge_map + new_edges := Difference(EdgesOfFace(surface1, new_face), [cur_edge]); + new_image_edges := Difference(EdgesOfFace(surface2, new_image_face), [edge_map[cur_edge]]); + for cur_new_edge in new_edges do + for cur_new_image_edge in new_image_edges do + if Set(__SIMPLICIAL_ImageCatFromListmap(vertex_map, VerticesOfEdge(surface1, cur_new_edge))) = Set(VerticesOfEdge(surface2, cur_new_image_edge)) then + if __SIMPLICIAL_UpdateListmap(edge_map, cur_new_edge, cur_new_image_edge) = false or __SIMPLICIAL_IsInjectiveListmap(edge_map) = false then + is_correct_morphism := false; + fi; + if cur_new_edge in cur_edges then + Add(finished_cur_edges, cur_new_edge); + fi; + fi; + od; od; + if is_correct_morphism = false then + break; + fi; + + # update cur_edges + cur_edges := Union(cur_edges, Filtered(EdgesOfFace(surface1, new_face), e -> IsInnerEdge(surface1, e))); + Add(finished_cur_edges, cur_edge); + cur_edges := Difference(cur_edges, finished_cur_edges); + + # update remaining_faces + remaining_faces := Difference(remaining_faces, [new_face]); od; - face_map := []; - face_map[face1] := face2; - Add(res, [vertex_map, edge_map, face_map]); - od; - return res; - end; - - MyUpdateMap := function(map, element, image_of_element) # is used to update maps with new images, also updates when used in if-clauses ! - if not IsBound(map[element]) then - map[element] := image_of_element; - return true; - elif map[element] = image_of_element then - return true; - else - return false; - fi; - end; - MyIsInjective := function(map) - return IsDuplicateFree(Compacted(map)); - end; - - AllMonomorphismsIntoSimplicialSurface := function(surface1, surface2) - local possible_vertex_maps, possible_monomorphisms, starting_face, image_starting_face, mapped_edges, mapped_faces, - remaining_faces, cur_edges, cur_edge, mapped_vertices, monomorphism, cur_face, face_map, edge_map, - vertex_map, i, new_face, new_image_face, is_correct_morphism, new_vertex, new_image_vertex, new_edges, new_image_edges, - cur_new_edge, cur_new_image_edge, finished_cur_edges, faces1, faces2, face_counter1, face_counter2, face_degrees1, face_degrees2, - min_degrees, min_pos, possible_image_faces, res; - - res := []; - faces1 := Filtered(Faces(surface1), face -> ForAll(VerticesOfFace(surface1, face), v -> IsInnerVertex(surface1, v))); - faces2 := Filtered(Faces(surface2), face -> ForAll(VerticesOfFace(surface2, face), v -> IsInnerVertex(surface2, v))); - possible_image_faces := Faces(surface2); - if not faces1 = [] then # inner vertex degrees heuristic - face_counter1 := List(faces1, face -> Set(List(VerticesOfFace(surface1, face), v -> DegreeOfVertex(surface1, v)))); - face_counter2 := List(faces1, face -> Set(List(VerticesOfFace(surface2, face), v -> DegreeOfVertex(surface2, v)))); - if ForAny(face_counter2, fdegs2 -> not fdegs2 in face_counter1) then - return res; # empty list - else - min_pos := PositionMinimum(List(Collected(face_counter2), fdeg2 -> fdeg2[2])); - min_degrees := Collected(face_counter2)[min_pos][1]; - starting_face := Filtered(faces1, face -> min_degrees = Set(List(VerticesOfFace(surface1, face), v -> DegreeOfVertex(surface1, v))))[1]; - possible_image_faces := Filtered(faces2, face -> min_degrees = Set(List(VerticesOfFace(surface2, face), v -> DegreeOfVertex(surface2, v)))); + if is_correct_morphism = true then + return PolygonalMorphismByLists(surface1, surface2, monomorphism[1], monomorphism[2], monomorphism[3]); fi; - else - starting_face := Faces(surface1)[1]; + od; + od; + return fail; + end +); + +InstallMethod(AllButterflyFaithfulMonomorphismsIntoSimplicialSurface, "for two simplicial surfaces", + [IsSimplicialSurface, IsSimplicialSurface], + function(surface1, surface2) + local possible_vertex_maps, possible_monomorphisms, starting_face, image_starting_face, mapped_edges, mapped_faces, + remaining_faces, cur_edges, cur_edge, mapped_vertices, monomorphism, cur_face, face_map, edge_map, + vertex_map, i, new_face, new_image_face, is_correct_morphism, new_vertex, new_image_vertex, new_edges, new_image_edges, + cur_new_edge, cur_new_image_edge, finished_cur_edges, faces1, faces2, face_counter1, face_counter2, face_degrees1, face_degrees2, + min_degrees, min_pos, possible_image_faces, res; + + res := []; + faces1 := Filtered(Faces(surface1), face -> ForAll(VerticesOfFace(surface1, face), v -> IsInnerVertex(surface1, v))); + faces2 := Filtered(Faces(surface2), face -> ForAll(VerticesOfFace(surface2, face), v -> IsInnerVertex(surface2, v))); + possible_image_faces := Faces(surface2); + if not faces1 = [] then # inner vertex degrees heuristic + face_counter1 := List(faces1, face -> Set(List(VerticesOfFace(surface1, face), v -> DegreeOfVertex(surface1, v)))); + face_counter2 := List(faces1, face -> Set(List(VerticesOfFace(surface2, face), v -> DegreeOfVertex(surface2, v)))); + if ForAny(face_counter2, fdegs2 -> not fdegs2 in face_counter1) then + return res; # empty list + else + min_pos := PositionMinimum(List(Collected(face_counter2), fdeg2 -> fdeg2[2])); + min_degrees := Collected(face_counter2)[min_pos][1]; + starting_face := Filtered(faces1, face -> min_degrees = Set(List(VerticesOfFace(surface1, face), v -> DegreeOfVertex(surface1, v))))[1]; + possible_image_faces := Filtered(faces2, face -> min_degrees = Set(List(VerticesOfFace(surface2, face), v -> DegreeOfVertex(surface2, v)))); fi; + else + starting_face := Faces(surface1)[1]; + fi; - for image_starting_face in possible_image_faces do - possible_monomorphisms := AllOneFaceIsomorphisms(starting_face, surface1, - image_starting_face, surface2); - for i in [1..Length(possible_monomorphisms)] do - is_correct_morphism := true; - monomorphism := possible_monomorphisms[i]; - vertex_map := monomorphism[1]; - edge_map := monomorphism[2]; - face_map := monomorphism[3]; - - cur_edges := Filtered(EdgesOfFace(surface1, starting_face), e -> IsInnerEdge(surface1, e)); - finished_cur_edges := []; - remaining_faces := Difference(Faces(surface1), [starting_face]); - mapped_faces := MyPreImages(face_map); - while not IsEmpty(remaining_faces) do - cur_edge := cur_edges[1]; - if Length(Difference(FacesOfEdge(surface2, edge_map[cur_edge]), face_map)) = 1 then - new_image_face := Difference(FacesOfEdge(surface2, edge_map[cur_edge]), face_map)[1]; - else - is_correct_morphism := false; - break; - fi; - new_face := Difference(FacesOfEdge(surface1, cur_edge), mapped_faces)[1]; - - if not new_face in remaining_faces then - is_correct_morphism := false; - break; - fi; - - if MyUpdateMap(face_map, new_face, new_image_face) = false or MyIsInjective(face_map) = false then - is_correct_morphism := false; - break; - fi; - mapped_faces := MyPreImages(face_map); - - new_vertex := Difference(VerticesOfFace(surface1, new_face), VerticesOfEdge(surface1, cur_edge))[1]; - new_image_vertex := Difference(VerticesOfFace(surface2, new_image_face), VerticesOfEdge(surface2, edge_map[cur_edge]))[1]; - if MyUpdateMap(vertex_map, new_vertex, new_image_vertex) = false or MyIsInjective(vertex_map) = false then - is_correct_morphism := false; - break; - fi; - - # update edge_map - new_edges := Difference(EdgesOfFace(surface1, new_face), [cur_edge]); - new_image_edges := Difference(EdgesOfFace(surface2, new_image_face), [edge_map[cur_edge]]); - for cur_new_edge in new_edges do - for cur_new_image_edge in new_image_edges do - if Set(MyImageCat(vertex_map, VerticesOfEdge(surface1, cur_new_edge))) = Set(VerticesOfEdge(surface2, cur_new_image_edge)) then - if MyUpdateMap(edge_map, cur_new_edge, cur_new_image_edge) = false or MyIsInjective(edge_map) = false then - is_correct_morphism := false; - fi; - if cur_new_edge in cur_edges then - Add(finished_cur_edges, cur_new_edge); - fi; - fi; - od; - od; - if is_correct_morphism = false then - break; - fi; + for image_starting_face in possible_image_faces do + possible_monomorphisms := __SIMPLICIAL_AllOneFaceIsomorphisms(starting_face, surface1, + image_starting_face, surface2); + for i in [1..Length(possible_monomorphisms)] do + is_correct_morphism := true; + monomorphism := possible_monomorphisms[i]; + vertex_map := monomorphism[1]; + edge_map := monomorphism[2]; + face_map := monomorphism[3]; + + cur_edges := Filtered(EdgesOfFace(surface1, starting_face), e -> IsInnerEdge(surface1, e)); + finished_cur_edges := []; + remaining_faces := Difference(Faces(surface1), [starting_face]); + mapped_faces := __SIMPLICIAL_PreImagesFromListmap(face_map); + while not IsEmpty(remaining_faces) do + cur_edge := cur_edges[1]; + if Length(Difference(FacesOfEdge(surface2, edge_map[cur_edge]), face_map)) = 1 then + new_image_face := Difference(FacesOfEdge(surface2, edge_map[cur_edge]), face_map)[1]; + else + is_correct_morphism := false; + break; + fi; + new_face := Difference(FacesOfEdge(surface1, cur_edge), mapped_faces)[1]; - # update cur_edges - cur_edges := Union(cur_edges, Filtered(EdgesOfFace(surface1, new_face), e -> IsInnerEdge(surface1, e))); - Add(finished_cur_edges, cur_edge); - cur_edges := Difference(cur_edges, finished_cur_edges); + if not new_face in remaining_faces then + is_correct_morphism := false; + break; + fi; - # update remaining_faces - remaining_faces := Difference(remaining_faces, [new_face]); - od; + if __SIMPLICIAL_UpdateListmap(face_map, new_face, new_image_face) = false or __SIMPLICIAL_IsInjectiveListmap(face_map) = false then + is_correct_morphism := false; + break; + fi; + mapped_faces := __SIMPLICIAL_PreImagesFromListmap(face_map); + + new_vertex := Difference(VerticesOfFace(surface1, new_face), VerticesOfEdge(surface1, cur_edge))[1]; + new_image_vertex := Difference(VerticesOfFace(surface2, new_image_face), VerticesOfEdge(surface2, edge_map[cur_edge]))[1]; + if __SIMPLICIAL_UpdateListmap(vertex_map, new_vertex, new_image_vertex) = false or __SIMPLICIAL_IsInjectiveListmap(vertex_map) = false then + is_correct_morphism := false; + break; + fi; - if is_correct_morphism = true then - Add(res,PolygonalMorphismByLists(surface1, surface2, monomorphism[1], monomorphism[2], monomorphism[3])); + # update edge_map + new_edges := Difference(EdgesOfFace(surface1, new_face), [cur_edge]); + new_image_edges := Difference(EdgesOfFace(surface2, new_image_face), [edge_map[cur_edge]]); + for cur_new_edge in new_edges do + for cur_new_image_edge in new_image_edges do + if Set(__SIMPLICIAL_ImageCatFromListmap(vertex_map, VerticesOfEdge(surface1, cur_new_edge))) = Set(VerticesOfEdge(surface2, cur_new_image_edge)) then + if __SIMPLICIAL_UpdateListmap(edge_map, cur_new_edge, cur_new_image_edge) = false or __SIMPLICIAL_IsInjectiveListmap(edge_map) = false then + is_correct_morphism := false; + fi; + if cur_new_edge in cur_edges then + Add(finished_cur_edges, cur_new_edge); + fi; + fi; + od; + od; + if is_correct_morphism = false then + break; fi; + + # update cur_edges + cur_edges := Union(cur_edges, Filtered(EdgesOfFace(surface1, new_face), e -> IsInnerEdge(surface1, e))); + Add(finished_cur_edges, cur_edge); + cur_edges := Difference(cur_edges, finished_cur_edges); + + # update remaining_faces + remaining_faces := Difference(remaining_faces, [new_face]); od; + + if is_correct_morphism = true then + Add(res,PolygonalMorphismByLists(surface1, surface2, monomorphism[1], monomorphism[2], monomorphism[3])); + fi; od; - return res; - end; - return AllMonomorphismsIntoSimplicialSurface(surface1, surface2); + od; + return res; end ); From 1e728c25bffeb7e24eef86a09f218595d6fe0299 Mon Sep 17 00:00:00 2001 From: Flynn Fehre Date: Tue, 9 Apr 2024 12:17:07 +0200 Subject: [PATCH 22/44] deleted .tex-files from another branch --- ...x_facegraph_icosahedron_default_spread.tex | 340 ----------------- ...nvex_facegraph_icosahedron_high_spread.tex | 341 ------------------ ...onvex_facegraph_icosahedron_low_spread.tex | 341 ------------------ 3 files changed, 1022 deletions(-) delete mode 100644 doc/tikz-files/_TIKZ_convex_facegraph_icosahedron_default_spread.tex delete mode 100644 doc/tikz-files/_TIKZ_convex_facegraph_icosahedron_high_spread.tex delete mode 100644 doc/tikz-files/_TIKZ_convex_facegraph_icosahedron_low_spread.tex diff --git a/doc/tikz-files/_TIKZ_convex_facegraph_icosahedron_default_spread.tex b/doc/tikz-files/_TIKZ_convex_facegraph_icosahedron_default_spread.tex deleted file mode 100644 index e527e1bc..00000000 --- a/doc/tikz-files/_TIKZ_convex_facegraph_icosahedron_default_spread.tex +++ /dev/null @@ -1,340 +0,0 @@ -\documentclass{standalone} - -\pagestyle{empty} -% This document contains the TikZ-header for all our LaTeX-computations. -% It especially contains all global graphic parameters. - -\usepackage{amsmath, amssymb, amsfonts} % Standard Math-stuff - -\usepackage{ifthen} - -\usepackage{tikz} -\usetikzlibrary{calc} -\usetikzlibrary{positioning} -\usetikzlibrary{shapes} -\usetikzlibrary{patterns} - - -% Sometimes we want to implement different behaviour for the generated -% HTML-pictures (for example, shading is not supported in HTML). -% For that we define a macro to check whether we run the code with -% htlatex. The code comes from -% https://tex.stackexchange.com/questions/93852/what-is-the-correct-way-to-check-for-latex-pdflatex-and-html-in-the-same-latex -\makeatletter -\edef\texforht{TT\noexpand\fi - \@ifpackageloaded{tex4ht} - {\noexpand\iftrue} - {\noexpand\iffalse}} -\makeatother - - -% Define a text=none option for nodes that ignores the given text, from -% https://tex.stackexchange.com/questions/59354/no-text-none-in-tikz -\makeatletter -\newif\iftikz@node@phantom -\tikzset{ - phantom/.is if=tikz@node@phantom, - text/.code=% - \edef\tikz@temp{#1}% - \ifx\tikz@temp\tikz@nonetext - \tikz@node@phantomtrue - \else - \tikz@node@phantomfalse - \let\tikz@textcolor\tikz@temp - \fi -} -\usepackage{etoolbox} -\patchcmd\tikz@fig@continue{\tikz@node@transformations}{% - \iftikz@node@phantom - \setbox\pgfnodeparttextbox\hbox{} - \fi\tikz@node@transformations}{}{} -\makeatother - -% Find the angle of a given line (within TikZ) -\newcommand{\tikzAngleOfLine}{\tikz@AngleOfLine} -\def\tikz@AngleOfLine(#1)(#2)#3{% - \pgfmathanglebetweenpoints{% - \pgfpointanchor{#1}{center}}{% - \pgfpointanchor{#2}{center}} - \pgfmathsetmacro{#3}{\pgfmathresult}% -} - -% Now we define the global styles -% The global styles are defined nestedly. 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- \coordinate (V18) at (-0.2810942085002772 , 0.06104281296509385); - \coordinate (V19) at (-0.03005439329815793 , 0.2932358838093986); - \coordinate (V20) at (0.2593032045979817 , 0.1658676993992546); - \draw[edge] (V1) -- node[edgeLabel] {$1$} (V2); - \draw[edge] (V1) -- node[edgeLabel] {$2$} (V5); - \draw[edge] (V2) -- node[edgeLabel] {$3$} (V3); - \draw[edge] (V3) -- node[edgeLabel] {$4$} (V4); - \draw[edge] (V4) -- node[edgeLabel] {$5$} (V5); - \draw[edge] (V1) -- node[edgeLabel] {$6$} (V6); - \draw[edge] (V2) -- node[edgeLabel] {$7$} (V7); - \draw[edge] (V6) -- node[edgeLabel] {$8$} (V11); - \draw[edge] (V7) -- node[edgeLabel] {$9$} (V11); - \draw[edge] (V5) -- node[edgeLabel] {$10$} (V10); - \draw[edge] (V6) -- node[edgeLabel] {$11$} (V15); - \draw[edge] (V10) -- node[edgeLabel] {$12$} (V15); - \draw[edge] (V3) -- node[edgeLabel] {$13$} (V8); - \draw[edge] (V7) -- node[edgeLabel] {$14$} (V12); - \draw[edge] (V8) -- node[edgeLabel] {$15$} (V12); - \draw[edge] (V4) -- node[edgeLabel] {$16$} (V9); - \draw[edge] (V8) -- node[edgeLabel] {$17$} (V13); - \draw[edge] (V9) -- node[edgeLabel] {$18$} (V13); - \draw[edge] (V9) -- node[edgeLabel] {$19$} (V14); - \draw[edge] (V10) -- node[edgeLabel] {$20$} (V14); - \draw[edge] (V11) -- node[edgeLabel] {$21$} (V16); - \draw[edge] (V15) -- node[edgeLabel] {$22$} (V20); - \draw[edge] (V16) -- node[edgeLabel] {$23$} (V20); - \draw[edge] (V12) -- node[edgeLabel] {$24$} (V17); - \draw[edge] (V16) -- node[edgeLabel] {$25$} (V17); - \draw[edge] (V13) -- node[edgeLabel] {$26$} (V18); - \draw[edge] (V17) -- node[edgeLabel] {$27$} (V18); - \draw[edge] (V14) -- node[edgeLabel] {$28$} (V19); - \draw[edge] (V18) -- node[edgeLabel] {$29$} (V19); - \draw[edge] (V19) -- node[edgeLabel] {$30$} (V20); - % Draw the faces - \vertexLabelR{V1}{left}{$1$} - \vertexLabelR{V2}{left}{$2$} - \vertexLabelR{V3}{left}{$3$} - \vertexLabelR{V4}{left}{$4$} - \vertexLabelR{V5}{left}{$5$} - \vertexLabelR{V6}{left}{$6$} - \vertexLabelR{V7}{left}{$7$} - \vertexLabelR{V8}{left}{$8$} - \vertexLabelR{V9}{left}{$9$} - \vertexLabelR{V10}{left}{$10$} - \vertexLabelR{V11}{left}{$11$} - \vertexLabelR{V12}{left}{$12$} - \vertexLabelR{V13}{left}{$13$} - \vertexLabelR{V14}{left}{$14$} - \vertexLabelR{V15}{left}{$15$} - \vertexLabelR{V16}{left}{$16$} - \vertexLabelR{V17}{left}{$17$} - \vertexLabelR{V18}{left}{$18$} - \vertexLabelR{V19}{left}{$19$} - \vertexLabelR{V20}{left}{$20$} - \end{tikzpicture} - -\end{document} - - diff --git a/doc/tikz-files/_TIKZ_convex_facegraph_icosahedron_high_spread.tex b/doc/tikz-files/_TIKZ_convex_facegraph_icosahedron_high_spread.tex deleted file mode 100644 index 4783561d..00000000 --- a/doc/tikz-files/_TIKZ_convex_facegraph_icosahedron_high_spread.tex +++ /dev/null @@ -1,341 +0,0 @@ -\documentclass{standalone} - -\pagestyle{empty} -% This document contains the TikZ-header for all our LaTeX-computations. -% It especially contains all global graphic parameters. - -\usepackage{amsmath, amssymb, amsfonts} % Standard Math-stuff - -\usepackage{ifthen} - -\usepackage{tikz} -\usetikzlibrary{calc} -\usetikzlibrary{positioning} -\usetikzlibrary{shapes} -\usetikzlibrary{patterns} - - -% Sometimes we want to implement different behaviour for the generated -% HTML-pictures (for example, shading is not supported in HTML). -% For that we define a macro to check whether we run the code with -% htlatex. The code comes from -% https://tex.stackexchange.com/questions/93852/what-is-the-correct-way-to-check-for-latex-pdflatex-and-html-in-the-same-latex -\makeatletter -\edef\texforht{TT\noexpand\fi - \@ifpackageloaded{tex4ht} - {\noexpand\iftrue} - {\noexpand\iffalse}} -\makeatother - - -% Define a text=none option for nodes that ignores the given text, from -% https://tex.stackexchange.com/questions/59354/no-text-none-in-tikz -\makeatletter -\newif\iftikz@node@phantom -\tikzset{ - phantom/.is if=tikz@node@phantom, - text/.code=% - \edef\tikz@temp{#1}% - \ifx\tikz@temp\tikz@nonetext - \tikz@node@phantomtrue - \else - \tikz@node@phantomfalse - \let\tikz@textcolor\tikz@temp - \fi -} -\usepackage{etoolbox} -\patchcmd\tikz@fig@continue{\tikz@node@transformations}{% - \iftikz@node@phantom - \setbox\pgfnodeparttextbox\hbox{} - \fi\tikz@node@transformations}{}{} -\makeatother - -% Find the angle of a given line (within TikZ) -\newcommand{\tikzAngleOfLine}{\tikz@AngleOfLine} -\def\tikz@AngleOfLine(#1)(#2)#3{% - \pgfmathanglebetweenpoints{% - \pgfpointanchor{#1}{center}}{% - \pgfpointanchor{#2}{center}} - \pgfmathsetmacro{#3}{\pgfmathresult}% -} - -% Now we define the global styles -% The global styles are defined nestedly. You have to give your tikzpicture -% the global options [vertexStyle, edgeStyle, faceStyle] to activate them. -% -% You can disable labels by using the option nolabels, i.e. -% vertexStyle=nolabels to deactivate vertex labels. -% -% If you want to have a specific style for your picture, you can also use -% this specific meta-style instead of the general style. For example if you -% want to use double edges in one single picture - no matter the style of -% the rest of the document - you can use edgeDouble instead of edgeStyle. -% -% To set the default style, modify the vertexStyle/.default entry. - -% Vertex styles -\tikzset{ - vertexNodePlain/.style = {fill=#1, shape=circle, inner sep=0pt, minimum size=2pt, text=none}, - vertexNodePlain/.default=gray, - vertexPlain/labels/.style = { - vertexNode/.style={vertexNodePlain=##1}, - vertexLabel/.style={gray} - }, - vertexPlain/nolabels/.style = { - vertexNode/.style={vertexNodePlain=##1}, - vertexLabel/.style={text=none} - }, - vertexPlain/.style = vertexPlain/#1, - vertexPlain/.default=labels -} -\tikzset{ - vertexNodeNormal/.style = {fill=#1, shape=circle, inner sep=0pt, minimum size=4pt, text=none}, - vertexNodeNormal/.default = blue, - vertexNormal/labels/.style = { - vertexNode/.style={vertexNodeNormal=##1}, - vertexLabel/.style={blue} - }, - vertexNormal/nolabels/.style = { - vertexNode/.style={vertexNodeNormal=##1}, - vertexLabel/.style={text=none} - }, - vertexNormal/.style = vertexNormal/#1, - vertexNormal/.default=labels -} -\tikzset{ - vertexNodeBallShading/pdf/.style = {ball color=#1}, - vertexNodeBallShading/svg/.style = {fill=#1}, - vertexNodeBallShading/.code = {% Conditional shading depending whether we want pdf or svg output - \if\texforht - \tikzset{vertexNodeBallShading/svg=#1!90!black} - \else - \tikzset{vertexNodeBallShading/pdf=#1} - \fi - }, - vertexNodeBall/.style = {shape=circle, vertexNodeBallShading=#1, inner sep=2pt, outer sep=0pt, minimum size=3pt, font=\tiny}, - vertexNodeBall/.default = white, - vertexBall/labels/.style = { - vertexNode/.style={vertexNodeBall=##1, text=black}, - vertexLabel/.style={text=none} - }, - vertexBall/nolabels/.style = { - vertexNode/.style={vertexNodeBall=##1, text=none}, - vertexLabel/.style={text=none} - }, - vertexBall/.style = vertexBall/#1, - vertexBall/.default=labels -} -\tikzset{ - vertexStyle/.style={vertexNormal=#1}, - vertexStyle/.default = labels -} - - -% 1) optional: colour of vertex -% 2) position of the vertex -% 3) relative position of the node -% 4) name of the vertex -\newcommand{\vertexLabelR}[4][]{ - \ifthenelse{ \equal{#1}{} } - { \node[vertexNode] (#2 name) at (#2) {#4}; } - { \node[vertexNode=#1] (#2 name) at (#2) {#4}; } - \node[vertexLabel, #3] at (#2) {#4}; -} -% 1) optional: colour of vertex -% 2) position of the vertex -% 3) absolute position of the node -% 4) name of the vertex -\newcommand{\vertexLabelA}[4][]{ - \ifthenelse{ \equal{#1}{} } - { \node[vertexNode] (#2 name) at (#2) {#4}; } - { \node[vertexNode=#1] (#2 name) at (#2) {#4}; } - \node[vertexLabel] at (#3) {#4}; -} - - -% Edge styles -% If you have trouble with the double-lines overlapping, this might (?) help: -% https://tex.stackexchange.com/questions/288159/closing-the-ends-of-double-line-in-tikz -\newcommand{\edgeLabelColor}{blue!20!white} -\tikzset{ - edgeLineNone/.style = {draw=none}, - edgeLineNone/.default=black, - edgeNone/labels/.style = { - edge/.style = {edgeLineNone=##1}, - edgeLabel/.style = {fill=\edgeLabelColor,font=\small} - }, - edgeNone/nolabels/.style = { - edge/.style = {edgeLineNone=##1}, - edgeLabel/.style = {text=none} - }, - edgeNone/.style = edgeNone/#1, - edgeNone/.default = labels -} -\tikzset{ - edgeLinePlain/.style={line join=round, draw=#1}, - edgeLinePlain/.default=black, - edgePlain/labels/.style = { - edge/.style={edgeLinePlain=##1}, - edgeLabel/.style={fill=\edgeLabelColor,font=\small} - }, - edgePlain/nolabels/.style = { - edge/.style={edgeLinePlain=##1}, - edgeLabel/.style={text=none} - }, - edgePlain/.style = edgePlain/#1, - edgePlain/.default = labels -} -\tikzset{ - edgeLineDouble/.style = {very thin, double=#1, double distance=.8pt, line join=round}, - edgeLineDouble/.default=gray!90!white, - edgeDouble/labels/.style = { - edge/.style = {edgeLineDouble=##1}, - edgeLabel/.style = {fill=\edgeLabelColor,font=\small} - }, - edgeDouble/nolabels/.style = { - edge/.style = {edgeLineDouble=##1}, - edgeLabel/.style = {text=none} - }, - edgeDouble/.style = edgeDouble/#1, - edgeDouble/.default = labels -} -\tikzset{ - edgeStyle/.style = {edgePlain=#1}, - edgeStyle/.default = labels -} - -% Face styles -% Here we have an exception - the style face is always defined. -% -\newcommand{\faceColorY}{yellow!60!white} % yellow -\newcommand{\faceColorB}{blue!60!white} % blue -\newcommand{\faceColorC}{cyan!60} % cyan -\newcommand{\faceColorR}{red!60!white} % red -\newcommand{\faceColorG}{green!60!white} % green -\newcommand{\faceColorO}{orange!50!yellow!70!white} % orange - -% define default face colour (and default swap colour) -\newcommand{\faceColor}{\faceColorY} -\newcommand{\faceColorSwap}{\faceColorC} - -% define secondary default colours (to use in a single section) -\newcommand{\faceColorFirst}{green!40!white} -\newcommand{\faceColorSecond}{gray!15!white} -\newcommand{\faceColorThird}{red!17!white} -\newcommand{\faceColorFourth}{olive!20!white} - -\tikzset{ - face/.style = {fill=#1}, - face/.default = \faceColor, - faceY/.style = {face=\faceColorY}, - faceB/.style = {face=\faceColorB}, - faceC/.style = {face=\faceColorC}, - faceR/.style = {face=\faceColorR}, - faceG/.style = {face=\faceColorG}, - faceO/.style = {face=\faceColorO} -} -\tikzset{ - faceStyle/labels/.style = { - faceLabel/.style = {} - }, - faceStyle/nolabels/.style = { - faceLabel/.style = {text=none} - }, - faceStyle/.style = faceStyle/#1, - faceStyle/.default = labels -} -\tikzset{ face/.style={fill=#1} } -\tikzset{ faceSwap/.code= - \ifdefined\swapColors - \tikzset{face=\faceColorSwap} - \else - \tikzset{face=\faceColor} - \fi -} - - - -\usepackage{hyperref} - - -\begin{document} - -\begin{tikzpicture}[vertexBall, edgeDouble=nolabels, faceStyle=nolabels, scale=4] - - \coordinate (V1) at (1. , 0.); - \coordinate (V2) at (0.3090169889123937 , -0.9510565180700449); - \coordinate (V3) at (-0.8090169969069803 , -0.5877852488074289); - \coordinate (V4) at (-0.8090169926869255 , 0.587785254615836); - \coordinate (V5) at (0.3090169957405858 , 0.9510565158514307); - \coordinate (V6) at (0.7927050976979469 , -3.327921271889523e-10); - \coordinate (V7) at (0.2424730992248824 , -0.7390375056311521); - \coordinate (V8) at (-0.6182970511232349 , -0.488652952881346); - \coordinate (V9) at (-0.6555846775013854 , 0.4363679932957395); - \coordinate (V10) at (0.2138651127700633 , 0.753907349238458); - \coordinate (V11) at (0.6257282990590397 , -0.1221815949309928); - \coordinate (V12) at (-0.4759335274339455 , -0.4043145436795418); - \coordinate (V13) at (-0.5299770435427567 , 0.3239876612138216); - \coordinate (V14) at (0.1445119225113219 , 0.6121867255933728); - \coordinate (V15) at (0.6209603013165698 , 0.1266425475472756); - \coordinate (V16) at (0.4597638254237214 , -0.1271779158715349); - \coordinate (V17) at (-0.3282846657626078 , -0.2658951127485535); - \coordinate (V18) at (-0.4273051358160279 , 0.2413450347190398); - \coordinate (V19) at (0.1004588251932902 , 0.5013390228086395); - \coordinate (V20) at (0.5253135731118553 , 0.1614011047413686); - \draw[edge] (V1) -- node[edgeLabel] {$1$} (V2); - \draw[edge] (V1) -- node[edgeLabel] {$2$} (V5); - \draw[edge] (V2) -- node[edgeLabel] {$3$} (V3); - \draw[edge] (V3) -- node[edgeLabel] {$4$} (V4); - \draw[edge] (V4) -- node[edgeLabel] {$5$} (V5); - \draw[edge] (V1) -- node[edgeLabel] {$6$} (V6); - \draw[edge] (V2) -- node[edgeLabel] {$7$} (V7); - \draw[edge] (V6) -- node[edgeLabel] {$8$} (V11); - \draw[edge] (V7) -- node[edgeLabel] {$9$} (V11); - \draw[edge] (V5) -- node[edgeLabel] {$10$} (V10); - \draw[edge] (V6) -- node[edgeLabel] {$11$} (V15); - \draw[edge] (V10) -- node[edgeLabel] {$12$} (V15); - \draw[edge] (V3) -- node[edgeLabel] {$13$} (V8); - \draw[edge] (V7) -- node[edgeLabel] {$14$} (V12); - \draw[edge] (V8) -- node[edgeLabel] {$15$} (V12); - \draw[edge] (V4) -- node[edgeLabel] {$16$} (V9); - \draw[edge] (V8) -- node[edgeLabel] {$17$} (V13); - \draw[edge] (V9) -- node[edgeLabel] {$18$} (V13); - \draw[edge] (V9) -- node[edgeLabel] {$19$} (V14); - \draw[edge] (V10) -- node[edgeLabel] {$20$} (V14); - \draw[edge] (V11) -- node[edgeLabel] {$21$} (V16); - \draw[edge] (V15) -- node[edgeLabel] {$22$} (V20); - \draw[edge] (V16) -- node[edgeLabel] {$23$} (V20); - \draw[edge] (V12) -- node[edgeLabel] {$24$} (V17); - \draw[edge] (V16) -- node[edgeLabel] {$25$} (V17); - \draw[edge] (V13) -- node[edgeLabel] {$26$} (V18); - \draw[edge] (V17) -- node[edgeLabel] {$27$} (V18); - \draw[edge] (V14) -- node[edgeLabel] {$28$} (V19); - \draw[edge] (V18) -- node[edgeLabel] {$29$} (V19); - \draw[edge] (V19) -- node[edgeLabel] {$30$} (V20); - % Draw the faces - \vertexLabelR{V1}{left}{$1$} - \vertexLabelR{V2}{left}{$2$} - \vertexLabelR{V3}{left}{$3$} - \vertexLabelR{V4}{left}{$4$} - \vertexLabelR{V5}{left}{$5$} - \vertexLabelR{V6}{left}{$6$} - \vertexLabelR{V7}{left}{$7$} - \vertexLabelR{V8}{left}{$8$} - \vertexLabelR{V9}{left}{$9$} - \vertexLabelR{V10}{left}{$10$} - \vertexLabelR{V11}{left}{$11$} - \vertexLabelR{V12}{left}{$12$} - \vertexLabelR{V13}{left}{$13$} - \vertexLabelR{V14}{left}{$14$} - \vertexLabelR{V15}{left}{$15$} - \vertexLabelR{V16}{left}{$16$} - \vertexLabelR{V17}{left}{$17$} - \vertexLabelR{V18}{left}{$18$} - \vertexLabelR{V19}{left}{$19$} - \vertexLabelR{V20}{left}{$20$} - \end{tikzpicture} - -\end{document} - - - diff --git a/doc/tikz-files/_TIKZ_convex_facegraph_icosahedron_low_spread.tex b/doc/tikz-files/_TIKZ_convex_facegraph_icosahedron_low_spread.tex deleted file mode 100644 index 15ae0fe6..00000000 --- a/doc/tikz-files/_TIKZ_convex_facegraph_icosahedron_low_spread.tex +++ /dev/null @@ -1,341 +0,0 @@ -\documentclass{standalone} - -\pagestyle{empty} -% This document contains the TikZ-header for all our LaTeX-computations. -% It especially contains all global graphic parameters. - -\usepackage{amsmath, amssymb, amsfonts} % Standard Math-stuff - -\usepackage{ifthen} - -\usepackage{tikz} -\usetikzlibrary{calc} -\usetikzlibrary{positioning} -\usetikzlibrary{shapes} -\usetikzlibrary{patterns} - - -% Sometimes we want to implement different behaviour for the generated -% HTML-pictures (for example, shading is not supported in HTML). -% For that we define a macro to check whether we run the code with -% htlatex. The code comes from -% https://tex.stackexchange.com/questions/93852/what-is-the-correct-way-to-check-for-latex-pdflatex-and-html-in-the-same-latex -\makeatletter -\edef\texforht{TT\noexpand\fi - \@ifpackageloaded{tex4ht} - {\noexpand\iftrue} - {\noexpand\iffalse}} -\makeatother - - -% Define a text=none option for nodes that ignores the given text, from -% https://tex.stackexchange.com/questions/59354/no-text-none-in-tikz -\makeatletter -\newif\iftikz@node@phantom -\tikzset{ - phantom/.is if=tikz@node@phantom, - text/.code=% - \edef\tikz@temp{#1}% - \ifx\tikz@temp\tikz@nonetext - \tikz@node@phantomtrue - \else - \tikz@node@phantomfalse - \let\tikz@textcolor\tikz@temp - \fi -} -\usepackage{etoolbox} -\patchcmd\tikz@fig@continue{\tikz@node@transformations}{% - \iftikz@node@phantom - \setbox\pgfnodeparttextbox\hbox{} - \fi\tikz@node@transformations}{}{} -\makeatother - -% Find the angle of a given line (within TikZ) -\newcommand{\tikzAngleOfLine}{\tikz@AngleOfLine} -\def\tikz@AngleOfLine(#1)(#2)#3{% - \pgfmathanglebetweenpoints{% - \pgfpointanchor{#1}{center}}{% - \pgfpointanchor{#2}{center}} - \pgfmathsetmacro{#3}{\pgfmathresult}% -} - -% Now we define the global styles -% The global styles are defined nestedly. You have to give your tikzpicture -% the global options [vertexStyle, edgeStyle, faceStyle] to activate them. -% -% You can disable labels by using the option nolabels, i.e. -% vertexStyle=nolabels to deactivate vertex labels. -% -% If you want to have a specific style for your picture, you can also use -% this specific meta-style instead of the general style. For example if you -% want to use double edges in one single picture - no matter the style of -% the rest of the document - you can use edgeDouble instead of edgeStyle. -% -% To set the default style, modify the vertexStyle/.default entry. - -% Vertex styles -\tikzset{ - vertexNodePlain/.style = {fill=#1, shape=circle, inner sep=0pt, minimum size=2pt, text=none}, - vertexNodePlain/.default=gray, - vertexPlain/labels/.style = { - vertexNode/.style={vertexNodePlain=##1}, - vertexLabel/.style={gray} - }, - vertexPlain/nolabels/.style = { - vertexNode/.style={vertexNodePlain=##1}, - vertexLabel/.style={text=none} - }, - vertexPlain/.style = vertexPlain/#1, - vertexPlain/.default=labels -} -\tikzset{ - vertexNodeNormal/.style = {fill=#1, shape=circle, inner sep=0pt, minimum size=4pt, text=none}, - vertexNodeNormal/.default = blue, - vertexNormal/labels/.style = { - vertexNode/.style={vertexNodeNormal=##1}, - vertexLabel/.style={blue} - }, - vertexNormal/nolabels/.style = { - vertexNode/.style={vertexNodeNormal=##1}, - vertexLabel/.style={text=none} - }, - vertexNormal/.style = vertexNormal/#1, - vertexNormal/.default=labels -} -\tikzset{ - vertexNodeBallShading/pdf/.style = {ball color=#1}, - vertexNodeBallShading/svg/.style = {fill=#1}, - vertexNodeBallShading/.code = {% Conditional shading depending whether we want pdf or svg output - \if\texforht - \tikzset{vertexNodeBallShading/svg=#1!90!black} - \else - \tikzset{vertexNodeBallShading/pdf=#1} - \fi - }, - vertexNodeBall/.style = {shape=circle, vertexNodeBallShading=#1, inner sep=2pt, outer sep=0pt, minimum size=3pt, font=\tiny}, - vertexNodeBall/.default = white, - vertexBall/labels/.style = { - vertexNode/.style={vertexNodeBall=##1, text=black}, - vertexLabel/.style={text=none} - }, - vertexBall/nolabels/.style = { - vertexNode/.style={vertexNodeBall=##1, text=none}, - vertexLabel/.style={text=none} - }, - vertexBall/.style = vertexBall/#1, - vertexBall/.default=labels -} -\tikzset{ - vertexStyle/.style={vertexNormal=#1}, - vertexStyle/.default = labels -} - - -% 1) optional: colour of vertex -% 2) position of the vertex -% 3) relative position of the node -% 4) name of the vertex -\newcommand{\vertexLabelR}[4][]{ - \ifthenelse{ \equal{#1}{} } - { \node[vertexNode] (#2 name) at (#2) {#4}; } - { \node[vertexNode=#1] (#2 name) at (#2) {#4}; } - \node[vertexLabel, #3] at (#2) {#4}; -} -% 1) optional: colour of vertex -% 2) position of the vertex -% 3) absolute position of the node -% 4) name of the vertex -\newcommand{\vertexLabelA}[4][]{ - \ifthenelse{ \equal{#1}{} } - { \node[vertexNode] (#2 name) at (#2) {#4}; } - { \node[vertexNode=#1] (#2 name) at (#2) {#4}; } - \node[vertexLabel] at (#3) {#4}; -} - - -% Edge styles -% If you have trouble with the double-lines overlapping, this might (?) help: -% https://tex.stackexchange.com/questions/288159/closing-the-ends-of-double-line-in-tikz -\newcommand{\edgeLabelColor}{blue!20!white} -\tikzset{ - edgeLineNone/.style = {draw=none}, - edgeLineNone/.default=black, - edgeNone/labels/.style = { - edge/.style = {edgeLineNone=##1}, - edgeLabel/.style = {fill=\edgeLabelColor,font=\small} - }, - edgeNone/nolabels/.style = { - edge/.style = {edgeLineNone=##1}, - edgeLabel/.style = {text=none} - }, - edgeNone/.style = edgeNone/#1, - edgeNone/.default = labels -} -\tikzset{ - edgeLinePlain/.style={line join=round, draw=#1}, - edgeLinePlain/.default=black, - edgePlain/labels/.style = { - edge/.style={edgeLinePlain=##1}, - edgeLabel/.style={fill=\edgeLabelColor,font=\small} - }, - edgePlain/nolabels/.style = { - edge/.style={edgeLinePlain=##1}, - edgeLabel/.style={text=none} - }, - edgePlain/.style = edgePlain/#1, - edgePlain/.default = labels -} -\tikzset{ - edgeLineDouble/.style = {very thin, double=#1, double distance=.8pt, line join=round}, - edgeLineDouble/.default=gray!90!white, - edgeDouble/labels/.style = { - edge/.style = {edgeLineDouble=##1}, - edgeLabel/.style = {fill=\edgeLabelColor,font=\small} - }, - edgeDouble/nolabels/.style = { - edge/.style = {edgeLineDouble=##1}, - edgeLabel/.style = {text=none} - }, - edgeDouble/.style = edgeDouble/#1, - edgeDouble/.default = labels -} -\tikzset{ - edgeStyle/.style = {edgePlain=#1}, - edgeStyle/.default = labels -} - -% Face styles -% Here we have an exception - the style face is always defined. -% -\newcommand{\faceColorY}{yellow!60!white} % yellow -\newcommand{\faceColorB}{blue!60!white} % blue -\newcommand{\faceColorC}{cyan!60} % cyan -\newcommand{\faceColorR}{red!60!white} % red -\newcommand{\faceColorG}{green!60!white} % green -\newcommand{\faceColorO}{orange!50!yellow!70!white} % orange - -% define default face colour (and default swap colour) -\newcommand{\faceColor}{\faceColorY} -\newcommand{\faceColorSwap}{\faceColorC} - -% define secondary default colours (to use in a single section) -\newcommand{\faceColorFirst}{green!40!white} -\newcommand{\faceColorSecond}{gray!15!white} -\newcommand{\faceColorThird}{red!17!white} -\newcommand{\faceColorFourth}{olive!20!white} - -\tikzset{ - face/.style = {fill=#1}, - face/.default = \faceColor, - faceY/.style = {face=\faceColorY}, - faceB/.style = {face=\faceColorB}, - faceC/.style = {face=\faceColorC}, - faceR/.style = {face=\faceColorR}, - faceG/.style = {face=\faceColorG}, - faceO/.style = {face=\faceColorO} -} -\tikzset{ - faceStyle/labels/.style = { - faceLabel/.style = {} - }, - faceStyle/nolabels/.style = { - faceLabel/.style = {text=none} - }, - faceStyle/.style = faceStyle/#1, - faceStyle/.default = labels -} -\tikzset{ face/.style={fill=#1} } -\tikzset{ faceSwap/.code= - \ifdefined\swapColors - \tikzset{face=\faceColorSwap} - \else - \tikzset{face=\faceColor} - \fi -} - - - -\usepackage{hyperref} - - -\begin{document} - -\begin{tikzpicture}[vertexBall, edgeDouble=nolabels, faceStyle=nolabels, scale=4] - - \coordinate (V1) at (1. , 0.); - \coordinate (V2) at (0.3090169889123937 , -0.9510565180700449); - \coordinate (V3) at (-0.8090169969069803 , -0.5877852488074289); - \coordinate (V4) at (-0.8090169926869255 , 0.587785254615836); - \coordinate (V5) at (0.3090169957405858 , 0.9510565158514307); - \coordinate (V6) at (0.5163118946285428 , -7.765149634408886e-10); - \coordinate (V7) at (0.1614864032665868 , -0.4460855978160754); - \coordinate (V8) at (-0.3197938757917752 , -0.4593389774950907); - \coordinate (V9) at (-0.5292706366829111 , 0.1424753670618677); - \coordinate (V10) at (-0.009741685598258207 , 0.4910417935991915); - \coordinate (V11) at (0.2412985701850865 , -0.1664845467062768); - \coordinate (V12) at (-0.1497258880922867 , -0.3025990736622617); - \coordinate (V13) at (-0.3151656185658844 , -0.02476406050888025); - \coordinate (V14) at (-0.1270187743825422 , 0.2664627757024033); - \coordinate (V15) at (0.1747098689598691 , 0.1979538832885492); - \coordinate (V16) at (0.08113396435917979 , -0.08657118064268243); - \coordinate (V17) at (-0.08457670923818356 , -0.1467718202157678); - \coordinate (V18) at (-0.1944452295320299 , -0.07340624254900144); - \coordinate (V19) at (-0.1356899517998978 , 0.1140932896727264); - \coordinate (V20) at (0.03635327717978389 , 0.1223482232574671); - \draw[edge] (V1) -- node[edgeLabel] {$1$} (V2); - \draw[edge] (V1) -- node[edgeLabel] {$2$} (V5); - \draw[edge] (V2) -- node[edgeLabel] {$3$} (V3); - \draw[edge] (V3) -- node[edgeLabel] {$4$} (V4); - \draw[edge] (V4) -- node[edgeLabel] {$5$} (V5); - \draw[edge] (V1) -- node[edgeLabel] {$6$} (V6); - \draw[edge] (V2) -- node[edgeLabel] {$7$} (V7); - \draw[edge] (V6) -- node[edgeLabel] {$8$} (V11); - \draw[edge] (V7) -- node[edgeLabel] {$9$} (V11); - \draw[edge] (V5) -- node[edgeLabel] {$10$} (V10); - \draw[edge] (V6) -- node[edgeLabel] {$11$} (V15); - \draw[edge] (V10) -- node[edgeLabel] {$12$} (V15); - \draw[edge] (V3) -- node[edgeLabel] {$13$} (V8); - \draw[edge] (V7) -- node[edgeLabel] {$14$} (V12); - \draw[edge] (V8) -- node[edgeLabel] {$15$} (V12); - \draw[edge] (V4) -- node[edgeLabel] {$16$} (V9); - \draw[edge] (V8) -- node[edgeLabel] {$17$} (V13); - \draw[edge] (V9) -- node[edgeLabel] {$18$} (V13); - \draw[edge] (V9) -- node[edgeLabel] {$19$} (V14); - \draw[edge] (V10) -- node[edgeLabel] {$20$} (V14); - \draw[edge] (V11) -- node[edgeLabel] {$21$} (V16); - \draw[edge] (V15) -- node[edgeLabel] {$22$} (V20); - \draw[edge] (V16) -- node[edgeLabel] {$23$} (V20); - \draw[edge] (V12) -- node[edgeLabel] {$24$} (V17); - \draw[edge] (V16) -- node[edgeLabel] {$25$} (V17); - \draw[edge] (V13) -- node[edgeLabel] {$26$} (V18); - \draw[edge] (V17) -- node[edgeLabel] {$27$} (V18); - \draw[edge] (V14) -- node[edgeLabel] {$28$} (V19); - \draw[edge] (V18) -- node[edgeLabel] {$29$} (V19); - \draw[edge] (V19) -- node[edgeLabel] {$30$} (V20); - % Draw the faces - \vertexLabelR{V1}{left}{$1$} - \vertexLabelR{V2}{left}{$2$} - \vertexLabelR{V3}{left}{$3$} - \vertexLabelR{V4}{left}{$4$} - \vertexLabelR{V5}{left}{$5$} - \vertexLabelR{V6}{left}{$6$} - \vertexLabelR{V7}{left}{$7$} - \vertexLabelR{V8}{left}{$8$} - \vertexLabelR{V9}{left}{$9$} - \vertexLabelR{V10}{left}{$10$} - \vertexLabelR{V11}{left}{$11$} - \vertexLabelR{V12}{left}{$12$} - \vertexLabelR{V13}{left}{$13$} - \vertexLabelR{V14}{left}{$14$} - \vertexLabelR{V15}{left}{$15$} - \vertexLabelR{V16}{left}{$16$} - \vertexLabelR{V17}{left}{$17$} - \vertexLabelR{V18}{left}{$18$} - \vertexLabelR{V19}{left}{$19$} - \vertexLabelR{V20}{left}{$20$} -\end{tikzpicture} - -\end{document} - - - From b5eb0fd8f3f5313938ebe26783137f5822b41560 Mon Sep 17 00:00:00 2001 From: Flynn Fehre Date: Tue, 9 Apr 2024 16:45:13 +0200 Subject: [PATCH 23/44] deleted one more .tex-file from another branch --- .../Image_convex_facegraph_Double6Gon.tex | 312 ------------------ 1 file changed, 312 deletions(-) delete mode 100644 doc/tikz-files/Image_convex_facegraph_Double6Gon.tex diff --git a/doc/tikz-files/Image_convex_facegraph_Double6Gon.tex b/doc/tikz-files/Image_convex_facegraph_Double6Gon.tex deleted file mode 100644 index 3e6fd2b7..00000000 --- a/doc/tikz-files/Image_convex_facegraph_Double6Gon.tex +++ /dev/null @@ -1,312 +0,0 @@ -\documentclass{standalone} - -\pagestyle{empty} -% This document contains the TikZ-header for all our LaTeX-computations. -% It especially contains all global graphic parameters. - -\usepackage{amsmath, amssymb, amsfonts} % Standard Math-stuff - -\usepackage{ifthen} - -\usepackage{tikz} -\usetikzlibrary{calc} -\usetikzlibrary{positioning} -\usetikzlibrary{shapes} -\usetikzlibrary{patterns} - - -% Sometimes we want to implement different behaviour for the generated -% HTML-pictures (for example, shading is not supported in HTML). -% For that we define a macro to check whether we run the code with -% htlatex. The code comes from -% https://tex.stackexchange.com/questions/93852/what-is-the-correct-way-to-check-for-latex-pdflatex-and-html-in-the-same-latex -\makeatletter -\edef\texforht{TT\noexpand\fi - \@ifpackageloaded{tex4ht} - {\noexpand\iftrue} - {\noexpand\iffalse}} -\makeatother - - -% Define a text=none option for nodes that ignores the given text, from -% https://tex.stackexchange.com/questions/59354/no-text-none-in-tikz -\makeatletter -\newif\iftikz@node@phantom -\tikzset{ - phantom/.is if=tikz@node@phantom, - text/.code=% - \edef\tikz@temp{#1}% - \ifx\tikz@temp\tikz@nonetext - \tikz@node@phantomtrue - \else - \tikz@node@phantomfalse - \let\tikz@textcolor\tikz@temp - \fi -} -\usepackage{etoolbox} -\patchcmd\tikz@fig@continue{\tikz@node@transformations}{% - \iftikz@node@phantom - \setbox\pgfnodeparttextbox\hbox{} - \fi\tikz@node@transformations}{}{} -\makeatother - -% Find the angle of a given line (within TikZ) -\newcommand{\tikzAngleOfLine}{\tikz@AngleOfLine} -\def\tikz@AngleOfLine(#1)(#2)#3{% - \pgfmathanglebetweenpoints{% - \pgfpointanchor{#1}{center}}{% - \pgfpointanchor{#2}{center}} - \pgfmathsetmacro{#3}{\pgfmathresult}% -} - -% Now we define the global styles -% The global styles are defined nestedly. You have to give your tikzpicture -% the global options [vertexStyle, edgeStyle, faceStyle] to activate them. -% -% You can disable labels by using the option nolabels, i.e. -% vertexStyle=nolabels to deactivate vertex labels. -% -% If you want to have a specific style for your picture, you can also use -% this specific meta-style instead of the general style. For example if you -% want to use double edges in one single picture - no matter the style of -% the rest of the document - you can use edgeDouble instead of edgeStyle. -% -% To set the default style, modify the vertexStyle/.default entry. - -% Vertex styles -\tikzset{ - vertexNodePlain/.style = {fill=#1, shape=circle, inner sep=0pt, minimum size=2pt, text=none}, - vertexNodePlain/.default=gray, - vertexPlain/labels/.style = { - vertexNode/.style={vertexNodePlain=##1}, - vertexLabel/.style={gray} - }, - vertexPlain/nolabels/.style = { - vertexNode/.style={vertexNodePlain=##1}, - vertexLabel/.style={text=none} - }, - vertexPlain/.style = vertexPlain/#1, - vertexPlain/.default=labels -} -\tikzset{ - vertexNodeNormal/.style = {fill=#1, shape=circle, inner sep=0pt, minimum size=4pt, text=none}, - vertexNodeNormal/.default = blue, - vertexNormal/labels/.style = { - vertexNode/.style={vertexNodeNormal=##1}, - vertexLabel/.style={blue} - }, - vertexNormal/nolabels/.style = { - vertexNode/.style={vertexNodeNormal=##1}, - vertexLabel/.style={text=none} - }, - vertexNormal/.style = vertexNormal/#1, - vertexNormal/.default=labels -} -\tikzset{ - vertexNodeBallShading/pdf/.style = {ball color=#1}, - vertexNodeBallShading/svg/.style = {fill=#1}, - vertexNodeBallShading/.code = {% Conditional shading depending whether we want pdf or svg output - \if\texforht - \tikzset{vertexNodeBallShading/svg=#1!90!black} - \else - \tikzset{vertexNodeBallShading/pdf=#1} - \fi - }, - vertexNodeBall/.style = {shape=circle, vertexNodeBallShading=#1, inner sep=2pt, outer sep=0pt, minimum size=3pt, font=\tiny}, - vertexNodeBall/.default = white, - vertexBall/labels/.style = { - vertexNode/.style={vertexNodeBall=##1, text=black}, - vertexLabel/.style={text=none} - }, - vertexBall/nolabels/.style = { - vertexNode/.style={vertexNodeBall=##1, text=none}, - vertexLabel/.style={text=none} - }, - vertexBall/.style = vertexBall/#1, - vertexBall/.default=labels -} -\tikzset{ - vertexStyle/.style={vertexNormal=#1}, - vertexStyle/.default = labels -} - - -% 1) optional: colour of vertex -% 2) position of the vertex -% 3) relative position of the node -% 4) name of the vertex -\newcommand{\vertexLabelR}[4][]{ - \ifthenelse{ \equal{#1}{} } - { \node[vertexNode] (#2 name) at (#2) {#4}; } - { \node[vertexNode=#1] (#2 name) at (#2) {#4}; } - \node[vertexLabel, #3] at (#2) {#4}; -} -% 1) optional: colour of vertex -% 2) position of the vertex -% 3) absolute position of the node -% 4) name of the vertex -\newcommand{\vertexLabelA}[4][]{ - \ifthenelse{ \equal{#1}{} } - { \node[vertexNode] (#2 name) at (#2) {#4}; } - { \node[vertexNode=#1] (#2 name) at (#2) {#4}; } - \node[vertexLabel] at (#3) {#4}; -} - - -% Edge styles -% If you have trouble with the double-lines overlapping, this might (?) help: -% https://tex.stackexchange.com/questions/288159/closing-the-ends-of-double-line-in-tikz -\newcommand{\edgeLabelColor}{blue!20!white} -\tikzset{ - edgeLineNone/.style = {draw=none}, - edgeLineNone/.default=black, - edgeNone/labels/.style = { - edge/.style = {edgeLineNone=##1}, - edgeLabel/.style = {fill=\edgeLabelColor,font=\small} - }, - edgeNone/nolabels/.style = { - edge/.style = {edgeLineNone=##1}, - edgeLabel/.style = {text=none} - }, - edgeNone/.style = edgeNone/#1, - edgeNone/.default = labels -} -\tikzset{ - edgeLinePlain/.style={line join=round, draw=#1}, - edgeLinePlain/.default=black, - edgePlain/labels/.style = { - edge/.style={edgeLinePlain=##1}, - edgeLabel/.style={fill=\edgeLabelColor,font=\small} - }, - edgePlain/nolabels/.style = { - edge/.style={edgeLinePlain=##1}, - edgeLabel/.style={text=none} - }, - edgePlain/.style = edgePlain/#1, - edgePlain/.default = labels -} -\tikzset{ - edgeLineDouble/.style = {very thin, double=#1, double distance=.8pt, line join=round}, - edgeLineDouble/.default=gray!90!white, - edgeDouble/labels/.style = { - edge/.style = {edgeLineDouble=##1}, - edgeLabel/.style = {fill=\edgeLabelColor,font=\small} - }, - edgeDouble/nolabels/.style = { - edge/.style = {edgeLineDouble=##1}, - edgeLabel/.style = {text=none} - }, - edgeDouble/.style = edgeDouble/#1, - edgeDouble/.default = labels -} -\tikzset{ - edgeStyle/.style = {edgePlain=#1}, - edgeStyle/.default = labels -} - -% Face styles -% Here we have an exception - the style face is always defined. -% -\newcommand{\faceColorY}{yellow!60!white} % yellow -\newcommand{\faceColorB}{blue!60!white} % blue -\newcommand{\faceColorC}{cyan!60} % cyan -\newcommand{\faceColorR}{red!60!white} % red -\newcommand{\faceColorG}{green!60!white} % green -\newcommand{\faceColorO}{orange!50!yellow!70!white} % orange - -% define default face colour (and default swap colour) -\newcommand{\faceColor}{\faceColorY} -\newcommand{\faceColorSwap}{\faceColorC} - -% define secondary default colours (to use in a single section) -\newcommand{\faceColorFirst}{green!40!white} -\newcommand{\faceColorSecond}{gray!15!white} -\newcommand{\faceColorThird}{red!17!white} -\newcommand{\faceColorFourth}{olive!20!white} - -\tikzset{ - face/.style = {fill=#1}, - face/.default = \faceColor, - faceY/.style = {face=\faceColorY}, - faceB/.style = {face=\faceColorB}, - faceC/.style = {face=\faceColorC}, - faceR/.style = {face=\faceColorR}, - faceG/.style = {face=\faceColorG}, - faceO/.style = {face=\faceColorO} -} -\tikzset{ - faceStyle/labels/.style = { - faceLabel/.style = {} - }, - faceStyle/nolabels/.style = { - faceLabel/.style = {text=none} - }, - faceStyle/.style = faceStyle/#1, - faceStyle/.default = labels -} -\tikzset{ face/.style={fill=#1} } -\tikzset{ faceSwap/.code= - \ifdefined\swapColors - \tikzset{face=\faceColorSwap} - \else - \tikzset{face=\faceColor} - \fi -} - - - -\usepackage{hyperref} - - -\begin{document} - -\begin{tikzpicture}[vertexBall, edgeDouble=nolabels, faceStyle=nolabels, scale=4] - - \coordinate (V1) at (1. , 0.); - \coordinate (V2) at (0.5000000010362841 , 0.8660254031861397); - \coordinate (V3) at (-0.4999999979274318 , 0.8660254049810364); - \coordinate (V4) at (-1. , 3.589793029841612e-09); - \coordinate (V5) at (-0.5000000041451365 , -0.866025401391243); - \coordinate (V6) at (0.4999999948185802 , -0.8660254067759328); - \coordinate (V7) at (0.8333333326424773 , -5.982988363998724e-10); - \coordinate (V8) at (0.3888888898100303 , 0.7216878361878827); - \coordinate (V9) at (-0.4351851836499495 , 0.6976315766169703); - \coordinate (V10) at (-0.8225308646325142 , -0.02806563506918342); - \coordinate (V11) at (-0.3870884810657467 , -0.7263654412350147); - \coordinate (V12) at (0.4077074718085085 , -0.698411178156174); - \draw[edge] (V1) -- node[edgeLabel] {$1$} (V6); - \draw[edge] (V1) -- node[edgeLabel] {$2$} (V2); - \draw[edge] (V2) -- node[edgeLabel] {$3$} (V3); - \draw[edge] (V3) -- node[edgeLabel] {$4$} (V4); - \draw[edge] (V4) -- node[edgeLabel] {$5$} (V5); - \draw[edge] (V5) -- node[edgeLabel] {$6$} (V6); - \draw[edge] (V1) -- node[edgeLabel] {$7$} (V7); - \draw[edge] (V6) -- node[edgeLabel] {$8$} (V12); - \draw[edge] (V7) -- node[edgeLabel] {$9$} (V12); - \draw[edge] (V2) -- node[edgeLabel] {$10$} (V8); - \draw[edge] (V7) -- node[edgeLabel] {$11$} (V8); - \draw[edge] (V3) -- node[edgeLabel] {$12$} (V9); - \draw[edge] (V8) -- node[edgeLabel] {$13$} (V9); - \draw[edge] (V4) -- node[edgeLabel] {$14$} (V10); - \draw[edge] (V9) -- node[edgeLabel] {$15$} (V10); - \draw[edge] (V5) -- node[edgeLabel] {$16$} (V11); - \draw[edge] (V10) -- node[edgeLabel] {$17$} (V11); - \draw[edge] (V11) -- node[edgeLabel] {$18$} (V12); - % Draw the faces - \vertexLabelR{V1}{left}{$1$} - \vertexLabelR{V2}{left}{$2$} - \vertexLabelR{V3}{left}{$3$} - \vertexLabelR{V4}{left}{$4$} - \vertexLabelR{V5}{left}{$5$} - \vertexLabelR{V6}{left}{$6$} - \vertexLabelR{V7}{left}{$7$} - \vertexLabelR{V8}{left}{$8$} - \vertexLabelR{V9}{left}{$9$} - \vertexLabelR{V10}{left}{$10$} - \vertexLabelR{V11}{left}{$11$} - \vertexLabelR{V12}{left}{$12$} - \end{tikzpicture} - -\end{document} - - From 053a2196a4ec99c2e4e654cc324c2b8b58b6d898 Mon Sep 17 00:00:00 2001 From: alice Date: Mon, 9 Sep 2024 21:14:36 +0200 Subject: [PATCH 24/44] bug fix in ConcatenationPaths --- gap/Paths/paths.gi | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/gap/Paths/paths.gi b/gap/Paths/paths.gi index f2060662..abf099dd 100644 --- a/gap/Paths/paths.gi +++ b/gap/Paths/paths.gi @@ -329,7 +329,7 @@ InstallMethod(ConcatenationOfPaths, "for a twisted polygonal complex and two ver if Last(VerticesAsList(path1))<>VerticesAsList(path2)[1] then Error("ConcatenationOfPaths: The last vertex of the first path has to be the first vertex of the second path"); fi; - edges:=Union(EdgesAsList(path1), EdgesAsList(path2)); + edges:=Concatenation(EdgesAsList(path1),EdgesAsList(path2)); return VertexEdgePathByEdges(surface, edges); end ); From 728b3c6e87bcdad1fe5fb5df2b82d57375fcc4c9 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Meike=20Wei=C3=9F?= Date: Tue, 10 Sep 2024 16:07:22 +0200 Subject: [PATCH 25/44] PackageInfo.g --- PackageInfo.g | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/PackageInfo.g b/PackageInfo.g index 94aa820c..ce5c2fd0 100644 --- a/PackageInfo.g +++ b/PackageInfo.g @@ -112,7 +112,7 @@ PackageDoc := rec( ), Dependencies := rec( - GAP := ">= 4.11", + GAP := ">= 4.12", NeededOtherPackages := [ [ "Grape", ">=4.8.2" ], [ "AttributeScheduler", ">=2018.08.03" ], ["Digraphs", ">=1.1.1"],[ "NautyTracesInterface", ">=0.2" ]], SuggestedOtherPackages := [ [ "GAPDoc", ">= 1.6" ], ["AutoDoc", ">=2019.05.20"], [ "IO", ">=2.2" ]], ExternalConditions := [ ], From 37f027f9f3d777a1383c3450dfdc40be48602760 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Meike=20Wei=C3=9F?= Date: Tue, 10 Sep 2024 19:05:47 +0200 Subject: [PATCH 26/44] changed github checks --- .github/workflows/CI.yml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/.github/workflows/CI.yml b/.github/workflows/CI.yml index 5c6ffe49..1091702b 100644 --- a/.github/workflows/CI.yml +++ b/.github/workflows/CI.yml @@ -25,8 +25,8 @@ jobs: matrix: gap-branch: - master + - stable-4.13 - stable-4.12 - - stable-4.11 steps: - uses: actions/checkout@v3 From 72858e1f468f28eaaa3a3aea0c9b7c77ff62b5bf Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Meike=20Wei=C3=9F?= Date: Wed, 11 Sep 2024 09:44:01 +0200 Subject: [PATCH 27/44] use cycle methods of Digraphs --- gap/Paths/paths.gd | 6 +- gap/Paths/paths.gi | 9 +- gap/PolygonalComplexes/graphs.gi | 296 ++++--------------------------- unit_tests/Test_Graphs.g | 2 +- 4 files changed, 45 insertions(+), 268 deletions(-) diff --git a/gap/Paths/paths.gd b/gap/Paths/paths.gd index 416e637c..4f297de6 100644 --- a/gap/Paths/paths.gd +++ b/gap/Paths/paths.gd @@ -604,8 +604,8 @@ DeclareAttribute( "AssociatedPolygonalComplex", IsVertexEdgePath ); #! gap> butterfly:=SimplicialSurfaceByDownwardIncidence( #! > [[1,2],[1,3],[2,3],[3,4],[1,4]],[[1,2,3],[2,4,5]]);; #! gap> AllClosedVertexEdgePaths(butterfly); -#! [ ( v1, E1, v2, E3, v3, E2, v1 ), ( v1, E1, v2, E3, v3, E4, v4, E5, v1 ), -#! ( v1, E5, v4, E4, v3, E2, v1 ) ] +#! [ ( v3, E2, v1, E5, v4, E4, v3 ), ( v3, E3, v2, E1, v1, E2, v3 ), +#! ( v3, E3, v2, E1, v1, E5, v4, E4, v3 ) ] #! @EndExampleSession #! @Returns a list of vertex-edge-paths #! @Arguments complex @@ -1305,7 +1305,7 @@ DeclareAttribute( "AllThreeWaistsOfComplex", IsTwistedPolygonalComplex); #! For example, consider the double tetrahedron from the start of section : #! @BeginExampleSession #! gap> AllWaistsOfComplex(doubleTetra); -#! [ ( v5, E10, v4, E7, v3, E8, v5 ), ( v5, E12, v6, E9, v3, E8, v5 ) ] +#! [ ( v4, E10, v5, E8, v3, E7, v4 ), ( v6, E12, v5, E8, v3, E9, v6 ) ] #! @EndExampleSession #! #! @Returns a set of closed vertex-edge-paths diff --git a/gap/Paths/paths.gi b/gap/Paths/paths.gi index f2060662..f067a577 100644 --- a/gap/Paths/paths.gi +++ b/gap/Paths/paths.gi @@ -406,20 +406,19 @@ InstallMethod(AllClosedVertexEdgePaths, "for a complex", # First calculate all cycles of the edge graph. # These cycles result in all closed vertex edge path of the complex except cycles of length two. graph:=EdgeDigraphsGraph(newComplex); - cycles:=__SIMPLICIAL_AllCyclesOfGraph(graph); + cycles:=DigraphAllUndirectedSimpleCircuits(graph); newCycles:=[]; # Compute for all cycles the corresponding edges in the complex. for c in cycles do - nodesOfCycle:=Flat(__SIMPLICIAL_NodesOfCycle(c)); # CommonEdgesOfVertices returns all edges that are possible between two vertices. edgeList:=[]; - for e in CommonEdgesOfVertices(newComplex, Last(nodesOfCycle),nodesOfCycle[1]) do + for e in CommonEdgesOfVertices(newComplex, Last(c),c[1]) do Add(edgeList,[e]); od; - for i in [1..Length(nodesOfCycle)-1] do - edges:=CommonEdgesOfVertices(newComplex, nodesOfCycle[i],nodesOfCycle[i+1]); + for i in [1..Length(c)-1] do + edges:=CommonEdgesOfVertices(newComplex, c[i],c[i+1]); newEdgeList:=[]; # Add the possibilities for the next edge to each edge list computed so far. diff --git a/gap/PolygonalComplexes/graphs.gi b/gap/PolygonalComplexes/graphs.gi index a31d9e9e..2c48a45a 100644 --- a/gap/PolygonalComplexes/graphs.gi +++ b/gap/PolygonalComplexes/graphs.gi @@ -803,272 +803,49 @@ BindGlobal("__SIMPLICIAL_AdjacencyMatrixFromList", return mat; end); +BindGlobal("__SIMPLICIAL_EdgesFromCycle", + function(digraph,cycle) -# The following function computes all cycles of a graph by: -# 1. Calculation of a cycle base (CyclesBasisOfGraph) by first computing a spanning tree and then adding each edge -# which is not in the tree. Each edge gives a different cycle named base cycles. -# 2. Iterate through all possible combinations of base cycles and combine them by applying XOR to the adjacency matrices. -# In this way you get all cycles of the graph. -BindGlobal("__SIMPLICIAL_AllCyclesOfGraph", - function(digraph) - - local CycleOnEdge,CycleBasisOfGraph,XORAdjacencyMatrices, - MultipleCyclesInMatrix,cyclebasis, allcycles, nullmat, mat, i, k, pos, neighs,c,cycle; - - # Find a cycle in the original graph all of whose edges are in - # tree except for the edge e. - CycleOnEdge := function( tree, root, e ) - - local cycle, i, path1, path2, l1, l2; - - if e[1] = e[2] then - Error("CycleOnEdge: edge is a loop"); - return false; - fi; - - # first find paths from the root to the two vertices of e - if root = e[1] then path1 := [root]; - else path1 := DigraphPath(tree, root, e[1])[1]; fi; - if root = e[2] then path2 := [root]; - else path2 := DigraphPath(tree, root, e[2])[1]; fi; - l1 := Length(path1); l2 := Length(path2); - - # now skip the common entries in the path - cycle := []; i := 1; - while i <= Minimum(l1,l2) and path1[i] = path2[i] do - i := i + 1; - od; - - cycle := [path1[i-1]]; - Append(cycle, path1{[i..l1]}); - Append(cycle, Reversed(path2{[i..l2]})); - - return __SIMPLICIAL_AdjacencyMatrixFromList(cycle,DigraphNrVertices(tree)); - end;; - - # This function computes a cycle basis for the undirected graph - # dig, which is assumed to be a symmetric digraph. - # The cycle Basis consists of lower triangular matrices whose - # entries are boolean lists. - CycleBasisOfGraph := function( dig ) - - local tree, dige, base, root, e; - - if not IsSymmetricDigraph(dig) then - Error("the digraph is assumed to be symmetric"); - fi; - - base := Set([]); - tree := UndirectedSpanningTree(dig); - dige := DigraphEdges(tree); - - root := DigraphVertices(dig)[1]; - - for e in DigraphEdges(dig) do - if not e in dige then - AddSet(base, CycleOnEdge(tree,root, e)); - fi; - od; - - - return base; - end;; - - # This method combines two adjacency matrices with the operator XOR. - XORAdjacencyMatrices := function( mat1, mat2 ) - - local j, res, nd; - - res :=[]; - for j in [1.. Length(mat1)] do - nd := IntersectionBlist(mat1[j],mat2[j]); - FlipBlist(nd); - res[j] := IntersectionBlist( UnionBlist(mat1[j],mat2[j]), nd ); - od; - - return res; - end;; - - cyclebasis := CycleBasisOfGraph( digraph ); - - if cyclebasis=[] then - return []; - fi; - - neighs := OutNeighbours(digraph); - allcycles := []; - - nullmat := XORAdjacencyMatrices(cyclebasis[1],cyclebasis[1]); - for k in [0..2^Length(cyclebasis)-1] do - # combine the matrices encoded by k - mat := nullmat; - i := k; - pos := 0; - while i>0 do - pos := pos + 1; - if i mod 2 <> 0 then - mat := XORAdjacencyMatrices(mat,cyclebasis[pos]); - fi; - i := Int(i/2); - od; + local edgesOfCycle, i, edge; - if SizeBlist(Flat(mat))<>0 then - for c in __SIMPLICIAL_NodesOfCycle(mat) do - cycle:=__SIMPLICIAL_AdjacencyMatrixFromList(c,Length(mat)); - if not cycle in allcycles then - Add(allcycles,cycle); - fi; - od; + edgesOfCycle:=[]; + for i in [1..Length(cycle)] do + if i0 then - blocked[u]:=blocked[u]-1; - fi; - od; - return blocked; - end; - - # Computes the degree labeling - DegreeLabeling:=function(digraph) - local degree,color,labeling,v,u,i,minDegree,x; - - degree:=List(DigraphVertices(digraph),i->0); - color:=List(DigraphVertices(digraph),i->false); - labeling:=List(DigraphVertices(digraph),i->0); - degree:=List(DigraphVertices(digraph),i->OutDegreeOfVertex(digraph,i)); - - for i in [1..DigraphNrVertices(digraph)] do - minDegree:=DigraphNrVertices(digraph); - for x in DigraphVertices(digraph) do - if color[x]=false and degree[x]key and blocked[v]=1 then - extendedPath:=Concatenation(path,[v]); - if IsDigraphEdge(digraph,v,First(path)) then - Add(C,extendedPath); - else - data:=CCExtension(digraph,extendedPath,C,key,blocked); - C:=data[1]; - blocked:=data[2]; - fi; - fi; - od; - blocked:=UnblockNeighbours(digraph,Last(path),blocked); - return [C,blocked]; - end; - - SetDigraphVertexLabels(digraph,DegreeLabeling(digraph)); - temp:=Triplets(digraph); - T:=temp[1]; - C:=temp[2]; - blocked:=List(DigraphVertices(digraph),i->0); - while T<>[] do - triple:=Remove(T); - blocked:=BlockNeighbours(digraph,triple[2],blocked); - temp:=CCExtension(digraph,triple,C,DigraphVertexLabel(digraph,triple[2]),blocked); - C:=temp[1]; - blocked:=temp[2]; - blocked:=UnblockNeighbours(digraph,triple[2],blocked); - od; - return C; - - end + end ); BindGlobal("__SIMPLICIAL_IsNonSeparating", function(digraph,cycle) - local edgesOfCycle, e, digraphRemoved; + local edgesOfCycle, e, digraphRemoved; - if not IsSymmetricDigraph(digraph) then - return false; - fi; + if not IsSymmetricDigraph(digraph) then + return false; + fi; - edgesOfCycle:=[]; - for e in __SIMPLICIAL_EdgesFromAdjacencyMat(cycle) do - Append(edgesOfCycle,[e,Reversed(e)]); - od; + edgesOfCycle:=__SIMPLICIAL_EdgesFromCycle(digraph,cycle); + #for e in __SIMPLICIAL_EdgesFromAdjacencyMat(cycle) do + # Append(edgesOfCycle,[e,Reversed(e)]); + #od; - digraphRemoved:=DigraphRemoveEdges(digraph,edgesOfCycle); - if IsConnectedDigraph(digraphRemoved) then - return true; - else - return false; - fi; + digraphRemoved:=DigraphRemoveEdges(digraph,edgesOfCycle); + if IsConnectedDigraph(digraphRemoved) then + return true; + else + return false; + fi; - end + end ); InstallOtherMethod(AllSimplicialSurfacesOfDigraph,"for a digraph", @@ -1089,17 +866,18 @@ InstallMethod(AllSimplicialSurfacesOfDigraph,"for a digraph and a Boolean", Error("SimplicialSurfaceOfDigraph: Given digraph has to be simple, symmetric and connected"); fi; if vertexFaithful then - allCycles:=List(__SIMPLICIAL_AllChordlessCyclesOfGraph(digraph),c->__SIMPLICIAL_AdjacencyMatrixFromList(c,DigraphNrVertices(digraph))); - allCycles:=Filtered(allCycles,c->__SIMPLICIAL_IsNonSeparating(digraph,c)); + #allCycles:=List(DigraphAllChordlessCycles(digraph),c->__SIMPLICIAL_AdjacencyMatrixFromList(c,DigraphNrVertices(digraph))); + allCycles:=DigraphAllChordlessCycles(digraph); + allCycles:=Filtered(allCycles,c->__SIMPLICIAL_IsNonSeparating(digraph,c)); else - allCycles:=__SIMPLICIAL_AllCyclesOfGraph(digraph); + allCycles:=DigraphAllUndirectedSimpleCircuits(digraph); fi; edgesOfGraph:=Filtered(DigraphEdges(digraph),e->not IsSortedList(e)); edgesOfCycles:=[]; for cycle in [1..Length(allCycles)] do; - edgesOfCycles[cycle]:=List(__SIMPLICIAL_EdgesFromAdjacencyMat(allCycles[cycle]),e->Position(edgesOfGraph,e)); + edgesOfCycles[cycle]:=List(__SIMPLICIAL_EdgesFromCycle(digraph,allCycles[cycle]),e->Position(edgesOfGraph,e)); od; possibleCyclesPairs:=[]; @@ -1195,10 +973,10 @@ InstallMethod(AllSimplicialSurfacesOfDigraph,"for a digraph and a Boolean", # if we search vertex-faithful simplicial surfaces all cycles of length three and four have to be part of the resulting cycle combination if vertexFaithful and IsIsomorphicDigraph(graph, CompleteDigraph(4)) then - smallCy:=Filtered([1..Length(allCycles)], c->SizeBlist(Flat(allCycles[c]))<4); + smallCy:=Filtered(allCycles, c->Length(c)<4); smallCy:=BlistList([1..Length(allCycles)],smallCy); elif vertexFaithful then - smallCy:=Filtered([1..Length(allCycles)], c->SizeBlist(Flat(allCycles[c]))<5); + smallCy:=Filtered(allCycles, c->Length(c)<5); smallCy:=BlistList([1..Length(allCycles)],smallCy); fi; @@ -1257,7 +1035,7 @@ InstallMethod(AllSimplicialSurfacesOfDigraph,"for a digraph and a Boolean", umbrellaDesk:=[]; for cycle in ListBlist([1..Length(vertexCycleComb)],vertexCycleComb) do - Add(umbrellaDesk,NodesOfCycle(allCycles[cycle])); + Add(umbrellaDesk,CycleFromList(allCycles[cycle])); od; face:=SimplicialSurfaceByUmbrellaDescriptor(umbrellaDesk); diff --git a/unit_tests/Test_Graphs.g b/unit_tests/Test_Graphs.g index e1b691a4..0eb2a73b 100644 --- a/unit_tests/Test_Graphs.g +++ b/unit_tests/Test_Graphs.g @@ -69,7 +69,7 @@ if IsPackageMarkedForLoading( "Digraphs", ">=0.10.1" ) then list1:=AllSimplicialSurfacesOfDigraph(dig,true); Assert(0,Length(list1)=1); Assert(0,IsIsomorphic(list1[1],surface)); - + list2:=AllSimplicialSurfacesOfDigraph(dig); Assert(0, Length(Filtered(list2,IsVertexFaithful))=1); Assert(0,IsIsomorphic(Filtered(list2,IsVertexFaithful)[1],surface)); From 3547e090110569655d465c838a79ec114af2397d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Meike=20Wei=C3=9F?= Date: Wed, 11 Sep 2024 10:10:56 +0200 Subject: [PATCH 28/44] added package requirement --- gap/Paths/paths.gi | 4 ++ gap/PolygonalComplexes/graphs.gi | 117 +------------------------------ 2 files changed, 7 insertions(+), 114 deletions(-) diff --git a/gap/Paths/paths.gi b/gap/Paths/paths.gi index f067a577..5fe355e1 100644 --- a/gap/Paths/paths.gi +++ b/gap/Paths/paths.gi @@ -391,6 +391,7 @@ InstallMethod(ShiftCyclicPath, end ); +if IsPackageMarkedForLoading( "Digraphs", ">=1.9.0" ) then InstallMethod(AllClosedVertexEdgePaths, "for a complex", [IsTwistedPolygonalComplex], function(complex) @@ -443,6 +444,7 @@ InstallMethod(AllClosedVertexEdgePaths, "for a complex", return Union(newCycles,AllTwoWaistsOfComplex(complex)); end ); +fi; ####################################### ## @@ -1003,6 +1005,7 @@ InstallMethod( AllThreeWaistsOfComplex, "for a twisted polygonal complex", end ); +if IsPackageMarkedForLoading( "Digraphs", ">=1.9.0" ) then InstallMethod(AllWaistsOfComplex, "for a twisted polygonal complex", [IsTwistedPolygonalComplex], function(complex) @@ -1019,6 +1022,7 @@ InstallMethod(AllWaistsOfComplex, "for a twisted polygonal complex", return waists; end ); +fi; ## ## End of waists ## diff --git a/gap/PolygonalComplexes/graphs.gi b/gap/PolygonalComplexes/graphs.gi index 2c48a45a..c038db10 100644 --- a/gap/PolygonalComplexes/graphs.gi +++ b/gap/PolygonalComplexes/graphs.gi @@ -722,87 +722,7 @@ InstallMethod( OnEdgeFacePaths, ## ## All Surfaces Of A Graph ## - -# Calculate from a adjacency matrix the corresponding edges -BindGlobal( "__SIMPLICIAL_EdgesFromAdjacencyMat", - function(mat) - local edges, i, j; - - edges := Set([]); - for j in [1 .. Length(mat)] do - edges := Union(edges, List(ListBlist([1..j],mat[j]), i-> [j,i] )); - od; - - return edges; -end); - -# The function converts a boolean list describing one or more cycles -# into lists of nodes of the cycles. -BindGlobal("__SIMPLICIAL_NodesOfCycle", - function(cycle) - local edges,firstNod,actualNod,nodes,found,e,cycles; - - edges:=__SIMPLICIAL_EdgesFromAdjacencyMat(cycle); - cycles:=[]; - # We have to use each edge exactly one time - while edges<>[] do - firstNod:=(edges[1])[1]; - actualNod:=(edges[1])[2]; - Remove(edges,1); - nodes:=[actualNod]; - # Walk along the cycle - while actualNod<>firstNod do - found:=false; - for e in edges do - if found=false then - if e[1]=actualNod then - actualNod:=e[2]; - Add(nodes,actualNod); - Remove(edges,Position(edges,e)); - found:=true; - elif e[2]=actualNod then - actualNod:=e[1]; - Add(nodes,actualNod); - Remove(edges,Position(edges,e)); - found:=true; - fi; - fi; - od; - od; - Add(cycles,nodes); - od; - return cycles; -end); - -# We want to store graphs as adjacency matrices. This function -# turns a cycle into a boolean lower triangular matrix. -BindGlobal("__SIMPLICIAL_AdjacencyMatrixFromList", - function(cycle, n) - - local mat, i, j, k; - - mat := []; - for i in [ 1 .. n] do - mat[i] := BlistList([1..i],[]); - od; - - for i in [ 1 .. Length(cycle)] do - if i < Length(cycle) then - j := cycle[i+1]; - else - j := cycle[1]; - fi; - k := cycle[i]; - if k < j then - mat[j]:= UnionBlist(mat[j],BlistList( [1..j],[k] )); - elif j < k then - mat[k] := UnionBlist(mat[k],BlistList([1..k],[j])); - fi; - od; - - return mat; -end); - +if IsPackageMarkedForLoading( "Digraphs", ">=1.9.0" ) then BindGlobal("__SIMPLICIAL_EdgesFromCycle", function(digraph,cycle) @@ -834,9 +754,6 @@ BindGlobal("__SIMPLICIAL_IsNonSeparating", fi; edgesOfCycle:=__SIMPLICIAL_EdgesFromCycle(digraph,cycle); - #for e in __SIMPLICIAL_EdgesFromAdjacencyMat(cycle) do - # Append(edgesOfCycle,[e,Reversed(e)]); - #od; digraphRemoved:=DigraphRemoveEdges(digraph,edgesOfCycle); if IsConnectedDigraph(digraphRemoved) then @@ -860,13 +777,12 @@ InstallMethod(AllSimplicialSurfacesOfDigraph,"for a digraph and a Boolean", function(digraph,vertexFaithful) local allCycles,edgesOfGraph, faces,edgesOfCycles,CyclesOfEdges,cyclesOfEdges,FindSurface,FindCycleComb, - NodesOfCycle,cycle,cyclePair,IsPartOf,possibleCyclesPairs,commonEdges,Possible,e; + cycle,cyclePair,IsPartOf,possibleCyclesPairs,commonEdges,Possible,e; if IsMultiDigraph(digraph) or DigraphHasLoops(digraph) or not IsSymmetricDigraph(digraph) or not IsConnectedDigraph(digraph) then Error("SimplicialSurfaceOfDigraph: Given digraph has to be simple, symmetric and connected"); fi; if vertexFaithful then - #allCycles:=List(DigraphAllChordlessCycles(digraph),c->__SIMPLICIAL_AdjacencyMatrixFromList(c,DigraphNrVertices(digraph))); allCycles:=DigraphAllChordlessCycles(digraph); allCycles:=Filtered(allCycles,c->__SIMPLICIAL_IsNonSeparating(digraph,c)); else @@ -930,34 +846,6 @@ InstallMethod(AllSimplicialSurfacesOfDigraph,"for a digraph and a Boolean", return true; end;; - # The function computes for a given cycle the sequence of nodes of the cycle. - NodesOfCycle:=function(cycle) - local edges,firstNod,actualNode,nodes,e; - - edges:=__SIMPLICIAL_EdgesFromAdjacencyMat(cycle); - - firstNod:=(edges[1])[1]; - actualNode:=(edges[1])[2]; - nodes:=[actualNode]; - Remove(edges,1); - - while actualNode<>firstNod do - for e in edges do - if e[1]=actualNode then - actualNode:=e[2]; - Add(nodes,actualNode); - Remove(edges,Position(edges,e)); - elif e[2]=actualNode then - actualNode:=e[1]; - Add(nodes,actualNode); - Remove(edges,Position(edges,e)); - fi; - od; - od; - - return CycleFromList(nodes); - end;; - IsPartOf:=function(face,faces) local f; for f in faces do @@ -1155,3 +1043,4 @@ InstallMethod(AllSimplicialSurfacesOfDigraph,"for a digraph and a Boolean", end ); +fi; \ No newline at end of file From f16a73c62015f74fde0c366a52308f9677064102 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Meike=20Wei=C3=9F?= Date: Wed, 11 Sep 2024 10:33:23 +0200 Subject: [PATCH 29/44] added package requirement in tests --- unit_tests/Test_Graphs.g | 2 ++ 1 file changed, 2 insertions(+) diff --git a/unit_tests/Test_Graphs.g b/unit_tests/Test_Graphs.g index 0eb2a73b..d5417cd0 100644 --- a/unit_tests/Test_Graphs.g +++ b/unit_tests/Test_Graphs.g @@ -61,7 +61,9 @@ if IsPackageMarkedForLoading( "Digraphs", ">=0.10.1" ) then od; Assert(0, Set(DigraphEdges(digButterfly))=Set(Filtered(Union(FacesOfEdges(butterfly),reversedButterfly),i->Length(i)=2))); end); +fi; +if IsPackageMarkedForLoading( "Digraphs", ">=1.9.0" ) then BindGlobal( "__SIMPLICIAL_Test_AllSimplicialSurfacesOfDigraph", function() local dig, surface, list1, list2; surface:=SimplicialSurfaceByVerticesInFaces([[1,4,5],[1,4,6],[1,5,7],[1,6,7],[2,3,5],[2,3,6],[2,4,5],[2,4,6],[3,5,7],[3,6,7]]); From 0c478811ef266756ca317aab5225c7de3120fa27 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Meike=20Wei=C3=9F?= Date: Wed, 11 Sep 2024 10:46:45 +0200 Subject: [PATCH 30/44] added requirement --- unit_tests/test_main.g | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/unit_tests/test_main.g b/unit_tests/test_main.g index 9099608d..69149f02 100644 --- a/unit_tests/test_main.g +++ b/unit_tests/test_main.g @@ -61,7 +61,9 @@ BindGlobal( "SIMPLICIAL_TestAll", function() __SIMPLICIAL_Test_EdgeNautyGraph(); __SIMPLICIAL_Test_FaceDigraphsGraph(); __SIMPLICIAL_Test_FaceNautyGraph(); - __SIMPLICIAL_Test_AllSimplicialSurfacesOfDigraph(); + if IsPackageMarkedForLoading( "Digraphs", ">=0.10.1" ) then + __SIMPLICIAL_Test_AllSimplicialSurfacesOfDigraph(); + fi; __SIMPLICIAL_Test_FaceTwoColouring(); From f532c7ddc832bff8408c9d9433d92244f6d7d93d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Meike=20Wei=C3=9F?= Date: Wed, 11 Sep 2024 10:54:41 +0200 Subject: [PATCH 31/44] corrected wrong package version --- unit_tests/test_main.g | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/unit_tests/test_main.g b/unit_tests/test_main.g index 69149f02..6744607b 100644 --- a/unit_tests/test_main.g +++ b/unit_tests/test_main.g @@ -61,7 +61,7 @@ BindGlobal( "SIMPLICIAL_TestAll", function() __SIMPLICIAL_Test_EdgeNautyGraph(); __SIMPLICIAL_Test_FaceDigraphsGraph(); __SIMPLICIAL_Test_FaceNautyGraph(); - if IsPackageMarkedForLoading( "Digraphs", ">=0.10.1" ) then + if IsPackageMarkedForLoading( "Digraphs", ">=1.9.0" ) then __SIMPLICIAL_Test_AllSimplicialSurfacesOfDigraph(); fi; From f4d62f89fb30881a36c8827d2e4fdfe74def1f59 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Meike=20Wei=C3=9F?= Date: Wed, 11 Sep 2024 11:13:49 +0200 Subject: [PATCH 32/44] no automatic generated tests --- gap/Paths/paths.gd | 8 ++++---- gap/PolygonalComplexes/graphs.gd | 8 ++++---- 2 files changed, 8 insertions(+), 8 deletions(-) diff --git a/gap/Paths/paths.gd b/gap/Paths/paths.gd index 416e637c..b3b72466 100644 --- a/gap/Paths/paths.gd +++ b/gap/Paths/paths.gd @@ -600,13 +600,13 @@ DeclareAttribute( "AssociatedPolygonalComplex", IsVertexEdgePath ); #! #! Image omitted in terminal text #! -#! @BeginExampleSession +#! @BeginLogSession #! gap> butterfly:=SimplicialSurfaceByDownwardIncidence( #! > [[1,2],[1,3],[2,3],[3,4],[1,4]],[[1,2,3],[2,4,5]]);; #! gap> AllClosedVertexEdgePaths(butterfly); #! [ ( v1, E1, v2, E3, v3, E2, v1 ), ( v1, E1, v2, E3, v3, E4, v4, E5, v1 ), #! ( v1, E5, v4, E4, v3, E2, v1 ) ] -#! @EndExampleSession +#! @EndLogSession #! @Returns a list of vertex-edge-paths #! @Arguments complex DeclareOperation( "AllClosedVertexEdgePaths", [IsTwistedPolygonalComplex] ); @@ -1303,10 +1303,10 @@ DeclareAttribute( "AllThreeWaistsOfComplex", IsTwistedPolygonalComplex); #! The definition of a waist is given at the beginning of section . #! #! For example, consider the double tetrahedron from the start of section : -#! @BeginExampleSession +#! @BeginLogSession #! gap> AllWaistsOfComplex(doubleTetra); #! [ ( v5, E10, v4, E7, v3, E8, v5 ), ( v5, E12, v6, E9, v3, E8, v5 ) ] -#! @EndExampleSession +#! @EndLogSession #! #! @Returns a set of closed vertex-edge-paths #! @Arguments complex diff --git a/gap/PolygonalComplexes/graphs.gd b/gap/PolygonalComplexes/graphs.gd index 95be24f0..8b168352 100644 --- a/gap/PolygonalComplexes/graphs.gd +++ b/gap/PolygonalComplexes/graphs.gd @@ -441,17 +441,17 @@ DeclareAttribute( "FaceNautyGraph", IsPolygonalComplex ); #! Image omitted in terminal text #! #! -#! @BeginExampleSession +#! @BeginLogSession #! gap> digraph:=CompleteDigraph(4);; #! gap> tet1 := AllSimplicialSurfacesOfDigraph(digraph,true); #! [ simplicial surface (4 vertices, 6 edges, and 4 faces) ] #! gap> IsIsomorphic(tet1[1],Tetrahedron()); #! true -#! @EndExampleSession +#! @EndLogSession #! #! So the only vertex-faithful simplicial surface of the digraph is the tetrahedron. #! But there is another simplicial surface, which is not vertex-faithful: -#! @BeginExampleSession +#! @BeginLogSession #! gap> list := AllSimplicialSurfacesOfDigraph(digraph,false); #! [ simplicial surface (4 vertices, 6 edges, and 4 faces), #! simplicial surface (3 vertices, 6 edges, and 4 faces)] @@ -459,7 +459,7 @@ DeclareAttribute( "FaceNautyGraph", IsPolygonalComplex ); #! [ simplicial surface (4 vertices, 6 edges, and 4 faces) ] #! gap> IsIsomorphic(tet2[1],Tetrahedron()); #! true -#! @EndExampleSession +#! @EndLogSession #! #! Since it takes a long time to compute all cycles, you should only call the method for digraphs with twelve or less nodes for vertexfaithful false. #! For vertexfaithful true, the method needs to consider only chordless and non-separating cycles. This makes the method fast for digraphs up to 28 nodes. From 067e9492d2706b8afa8af3f3b5f00bc3d6a06359 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Meike=20Wei=C3=9F?= Date: Wed, 11 Sep 2024 11:35:57 +0200 Subject: [PATCH 33/44] changed ExampleSession to LogSession --- gap/PolygonalComplexes/graphs.gd | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/gap/PolygonalComplexes/graphs.gd b/gap/PolygonalComplexes/graphs.gd index 95be24f0..ed76b65b 100644 --- a/gap/PolygonalComplexes/graphs.gd +++ b/gap/PolygonalComplexes/graphs.gd @@ -451,7 +451,7 @@ DeclareAttribute( "FaceNautyGraph", IsPolygonalComplex ); #! #! So the only vertex-faithful simplicial surface of the digraph is the tetrahedron. #! But there is another simplicial surface, which is not vertex-faithful: -#! @BeginExampleSession +#! @BeginLogSession #! gap> list := AllSimplicialSurfacesOfDigraph(digraph,false); #! [ simplicial surface (4 vertices, 6 edges, and 4 faces), #! simplicial surface (3 vertices, 6 edges, and 4 faces)] @@ -459,7 +459,7 @@ DeclareAttribute( "FaceNautyGraph", IsPolygonalComplex ); #! [ simplicial surface (4 vertices, 6 edges, and 4 faces) ] #! gap> IsIsomorphic(tet2[1],Tetrahedron()); #! true -#! @EndExampleSession +#! @EndLogSession #! #! Since it takes a long time to compute all cycles, you should only call the method for digraphs with twelve or less nodes for vertexfaithful false. #! For vertexfaithful true, the method needs to consider only chordless and non-separating cycles. This makes the method fast for digraphs up to 28 nodes. From 955957c608056d5f7bcf0e59c8c61859e84f000c Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Meike=20Wei=C3=9F?= Date: Wed, 11 Sep 2024 11:43:08 +0200 Subject: [PATCH 34/44] confused --- gap/PolygonalComplexes/graphs.gd | 1 - 1 file changed, 1 deletion(-) diff --git a/gap/PolygonalComplexes/graphs.gd b/gap/PolygonalComplexes/graphs.gd index 8b168352..73d6d30c 100644 --- a/gap/PolygonalComplexes/graphs.gd +++ b/gap/PolygonalComplexes/graphs.gd @@ -448,7 +448,6 @@ DeclareAttribute( "FaceNautyGraph", IsPolygonalComplex ); #! gap> IsIsomorphic(tet1[1],Tetrahedron()); #! true #! @EndLogSession -#! #! So the only vertex-faithful simplicial surface of the digraph is the tetrahedron. #! But there is another simplicial surface, which is not vertex-faithful: #! @BeginLogSession From 5bf45794d44de228e8ddaed02c6826ab8d455ab1 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Meike=20Wei=C3=9F?= Date: Wed, 11 Sep 2024 12:00:40 +0200 Subject: [PATCH 35/44] changed documentation --- gap/Paths/paths.gd | 35 +++++++++++++++++++++-------------- 1 file changed, 21 insertions(+), 14 deletions(-) diff --git a/gap/Paths/paths.gd b/gap/Paths/paths.gd index e8cfd924..c3693517 100644 --- a/gap/Paths/paths.gd +++ b/gap/Paths/paths.gd @@ -1197,11 +1197,18 @@ DeclareAttribute( "ViewInformation", IsEdgeFacePath ); #! @Section Waists #! @SectionLabel Waists #! This section deals with a specific type of closed vertex-edge-paths, namely waists. -#! A n-waist is a closed vertex-edge path of length n such that all edges are inner and no two are incident to the same face. -#! Moreover, a simplicial surface X can only have a n-waist for n>3 if X does not have a 3-waist and the vertex-edge path describing the n-waist must be distance-faithful. -#! A closed vertex-edge path P is distance-faithful if for any two vertices of P at least one shortest edge path between them is contained in P. +#! In order to introduce the definition of a waist of a simplicial surface, we first +#! present the definition of a distance-faithful path. Here, a closed edge path P of +#! a given simplicial surface is called distance-faithful if for any two vertices of the +#! path P at least one shortest edge path between them is contained in P. +#! Using the above notion we introduce waists of simplicial surfaces. +#! Let therefore n be a natural number. If n satisfies 2<=n<=3, +#! then an n-waist of a given simplicial surface is defined as a circular edge +#! path of length n such that all edges are inner and no two are incident to the same face. +#! Moreover, if the given simplicial surface is closed without 3-waists and the inequality +#! n>=4 holds, we define an n-waist as a closed distance-faithful edge path of length n. #! -#! This will be illustrated on the following double tetrahedron: +#! This will be illustrated on the following simplicial surface constructed by three tetrahedra: #! #! <img src="./images/_Wrapper_Image_Example3Waist-1.svg"> </img> #! @@ -1214,7 +1221,7 @@ DeclareAttribute( "ViewInformation", IsEdgeFacePath ); #! Image omitted in terminal text #! #! @BeginExampleSession -#! gap> doubleTetra:=SimplicialSurfaceByVerticesInFaces( +#! gap> tripleTetra:=SimplicialSurfaceByVerticesInFaces( #! > [[1,3,5],[2,5,6],[2,3,5],[2,3,6],[1,4,5],[3,4,6],[1,3,4],[4,5,6]]);; #! @EndExampleSession @@ -1223,17 +1230,17 @@ DeclareAttribute( "ViewInformation", IsEdgeFacePath ); #! Return whether the given path vertexEdgePath is a waist in complex. #! The definition of a waist is given at the beginning of section . #! -#! For example, consider the double tetrahedron from the start of section . +#! For example, consider the simplicial surface from the start of section . #! The path around a face is not a waist: #! @BeginExampleSession -#! gap> path:=VertexEdgePathByEdges(doubleTetra,[1,3,8]);; -#! gap> IsWaist(doubleTetra, path); +#! gap> path:=VertexEdgePathByEdges(triple,[1,3,8]);; +#! gap> IsWaist(tripleTetra, path); #! false #! @EndExampleSession #! A path of length three, where the edges are pairwise incident to two different faces, is a waist: #! @BeginExampleSession -#! gap> waist:=VertexEdgePathByEdges(doubleTetra,[7,8,10]);; -#! gap> IsWaist(doubleTetra, waist); +#! gap> waist:=VertexEdgePathByEdges(tripleTetra,[7,8,10]);; +#! gap> IsWaist(tripleTetra, waist); #! true #! @EndExampleSession #! @@ -1284,9 +1291,9 @@ DeclareAttribute( "AllTwoWaistsOfComplex", IsTwistedPolygonalComplex); #! vertices so that there exist no face in complex that is incident to more #! than one of the visited edges. #! -#! For example, consider the double tetrahedron from the start of section : +#! For example, consider the simplicial surface from the start of section : #! @BeginExampleSession -#! gap> AllThreeWaistsOfComplex(doubleTetra); +#! gap> AllThreeWaistsOfComplex(tripleTetra); #! [ ( v4, E7, v3, E8, v5, E10, v4 ), ( v5, E8, v3, E9, v6, E12, v5 ) ] #! @EndExampleSession #! The tetrahedron does not have any 3-waist: @@ -1305,9 +1312,9 @@ DeclareAttribute( "AllThreeWaistsOfComplex", IsTwistedPolygonalComplex); #! Return the set of all waists contained in the given polygonal complex complex. #! The definition of a waist is given at the beginning of section . #! -#! For example, consider the double tetrahedron from the start of section : +#! For example, consider the simplicial surface from the start of section : #! @BeginExampleSession -#! gap> AllWaistsOfComplex(doubleTetra); +#! gap> AllWaistsOfComplex(tripleTetra); #! [ ( v4, E7, v3, E8, v5, E10, v4 ), ( v5, E8, v3, E9, v6, E12, v5 ) ] #! gap> AllWaistsOfComplex(Octahedron()); #! [ ( v1, E1, v2, E7, v6, E11, v4, E3, v1 ), ( v3, E2, v1, E4, v5, E12, v6, E9, v3 ), From 714a6ed38fa52cc6af248080a3af57c62217b1ed Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Meike=20Wei=C3=9F?= Date: Wed, 11 Sep 2024 12:12:10 +0200 Subject: [PATCH 36/44] corrected error --- gap/Paths/paths.gd | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/gap/Paths/paths.gd b/gap/Paths/paths.gd index c3693517..a8c5b602 100644 --- a/gap/Paths/paths.gd +++ b/gap/Paths/paths.gd @@ -1202,11 +1202,11 @@ DeclareAttribute( "ViewInformation", IsEdgeFacePath ); #! a given simplicial surface is called distance-faithful if for any two vertices of the #! path P at least one shortest edge path between them is contained in P. #! Using the above notion we introduce waists of simplicial surfaces. -#! Let therefore n be a natural number. If n satisfies 2<=n<=3, +#! Let therefore n be a natural number. If n is equal to 2 or 3, #! then an n-waist of a given simplicial surface is defined as a circular edge #! path of length n such that all edges are inner and no two are incident to the same face. -#! Moreover, if the given simplicial surface is closed without 3-waists and the inequality -#! n>=4 holds, we define an n-waist as a closed distance-faithful edge path of length n. +#! Moreover, if the given simplicial surface is closed without 3-waists and n is at least 4, +#! then we define an n-waist as a closed distance-faithful edge path of length n. #! #! This will be illustrated on the following simplicial surface constructed by three tetrahedra: #! From c8915fc6a08502ae19e41e50b8c2c2d11d30e0df Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Meike=20Wei=C3=9F?= Date: Wed, 11 Sep 2024 12:21:04 +0200 Subject: [PATCH 37/44] fixed hopefully --- gap/Paths/paths.gd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/gap/Paths/paths.gd b/gap/Paths/paths.gd index 36ce1cba..f67d62f0 100644 --- a/gap/Paths/paths.gd +++ b/gap/Paths/paths.gd @@ -1233,7 +1233,7 @@ DeclareAttribute( "ViewInformation", IsEdgeFacePath ); #! For example, consider the simplicial surface from the start of section . #! The path around a face is not a waist: #! @BeginExampleSession -#! gap> path:=VertexEdgePathByEdges(triple,[1,3,8]);; +#! gap> path:=VertexEdgePathByEdges(tripleTetra,[1,3,8]);; #! gap> IsWaist(tripleTetra, path); #! false #! @EndExampleSession From 65a4bf6b6bf51f6e778d5e64538f06be1be5e4f6 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Meike=20Wei=C3=9F?= Date: Wed, 11 Sep 2024 12:38:22 +0200 Subject: [PATCH 38/44] added example --- gap/Paths/paths.gd | 7 +++++++ 1 file changed, 7 insertions(+) diff --git a/gap/Paths/paths.gd b/gap/Paths/paths.gd index f67d62f0..c906f4c6 100644 --- a/gap/Paths/paths.gd +++ b/gap/Paths/paths.gd @@ -1243,6 +1243,13 @@ DeclareAttribute( "ViewInformation", IsEdgeFacePath ); #! gap> IsWaist(tripleTetra, waist); #! true #! @EndExampleSession +#! The octahedron has a waist of length four: +#! @BeginExampleSession +#! gap> path:=VertexEdgePathByEdges(Octahedron(),[5,6,10,8]); +#! ( v3, E5, v2, E6, v5, E10, v4, E8, v3 ) +#! gap> IsWaist(Octahedron(),path); +#! true +#! @EndExampleSession #! #! @Returns true or false #! @Arguments complex, vertexEdgePath From 90f847b55599f62ef0c14ca3c99c6be821e8d742 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Meike=20Wei=C3=9F?= Date: Wed, 11 Sep 2024 13:03:26 +0200 Subject: [PATCH 39/44] changed doc --- gap/PolygonalComplexes/modification.gd | 11 ++++++++--- 1 file changed, 8 insertions(+), 3 deletions(-) diff --git a/gap/PolygonalComplexes/modification.gd b/gap/PolygonalComplexes/modification.gd index 48f8c05f..8c26ba03 100755 --- a/gap/PolygonalComplexes/modification.gd +++ b/gap/PolygonalComplexes/modification.gd @@ -577,13 +577,18 @@ DeclareOperation( "SplitEdgePathNC", [IsPolygonalComplex, IsVertexEdgePath and I #! actually consists only of faces in complex. It also does not #! check whether the result of SubsurfaceByFaces is a surface. #! -#! In Chapter edge colouring will be introduced. -#! If we compute a subcomplex of an edge-coloured complex, it will be edge-coloured again, -#! induced by the edge-colouring of the given complex. +#! In Chapter the edge colouring of twisted +#! polygonal complexes will be introduced. +#! +#! The hexagon from above can be coloured as follows: #! @BeginExampleSession #! gap> colEdges:=[ 1, 2, 1, 2, 1, 2, 3, 3, 3, 3, 3, 3 ];; #! gap> colSurface:=EdgeColouredPolygonalComplex(hex,colEdges); #! tame coloured surface (MMB with 7 vertices, 12 edges and 6 faces) +#! @EndExampleSession +#! If we compute a subcomplex of an edge-coloured complex, it will be edge-coloured again, +#! induced by the edge-colouring of the given complex: +#! @BeginExampleSession #! gap> SubsurfaceByFaces(colSurface,[1,2]); #! tame coloured surface (BMB with 4 vertices, 5 edges and 2 faces) #! @EndExampleSession From dc8582f7d4b047c1acb1e3d6e9c8870c6cf251c2 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Meike=20Wei=C3=9F?= Date: Wed, 11 Sep 2024 13:25:07 +0200 Subject: [PATCH 40/44] just a test for understanding the problem --- unit_tests/test_main.g | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/unit_tests/test_main.g b/unit_tests/test_main.g index 6744607b..c755132b 100644 --- a/unit_tests/test_main.g +++ b/unit_tests/test_main.g @@ -61,9 +61,9 @@ BindGlobal( "SIMPLICIAL_TestAll", function() __SIMPLICIAL_Test_EdgeNautyGraph(); __SIMPLICIAL_Test_FaceDigraphsGraph(); __SIMPLICIAL_Test_FaceNautyGraph(); - if IsPackageMarkedForLoading( "Digraphs", ">=1.9.0" ) then - __SIMPLICIAL_Test_AllSimplicialSurfacesOfDigraph(); - fi; + #if IsPackageMarkedForLoading( "Digraphs", ">=1.9.0" ) then + # __SIMPLICIAL_Test_AllSimplicialSurfacesOfDigraph(); + #fi; __SIMPLICIAL_Test_FaceTwoColouring(); From 3b653ab3e3995fcb208e9e75104d693977dd9ec9 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Meike=20Wei=C3=9F?= Date: Wed, 11 Sep 2024 13:37:42 +0200 Subject: [PATCH 41/44] does it works now? --- unit_tests/Test_Graphs.g | 15 ++++++++------- unit_tests/test_main.g | 6 +++--- 2 files changed, 11 insertions(+), 10 deletions(-) diff --git a/unit_tests/Test_Graphs.g b/unit_tests/Test_Graphs.g index d5417cd0..0fc0cbe1 100644 --- a/unit_tests/Test_Graphs.g +++ b/unit_tests/Test_Graphs.g @@ -68,21 +68,22 @@ if IsPackageMarkedForLoading( "Digraphs", ">=1.9.0" ) then local dig, surface, list1, list2; surface:=SimplicialSurfaceByVerticesInFaces([[1,4,5],[1,4,6],[1,5,7],[1,6,7],[2,3,5],[2,3,6],[2,4,5],[2,4,6],[3,5,7],[3,6,7]]); dig:=FaceDigraphsGraph(surface); - list1:=AllSimplicialSurfacesOfDigraph(dig,true); - Assert(0,Length(list1)=1); - Assert(0,IsIsomorphic(list1[1],surface)); list2:=AllSimplicialSurfacesOfDigraph(dig); Assert(0, Length(Filtered(list2,IsVertexFaithful))=1); Assert(0,IsIsomorphic(Filtered(list2,IsVertexFaithful)[1],surface)); Assert(0,Length(list2)=11); + list1:=AllSimplicialSurfacesOfDigraph(dig,true); + Assert(0,Length(list1)=1); + Assert(0,IsIsomorphic(list1[1],surface)); + dig:=DigraphByEdges([ [ 1, 2 ], [ 1, 4 ], [ 1, 5 ], [ 2, 1 ], [ 2, 3 ], [ 2, 6 ], [ 3, 2 ], [ 3, 4 ], [ 3, 5 ], [ 4, 1 ], [ 4, 3 ], [ 4, 6 ], [ 5, 1 ],[ 5, 3 ], [ 5, 6 ], [ 6, 2 ], [ 6, 4 ], [ 6, 5 ] ]); - list1:=AllSimplicialSurfacesOfDigraph(dig,true); - list2:=AllSimplicialSurfacesOfDigraph(dig,false); - Assert(0,Length(list1)=0); - Assert(0,Length(list2)=2); + list1:=AllSimplicialSurfacesOfDigraph(dig,false); + list2:=AllSimplicialSurfacesOfDigraph(dig,true); + Assert(0,Length(list1)=2); + Assert(0,Length(list2)=0); #One of the smallest face graph with more than one vertex-faithful surface dig:=DigraphByEdges([ [ 1, 9 ], [ 9, 1 ], [ 1, 13 ], [ 13, 1 ], [ 1, 14 ], [ 14, 1 ], [ 2, 6 ], [ 6, 2 ], [ 2, 7 ], [ 7, 2 ], [ 2, 10 ], diff --git a/unit_tests/test_main.g b/unit_tests/test_main.g index c755132b..6744607b 100644 --- a/unit_tests/test_main.g +++ b/unit_tests/test_main.g @@ -61,9 +61,9 @@ BindGlobal( "SIMPLICIAL_TestAll", function() __SIMPLICIAL_Test_EdgeNautyGraph(); __SIMPLICIAL_Test_FaceDigraphsGraph(); __SIMPLICIAL_Test_FaceNautyGraph(); - #if IsPackageMarkedForLoading( "Digraphs", ">=1.9.0" ) then - # __SIMPLICIAL_Test_AllSimplicialSurfacesOfDigraph(); - #fi; + if IsPackageMarkedForLoading( "Digraphs", ">=1.9.0" ) then + __SIMPLICIAL_Test_AllSimplicialSurfacesOfDigraph(); + fi; __SIMPLICIAL_Test_FaceTwoColouring(); From 3a026aff7ed0ca93821809644d408e8dfbbb7007 Mon Sep 17 00:00:00 2001 From: Lukas Schnelle Date: Thu, 12 Sep 2024 08:50:10 +0200 Subject: [PATCH 42/44] remove old code from manual generation --- makedoc.g | 470 +----------------------------------------------------- 1 file changed, 2 insertions(+), 468 deletions(-) diff --git a/makedoc.g b/makedoc.g index f28e054a..0ffcdf1f 100644 --- a/makedoc.g +++ b/makedoc.g @@ -8,491 +8,25 @@ if fail = LoadPackage("GAPDoc", "1.6") then QUIT_GAP(1); fi; - -# We generate the names automatically by a hash-function. Therefore we -# have to clean up old files periodically. To know which files have -# become obsolete, we save the current files in this global list. -BindGlobal("__SIMPLICIAL_ImageNames",[]); -MakeReadWriteGlobal("__SIMPLICIAL_ImageNames"); - -# We specify the documentation directory directly since we want to use it -# in our preprocessing method. -BindGlobal("__SIMPLICIAL_DocDirectory", "doc/"); - - -# The additional LaTeX-header to make tikz-pictures -# Careful: The file TikZHeader.tex has to lie in the same directory as -# the primary documentation file and the generated image files. -BindGlobal("__SIMPLICIAL_TikZHeader", "\\input{TikZHeader.tex}\n\n" ); - # We load the package since we need it for some computations in the manual if fail = LoadPackage("SimplicialSurfaces") then Error("SimplicialSurfaces package has to be available."); fi; -Exec( "pwd > _TMP_foo"); -manualposition := StringFile("_TMP_foo"); -Exec("rm _TMP_foo"); -RemoveCharacters(manualposition, "\n"); -manualposition := Concatenation(manualposition,"/doc/manual.pdf"); -manualposition := Concatenation("You can find the image in the manual. Most probably it is here: ", manualposition); - -# Now we have the XML-tree of the documentation -# We need to change the -Tags into proper GAPDoc tags -# For that we define a function that changes one node -preProcessTikz := function( node ) - local cont, n1, n2, n3, file, output, name, htmlString, consoleString, - path, tmpName, tmpFile, sysDirPath, md5, out, inStream, outStream, - hash, tmpImageName, latexString; - - if node.name = "Alt" and IsBound(node.attributes.Only) and - node.attributes.Only in ["TikZ","Tikz"] then - - # get the content of the tag - cont := GetTextXMLTree(node); - - - # We want to save our image in the file - # _IMAGE_.tex - # (that gives _IMAGE_-1.svg) - # - # This gives us the benefit of recognizing duplicates and - # minimizing compiling time (especially if we don't change the pictures - # between different versions of the code). - # - # At the same time this is problematic if we have \input-clauses inside - # our document since a change in the referred document should be - # reflected in a different overall image. - # - # To circumvent this issue, we proceed as follows: - # 1) Write the picture into a temporary file _IMAGE_TMP.tex - # We use a sed-command to remove all leading whitespaces - # (otherwise the same picture might be compiled twice). - # 2) Call ../flatex/flatex _IMAGE_TMP.tex - # This creates the file _IMAGE_TMP.flt - # 3) Calculate the hash of this file - # 4) Check if _IMAGE_-1.svg (and the tex-file) already exist - # If they do, do nothing. - # 5) Otherwise call mv _IMAGE_TMP.tex _IMAGE_.tex - # 6) Compile this image via htlatex _IMAGE_.tex - # 7) Store the name _IMAGE_ in our list - # 8) Include _IMAGE_-1.svg in the HTML document - - # Step 1 - path := __SIMPLICIAL_DocDirectory; - tmpImageName := "_IMAGE_TMP"; - tmpName := Concatenation( path, tmpImageName, ".tex"); - tmpFile := Filename( DirectoryCurrent(), tmpName ); - output := OutputTextFile( tmpFile, false ); - SetPrintFormattingStatus( output, false ); - AppendTo( output, - "\\nonstopmode\n", - "\\documentclass{standalone}\n\n", - __SIMPLICIAL_TikZHeader, - "\\def\\pgfsysdriver{pgfsys-tex4ht.def}\n\n", - "\\begin{document}\n"); - AppendTo( output, cont ); - AppendTo( output, "\\end{document}" ); - CloseStream(output); - - # Now we remove the leading whitespace - Exec( "sh -c \" cd ", path, - "; sed 's/^[ \\t]*//g' -i ", - Concatenation(tmpImageName, ".tex"), "; \"" ); - - # Step 2 - # TODO separate the calls to these shell-files into a function and call - # that. Furthermore, add into the README a short test if a user has all - # necessary capabilities (and maybe an installation for them) - Exec( "sh -c \" cd ", path, "; ../flatex/flatex ", - Concatenation(tmpImageName, ".tex"), "> /dev/null; \"" ); - - # Step 3 - sysDirPath := DirectoriesSystemPrograms(); - md5 := Filename( sysDirPath, "md5sum" ); - if md5 = fail then - Error("There is no md5sum installed."); - fi; - - inStream := InputTextNone(); - out := ""; - outStream := OutputTextString(out, true); - Process( Directory(path), md5, inStream, outStream, [ Concatenation(tmpImageName, ".flt") ] ); - CloseStream(inStream); - CloseStream(outStream); - hash := SplitString( out, " " )[1]; - - # Step 4 - name := Concatenation( "_IMAGE_", hash ); - if not IsExistingFile( - Filename( DirectoryCurrent(), - Concatenation( path, name, ".tex" ) ) ) or - not IsExistingFile( - Filename( DirectoryCurrent(), - Concatenation( path, name, "-1.svg" )) ) or - not IsExistingFile( - Filename( DirectoryCurrent(), - Concatenation( path, name, ".pdf" )) ) then - # Either tex or svg or pdf are not there. We will write them now. - - # Step 5 - Exec( "sh -c \" cd ", path, "; mv _IMAGE_TMP.tex ", Concatenation(name, ".tex"), "; \" " ); - - # Step 6 - Exec( "sh -c \" cd ", path, "; pdflatex -halt-on-error ", Concatenation(name, ".tex"), "; \" " ); - Exec( "sh -c \" cd ", path, "; htlatex ", Concatenation(name, ".tex"), "; \" " ); - - # After compiling we do some post-processing on the image. - # We will modify - # - subscripts, since baseline-shift is not supported in Firefox - # (see https://stackoverflow.com/questions/12332448/subscripts-and-superscripts-in-svg) - # As this bug was recognized 16 years ago it is unlikely to - # change in the near future. We therefore apply the suggested - # fix in the stackoverflow-answer. - # WARNING: I am just messing around on the assumption that all - # subscripts have the same height. If that turns out to be - # wrong, you have to think of a more sophisticated mechanism. - Exec( "sh -c \" cd ", path, - "; sed 's/baseline-shift=\\\"sub\\\"/dy=\\\"3\\\"/g' -i ", - Concatenation(name, "-1.svg"), ";\" "); - # I do not really understand why there has to be so much - # escaping but it does not work with less. - fi; - - # Step 7 - Add( __SIMPLICIAL_ImageNames, name); - - # Step 8 will be done in the htmlString below - - - # Inclusion in the LaTeX-version is centered - latexString := Concatenation( "\n\\begin{center}\n", - "\\includegraphics{", name, ".pdf}\n\\end{center}\n" ); - n1 := ParseTreeXMLString(latexString); - n1.name := "Alt"; - n1.attributes.Only := "LaTeX"; - - # To include it in the HTML-version we have to use a different node - htmlString := Concatenation( - "

]]>"); - n2 := ParseTreeXMLString(htmlString); - n2.name := "Alt"; - n2.attributes.Only := "HTML"; - - - # Generate the text version - consoleString := "\n[an image that is not shown in text version. "; - consoleString := Concatenation( consoleString, manualposition); - consoleString := Concatenation( consoleString, "]\n"); - n3 := ParseTreeXMLString(consoleString); - n3.name := "Alt"; - n3.attributes.Only := "Text"; - - - # Replace this node by the new nodes - node.content := [n1,n2,n3]; - node.attributes.Only := "HTML,LaTeX,Text"; - fi; -end; - - - -# Now we have the XML-tree of the documentation -# We need to change the -Tags into proper GAPDoc tags -# For that we define a function that changes one node -preProcessJavaScript := function( node ) - local cont, name, path, n1, n2, n3, consoleString, htmlString, latexString, tmpImageName, tmpName; - - if node.name = "Alt" and IsBound(node.attributes.Only) and - node.attributes.Only in ["JavaScript","Javascript"] then - - # get the content of the tag (we need to remove whitespaces) - cont := GetTextXMLTree(node); - cont := ReplacedString( cont, " ", "" ); - cont := ReplacedString( cont, "\n", "" ); - cont := ReplacedString( cont, ".html", "" ); - path := __SIMPLICIAL_DocDirectory; - tmpImageName := "_IMAGE_TMP"; - tmpName := Concatenation( path, tmpImageName, ".tex"); - PrintTo("doc/Test.js", "var page = require('webpage').create();\n"); - AppendTo( "doc/Test.js", "page.viewportSize = { width: 1920, height: 1080 };\n"); - AppendTo( "doc/Test.js", "page.clipRect = { top: 400, left: 750, width: 375, height: 300 };\n"); - AppendTo( "doc/Test.js", Concatenation("page.open('doc/", cont, ".html', function() {\n") ); - AppendTo( "doc/Test.js", Concatenation("page.render('doc/", cont, ".png');\n") ); - AppendTo( "doc/Test.js", "phantom.exit();\n" ); - AppendTo( "doc/Test.js", "});" ); - Exec("./doc/phantomjs /doc/Test.js"); - name := cont; - - - - Add( __SIMPLICIAL_ImageNames, name); - - - - - # Inclusion in the LaTeX-version is centered - latexString := Concatenation( "\n\\begin{center}\n", "\\includegraphics{", name, ".png}\n\\end{center}\n" ); - n1 := ParseTreeXMLString(latexString); - n1.name := "Alt"; - n1.attributes.Only := "LaTeX"; - - # To include it in the HTML-version we have to use a different node - htmlString := Concatenation( - "

]]>"); - n2 := ParseTreeXMLString(htmlString); - n2.name := "Alt"; - n2.attributes.Only := "HTML"; - - - # Generate the text version - consoleString := "\n[an image that is not shown in text version]\n"; - n3 := ParseTreeXMLString(consoleString); - n3.name := "Alt"; - n3.attributes.Only := "Text"; - - - # Replace this node by the new nodes - node.content := [n1,n2,n3]; - node.attributes.Only := "HTML,LaTeX,Text"; - - fi; -end; - - - -BindGlobal( "CleanImageDirectory", function( ) - local allFiles, file; - - # First we remove the temporary files - Exec( "sh -c \" cd ", __SIMPLICIAL_DocDirectory, "; rm -f _IMAGE_TMP*;\"" ); - - # Secondly we remove all old image files - allFiles := DirectoryContents( __SIMPLICIAL_DocDirectory ); - for file in allFiles do - # We only do something with temporary image files - if StartsWith( file, "_IMAGE_" ) then - if ForAny( __SIMPLICIAL_ImageNames, n -> StartsWith(file,n) ) then - # This is a file to an existing picture - if not ForAny( [".tex", ".svg", ".pdf"], e -> EndsWith(file,e) ) then - # Does not end in one of those file extensions - Exec( "sh -c \" cd ", __SIMPLICIAL_DocDirectory, "; rm -f ", file, ";\"" ); - fi; - else - # This is an old file that can be removed - Exec( "sh -c \" cd ", __SIMPLICIAL_DocDirectory, "; rm -f ", file, ";\"" ); - fi; - fi; - od; -end -); - -# We now want to put this preprocessing within the MakeGAPDocDoc-function. -# To do so we have to redefine the original global variable and add our -# method into the code. All code that is not commented with MB is original -# GAPDoc-code. - -MakeReadWriteGlobal("MakeGAPDocDoc"); -UnbindGlobal("MakeGAPDocDoc"); # MB unbind this to modify it -BindGlobal("MakeGAPDocDoc", function(path, main, files, bookname, opts...) - local special, gaproot, str, r, t, l, latex, null, log, pos, h, i, j; - special := Filtered(opts, a-> a in ["MathML", "Tth", "MathJax", "nopdf"]); - if Length(special) > 0 then - opts := Filtered(opts, a-> not a in ["MathML", "Tth", "MathJax", "nopdf"]); - fi; - if IsBound(opts[1]) then - gaproot := opts[1]; - else - gaproot := false; - fi; - # ensure that path is directory object - if IsString(path) then - path := Directory(path); - fi; - # ensure that .xml is stripped from name of main file - if Length(main)>3 and main{[Length(main)-3..Length(main)]} = ".xml" then - main := main{[1..Length(main)-4]}; - fi; - # compose the XML document - Info(InfoGAPDoc, 1, "#I Composing XML document . . .\n"); - str := ComposedDocument("GAPDoc", path, - Concatenation(main, ".xml"), files, true); - # parse the XML document - Info(InfoGAPDoc, 1, "#I Parsing XML document . . .\n"); - r := ParseTreeXMLString(str[1], str[2]); - - #MB precompile the images - Exec( "sh -c \" cd ", __SIMPLICIAL_DocDirectory, "; rm -f _TIKZ_*;\"" ); - __SIMPLICIAL_MANUAL_MODE := true; - Read("gap/PolygonalComplexes/drawing.gd"); - Read("gap/Library/library_images.gd"); - Read("gap/PolygonalComplexes/distances_images.gd"); - Read("gap/PolygonalComplexes/animating_images.gd"); - Read("gap/ColouredComplexes/edgeColouring_images.gd"); - Read("gap/ColouredComplexes/variColouring_images.gd"); - Read("gap/ColouredComplexes/isoscelesColouring_images.gd"); - Read("gap/Flags/flags_images.gd"); - __SIMPLICIAL_MANUAL_MODE := false; - # Fortunately there already is a method to apply this function to all nodes of the tree - ApplyToNodesParseTree( r, preProcessTikz ); - ApplyToNodesParseTree( r, preProcessJavaScript ); - - CleanImageDirectory(); - - # clean the result - Info(InfoGAPDoc, 1, "#I Checking XML structure . . .\n"); - CheckAndCleanGapDocTree(r); - # produce text version - Info(InfoGAPDoc, 1, - "#I Text version (also produces labels for hyperlinks):\n"); - t := GAPDoc2Text(r, path); - GAPDoc2TextPrintTextFiles(t, path); - # produce LaTeX version - Info(InfoGAPDoc, 1, "#I Constructing LaTeX version and calling pdflatex:\n"); - r.bibpath := path; - l := GAPDoc2LaTeX(r); - Info(InfoGAPDoc, 1, "#I Writing LaTeX file, \c"); - Info(InfoGAPDoc, 2, Concatenation(main, ".tex"), "\n#I "); - FileString(Filename(path, Concatenation(main, ".tex")), l); - if "nopdf" in special then - Info(InfoGAPDoc, 1, " NO PDF generated!\n"); - PrintSixFile(Filename(path, "manual.six"), r, bookname); - else - if Filename(DirectoriesSystemPrograms(), "pdflatex") = fail then - Info(InfoGAPDoc, 1, "\n#W WARNING: cannot find 'pdflatex', please install TeX.\n"); - Info(InfoGAPDoc, 1, "#W WARNING: will NOT produce pdf version from LaTeX file.\n"); - else - # call latex and pdflatex (with bibtex, makeindex and dvips) - latex := "latex -interaction=nonstopmode "; - # sh-syntax for redirecting stderr and stdout to /dev/null - null := " > /dev/null 2>&1 "; - Info(InfoGAPDoc, 1, "4 x pdflatex with bibtex and makeindex, \c"); - Exec(Concatenation("sh -c \" cd ", Filename(path,""), - "; rm -f ", main, ".aux ", main, ".pdf ", main, ".log ", - "; pdf", latex, main, null, - "; bibtex ", main, null, - "; pdf", latex, main, null, - "; makeindex ", main, null, - "; pdf", latex, main, null, - "; pdf", latex, main, null,"\"")); - # check log file for errors, warning, overfull boxes - log := Filename(path, Concatenation(main, ".log")); - log := StringFile(log); - if log = fail then - Info(InfoGAPDoc, 1, "\n#W WARNING: Something wrong, don't find log file ", - Filename(path, Concatenation(main, ".log")), "\n"); - else - log := SplitString(log, "\n", ""); - pos := Filtered([1..Length(log)], i-> Length(log[i]) > 0 - and log[i][1] = '!'); - if Length(pos) > 0 then - Info(InfoGAPDoc, 1, "\n#W There were LaTeX errors:\n"); - for i in pos do - for j in [i..Minimum(i+2, Length(log))] do - Info(InfoGAPDoc, 1, log[j], "\n"); - od; - Info(InfoGAPDoc, 1, "____________________\n"); - od; - fi; - pos := Filtered([1..Length(log)], i-> Length(log[i]) > 13 - and log[i]{[1..14]} = "LaTeX Warning:"); - if Length(pos) > 0 then - Info(InfoGAPDoc, 1, "\n#W There were LaTeX Warnings:\n"); - for i in pos do - for j in [i..Minimum(i+2, Length(log))] do - Info(InfoGAPDoc, 1, log[j], "\n"); - od; - Info(InfoGAPDoc, 1, "____________________\n"); - od; - fi; - pos := Filtered([1..Length(log)], i-> Length(log[i]) > 7 - and log[i]{[1..8]} = "Overfull"); - if Length(pos) > 0 then - Info(InfoGAPDoc, 1, "\n#W There are overfull boxes:\n"); - for i in pos do - Info(InfoGAPDoc, 1, log[i], "\n"); - od; - fi; - fi; - # check for BibTeX warnings - log := StringFile(Filename(path, Concatenation(main, ".blg"))); - if log <> fail then - log := SplitString(log, "\n", ""); - log := Filtered(log, z-> PositionSublist(z, "Warning--") = 1); - if Length(log) > 0 then - Info(InfoGAPDoc, 1, "\n#W BibTeX had warnings:\n", - JoinStringsWithSeparator(log, "\n")); - fi; - fi; - - if not IsExistingFile(Filename(path, Concatenation(main, ".pdf"))) then - Info(InfoGAPDoc, 1, "\n#I ERROR: no .pdf file produced (writing incomplete .six file)\n"); - PrintSixFile(Filename(path, "manual.six"), r, bookname); - else - Exec(Concatenation("sh -c \" cd ", Filename(path,""), - "; mv ", main, ".pdf manual.pdf; ", - "\"")); - Info(InfoGAPDoc, 1, "\n"); - # read page number information for .six file - Info(InfoGAPDoc, 1, "#I Writing manual.six file ... \c"); - Info(InfoGAPDoc, 2, Filename(path, "manual.six"), "\n"); - Info(InfoGAPDoc, 1, "\n"); - AddPageNumbersToSix(r, Filename(path, Concatenation(main, ".pnr"))); - # print manual.six file - PrintSixFile(Filename(path, "manual.six"), r, bookname); - fi; - fi; - fi; - # produce html version - Info(InfoGAPDoc, 1, "#I Finally the HTML version . . .\n"); - # if MathJax version is also produced we include links to them - if "MathJax" in special then - r.LinkToMathJax := true; - fi; - h := GAPDoc2HTML(r, path, gaproot); - GAPDoc2HTMLPrintHTMLFiles(h, path); - Unbind(r.LinkToMathJax); - if "Tth" in special then - Info(InfoGAPDoc, 1, - "#I - also HTML version with 'tth' translated formulae . . .\n"); - h := GAPDoc2HTML(r, path, gaproot, "Tth"); - GAPDoc2HTMLPrintHTMLFiles(h, path); - fi; - if "MathML" in special then - Info(InfoGAPDoc, 1, "#I - also HTML + MathML version with 'ttm' . . .\n"); - h := GAPDoc2HTML(r, path, gaproot, "MathML"); - GAPDoc2HTMLPrintHTMLFiles(h, path); - fi; - if "MathJax" in special then - Info(InfoGAPDoc, 1, "#I - also HTML version for MathJax . . .\n"); - h := GAPDoc2HTML(r, path, gaproot, "MathJax"); - GAPDoc2HTMLPrintHTMLFiles(h, path); - fi; - - return r; -end); - # Create binary and index files for the library __SIMPLICIAL_LibraryConstructBinary(); __SIMPLICIAL_LibraryConstructIndex(); -# After all this preparatory work we can finally call the function to create -# the documentation - AutoDoc( rec( scaffold := rec( MainPage := false), - dir := __SIMPLICIAL_DocDirectory, + dir := "doc/", extract_examples := true, autodoc := rec( files := [ ], scan_dirs := ["doc", "gap", "gap/PolygonalComplexes", "gap/Paths", "gap/Library", "gap/ColouredComplexes", "gap/Flags", "gap/Morphisms"]), gapdoc := rec( files := ["doc/PolygonalStructuresDefinitions.xml", "doc/ExampleImplementations.xml"], - LaTeXOptions := rec( LateExtraPreamble := __SIMPLICIAL_TikZHeader ) + LaTeXOptions := rec( LateExtraPreamble := "\\input{TikZHeader.tex}\n\n" ) )) ); From e3c1efeb68bbb3f2bd18a1c914b6ec3985f0a8fb Mon Sep 17 00:00:00 2001 From: alice Date: Thu, 12 Sep 2024 11:27:21 +0200 Subject: [PATCH 43/44] Bug fix in __SIMPLICIAL_ComputeNewVertexEdgePaths --- gap/PolygonalComplexes/modification.gi | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/gap/PolygonalComplexes/modification.gi b/gap/PolygonalComplexes/modification.gi index 132b5f1e..545862e7 100755 --- a/gap/PolygonalComplexes/modification.gi +++ b/gap/PolygonalComplexes/modification.gi @@ -309,7 +309,7 @@ BindGlobal( "__SIMPLICIAL_ComputeNewVertexEdgePaths", Add(extOld, PathAsList(vePath)[i]); Add(newPaths, [ extNew, extOld ]); - + new := new + 1; used:=true; fi; od; From b18e577b674576036e868392fad539ab0344ef37 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Meike=20Wei=C3=9F?= Date: Thu, 12 Sep 2024 11:29:44 +0200 Subject: [PATCH 44/44] bugfix --- gap/Paths/paths.gi | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/gap/Paths/paths.gi b/gap/Paths/paths.gi index 21cf374b..9f3aec5c 100644 --- a/gap/Paths/paths.gi +++ b/gap/Paths/paths.gi @@ -647,7 +647,7 @@ InstallMethod( EdgeFacePathByFaces, local i; __SIMPLICIAL_CheckEdge(complex, firstEdge, "EdgeFacePathByFaces"); - __SIMPLICIAL_CheckFace(complex, lastEdge, "EdgeFacePathByFaces"); + __SIMPLICIAL_CheckEdge(complex, lastEdge, "EdgeFacePathByFaces"); if Length(faceList) > 0 then __SIMPLICIAL_CheckFace(complex, faceList[1], "EdgeFacePathByFaces"); for i in [2..Length(faceList)] do