Simplicial Complex

[linuskuehnle]

Contains a possible integration of type Simplicial Complex as a special case of type Triangular Complex.

[codecov]

Codecov Report

❌ Patch coverage is 88.98305% with 104 lines in your changes missing coverage. Please review.
✅ Project coverage is 73.86%. Comparing base (2e398f8) to head (60caec4).
⚠️ Report is 18 commits behind head on master.

Files with missing lines	Patch %	Lines
gap/PolygonalComplexes/constructors.gi	86.63%	62 Missing ⚠️
gap/PolygonalComplexes/modification.gi	48.38%	16 Missing ⚠️
gap/PolygonalComplexes/properties.gi	86.32%	16 Missing ⚠️
unit_tests/Test_Inferences_PolygonalComplex.g	96.66%	4 Missing ⚠️
gap/Paths/connectivity.gi	96.15%	2 Missing ⚠️
gap/PolygonalComplexes/main.gi	66.66%	2 Missing ⚠️
gap/ColouredComplexes/variColouring.gi	66.66%	1 Missing ⚠️
gap/PolygonalComplexes/incidence_geometry.gi	95.65%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #351      +/-   ##
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... and 1 file with indirect coverage changes

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[MeikeWeiss]

I wanted to create a simplicial complex consisting of a single vertex, a triangle and an edge connected to the triangle by SimplicialComplexByDownwardIncidence([1,2,3,4,5],[[2,3],[3,4],[4,5],[3,5]],[[2,3,4]]);. But I get an error and the same for SimplicialComplexByDownwardIncidence([1,2,3,4,5],[1,2,3,4],[1],[[2,3],[3,4],[4,5],[3,5]],[[2,3,4]]); but with a different error.

UpwardIncidence for this example is also not working SimplicialComplexByUpwardIncidence([1..5],[[],[1],[1,2,4],[2,3],[3,4]],[[],[1],[1],[1]]); .

Could it be that "isolated" edges are not included in the implementation? As it is not possible to include them in the constructor VerticesInFaces.

[linuskuehnle]

I wanted to create a simplicial complex consisting of a single vertex, a triangle and an edge connected to the triangle by SimplicialComplexByDownwardIncidence([1,2,3,4,5],[[2,3],[3,4],[4,5],[3,5]],[[2,3,4]]);. But I get an error and the same for SimplicialComplexByDownwardIncidence([1,2,3,4,5],[1,2,3,4],[1],[[2,3],[3,4],[4,5],[3,5]],[[2,3,4]]); but with a different error.

UpwardIncidence for this example is also not working SimplicialComplexByUpwardIncidence([1..5],[[],[1],[1,2,4],[2,3],[3,4]],[[],[1],[1],[1]]); .

Could it be that "isolated" edges are not included in the implementation? As it is not possible to include them in the constructor VerticesInFaces.

SimplicialComplexByDownwardIncidence([1,2,3,4,5],[[2,3],[3,4],[4,5],[3,5]],[[2,3,4]]); fails because for some reason [1,2,3,4,5] does not satisfy the IsSet filter, if you use SimplicialComplexByDownwardIncidence([1..5],[[2,3],[3,4],[4,5],[3,5]],[[2,3,4]]);

One issue you encounter when calling the constructors like that is that lists like [1,2,3,4,5] for vertices or [1,2,3,4] for edges seem to not satisfy the IsSet filter even though IsSet is obviously true for them. It finds the correct function with [1..5] for vertices or [1..4] for edges as args though:

SimplicialComplexByDownwardIncidence([1..5],[[2,3],[3,4],[4,5],[3,5]],[[2,3,4]]);
SimplicialComplexByDownwardIncidence([1..5],[1..4],[1],[[2,3],[3,4],[4,5],[3,5]],[[2,3,4]]);

Right now they throw an error because SimplicialComplex is supposed to be a Simplicial Complex with isolated vertices. It is not supposed to work with triangles that have an edge connected to it as in your example. I will work on that so that will be possible too.
Here is an example on how i construct Simplicial Complexes for now:

vertices := [1..4];
edges := [1..3];
faces := [1..2];
verticesOfEdges := [ [ 1, 2 ], [ 1, 3 ], [ 2, 3 ] ];
edgesOfFaces := [ [ 1, 2, 3 ], [ 1, 2, 3 ] ];

SimplicialComplexByDownwardIncidence(vertices, edges, faces, verticesOfEdges, edgesOfFaces);
SimplicialComplexByDownwardIncidenceNC(vertices, edges, faces, verticesOfEdges, edgesOfFaces);
SimplicialComplexByDownwardIncidence(vertices, verticesOfEdges, edgesOfFaces);
comp := SimplicialComplexByDownwardIncidenceNC(vertices, verticesOfEdges, edgesOfFaces);

edgesOfVertices := EdgesOfVertices(comp);
facesOfEdges := FacesOfEdges(comp);

SimplicialComplexByUpwardIncidence(vertices, edges, faces, edgesOfVertices, facesOfEdges);
SimplicialComplexByUpwardIncidenceNC(vertices, edges, faces, edgesOfVertices, facesOfEdges);
SimplicialComplexByUpwardIncidence(vertices, edgesOfVertices, facesOfEdges);
SimplicialComplexByUpwardIncidenceNC(vertices, edgesOfVertices, facesOfEdges);

verticesInFaces := VerticesOfFaces(comp);

SimplicialComplexByVerticesInFaces(vertices, faces, verticesInFaces);
SimplicialComplexByVerticesInFacesNC(vertices, faces, verticesInFaces);
SimplicialComplexByVerticesInFaces(vertices, verticesInFaces);
SimplicialComplexByVerticesInFacesNC(vertices, verticesInFaces);

[MeikeWeiss]

Is there any possibility such that [1,2,3,4] is also allowed?

Thanks! Here is an image with some examples that all should be possible to construct: https://en.wikipedia.org/wiki/Simplicial_complex

[MeikeWeiss]

Nice progress!

Check in all examples that the lines are not too long in the manual.pdf.