Corrected IsWaist #260
Corrected IsWaist #260
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Additional details and impacted files@@ Coverage Diff @@
## master #260 +/- ##
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- Coverage 76.74% 76.73% -0.01%
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Files 61 61
Lines 16363 16381 +18
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+ Hits 12557 12570 +13
- Misses 3806 3811 +5
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gap/Paths/paths.gd
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| @@ -1305,7 +1308,10 @@ DeclareAttribute( "AllThreeWaistsOfComplex", IsTwistedPolygonalComplex); | |||
| #! For example, consider the double tetrahedron from the start of section <Ref Sect="Section_Waists"/>: | |||
| #! @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 ) ] | |||
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The DoubleTetrahedron should have exactly one waist, namely a 3-waist.
I think the surface that is referenced at this point is the multi-tetrahedral sphere with 8 faces. (obtained by applying two tetrahedral extensions to the tetrahedron)
Renaming the surface and also the parameter would be better in order to not cause any confusion.
gap/Paths/paths.gd
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| @@ -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 <M>n</M>-waist is a closed vertex-edge path of length <M>n</M> such that all edges are inner and no two are incident to the same face. | |||
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I tried to write the following paragraph based on the definition of a waist that is provided in the book. Maybe this can replace the lines 1200-1203.
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.
In the definition of waists it was missing that the paths of n-waist for n>3 must be distance-faithful. I added this to the definition and in the method IsWaist.