# Re: [fricas-devel] Algebraic Topology Issue 1

Kurt Pagani wrote:
> -- Diabolo
>
>  v2:List(List(NNI)) := [[1],[2],[3],[4],[5],[6], _
>                         [1,2],[1,3],[2,3],[3,4],[4,5],[4,6],[5,6], _
>                         [4,5,6]]
>
>
> diabolo:= simplicialComplex(vertexSeta(6::NNI),v2)\$ASIMP
>
> homology diabolo
>
> -- [Z,Z*4,0] , actually H0=Z, H1=Z, H2=0.

If you do:

v2a := [[1,2],[1,3],[2,3],[3,4],[4,5,6]]
diabolo := simplicialComplex(vertexSeta(6::NNI),v2a)\$ASIMP

then it works.  AFAICS code which allows omiting lower
dimensional faces is buggy, if we include lower dimensional
faces we get duplicate simplices.  In particular, all
faces of triangle are duplicated and we get three extra
loops.

This is visible in the generated chain:

(15) -> chain(diabolo)

(15)
+ 0 +
|   |
| 0 |
|   |
+ 1    1    0    0    0    0    0    0    0    0 + | 0 |
|                                                | |   |
|- 1   0    1    0    0    0    0    0    0    0 | | 0 |
|                                                | |   |
| 0   - 1  - 1   1    0    0    0    0    0    0 | | 1 |
[0  0  0  0  0  0],|                                                |,|   |
| 0    0    0   - 1   1    1    1    1    0    0 | | 0 |
|                                                | |   |
| 0    0    0    0   - 1  - 1   0    0    1    1 | |- 1|
|                                                | |   |
+ 0    0    0    0    0    0   - 1  - 1  - 1  - 1+ | 0 |
|   |
| 1 |
|   |
+ 0 +
,

edeges 5 and 6 form duplicate pair, with 5 beeing boundary of triangle.
The same for pairs 7 and 8 and for pair 9 and 10.

--
Waldek Hebisch

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