Re: [fricas-devel] Algebraic Topology Issue 1

[Kurt Pagani]

Hello Martin

As promised (before vacation) below two examples which I'm unable to
interpret (otherwise I recognized that you've improved your code and
that it's now included in fricas -- great :). A lot more examples work
now (i.e same results as Kenzo).

BTW: why didn't you allow '0'? NNI=0,1,2,... ;)


-- from https://www-fourier.ujf-grenoble.fr/~sergerar/Kenzo/Kenzo-doc.pdf


---

ASIMP := FiniteSimplicialComplex(VertexSetAbstract)

 v0:List(List(NNI)) :=[[0],[1],[2],[3],[4],[5],[6],[7], _
                       [0,1],[0,2],[0,3], _
                       [0,4],[0,5],[0,6], _
                       [0,7],[1,2],[1,3], _
                       [1,4],[1,5],[1,6], _
                       [1,7],[2,3],[2,4], _
                       [2,6],[2,7],[3,4], _
                       [3,5],[4,5],[4,6], _
                       [5,6],[5,7],[6,7], _
                       [0,1,5],[0,1,6],[0,1,7], _
                       [0,2,3],[0,2,4],[0,2,6], _
                       [0,3,4],[0,5,7],[1,2,3], _
                       [1,2,4],[1,2,7],[1,3,5], _
                       [1,4,6],[2,6,7],[3,4,5], _
                       [4,5,6],[5,6,7]]


-- Dunce hat
-- https://en.wikipedia.org/wiki/Dunce_hat_(topology)

 v1:List(List(NNI)) :=[[1],[2],[3],[4],[5],[6],[7],[8], _
                       [1,2],[1,3],[1,4], _
                       [1,5],[1,6],[1,7], _
                       [1,8],[2,3],[2,4], _
                       [2,5],[2,6],[2,7], _
                       [2,8],[3,4],[3,5], _
                       [3,7],[3,8],[4,5], _
                       [4,6],[5,6],[5,7], _
                       [6,7],[6,8],[7,8], _
                       [1,2,6],[1,2,7],[1,2,8], _
                       [1,3,4],[1,3,5],[1,3,7], _
                       [1,4,5],[1,6,8],[2,3,4], _
                       [2,3,5],[2,3,8],[2,4,6], _
                       [2,5,7],[3,7,8],[4,5,6], _
                       [5,6,7],[6,7,8]]



dunceHat := simplicialComplex(vertexSeta(8::NNI),v1)$ASIMP

homology dunceHat

-- [Z,Z*24,0] , actually H0=Z, others 0.



-- 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.


Am 06.09.2016 um 11:24 schrieb Martin Baker:

> Martin B
> 
Kurt

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