Martin, after a look into your code I think there was a deep misunderstanding - my fault :(

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Kenzo indeed works slightly different, so I tacitly assumed one needs the full base of the triangulation w.r.t the bdry homomorphism. Your method instead requires properly oriented input. Now I also conceive that you find the idea of vertex sets rather odd. So, actually, your UI is expecting a formal sum (a Z2-Module over a set of cells if you like): dunceHat = [1,2,8]+[2,3,8]+[3,7,8]+[3,1,7]+[1,2,7]+[1,8,6]+[1,6,2]+[8,7,6]+[2,6,4]+[6,7,5]+[7,2,5]+[6,5,4]+[2,4,3]+[2,3,5]+[4,1,3]+[4,5,1]+[5,3,1] = [1,2,8]+[2,3,8]+[3,7,8]-[1,3,7]+[1,2,7]-[1,6,8]-[1,2,6]-[6,7,8]-[2,4,6]+[5,6,7]+[2,5,7]-[4,5,6]-[2,3,4]+[2,3,5]+[1,3,4]+[1,4,5]-[1,3,5] => now we get the correct result (cmp fig. on p.67): ASIMP := FiniteSimplicialComplex(VertexSetAbstract) (1) -> v1:List(List(NNI)) :=[[1,2,8],[2,3,8],[3,7,8],[3,1,7],[1,2,7], _ [1,8,6],[1,6,2],[8,7,6],[2,6,4],[6,7,5],[7,2,5],[6,5,4], _ [2,4,3],[2,3,5],[4,1,3],[4,5,1],[5,3,1]] (1) [[1,2,8], [2,3,8], [3,7,8], [3,1,7], [1,2,7], [1,8,6], [1,6,2], [8,7,6], [2,6,4], [6,7,5], [7,2,5], [6,5,4], [2,4,3], [2,3,5], [4,1,3], [4,5,1], [5,3,1]] Type: List(List(NonNegativeInteger)) (2) -> dunceHat := simplicialComplex(vertexSeta(8::NNI),v1)$ASIMP (2) (1,2,8) (2,3,8) (3,7,8) -(1,3,7) (1,2,7) -(1,6,8) -(1,2,6) -(6,7,8) -(2,4,6) (5,6,7) (2,5,7) -(4,5,6) -(2,3,4) (2,3,5) (1,3,4) (1,4,5) -(1,3,5) Type: FiniteSimplicialComplex(VertexSetAbstract) (3) -> homology dunceHat (3) [Z,0,0] Type: List(Homology) Sorry for any inconvenience caused. Kurt > AFAICS we need to take orientation into account and orientation requires > a consistent set of notation standards. Could it be that other programs > are using different conventions? > > (1) -> triangle := sphereSolid(2)$SimplicialComplexFactory > > (1) > (1,2,3) > Type: FiniteSimplicialComplex(VertexSetAbstract) > (2) -> delta(triangle) > > (2) > (1,2) > -(1,3) > (2,3) > Type: FiniteSimplicialComplex(VertexSetAbstract) > > So [(1,2),-(1,3), (2,3)] represents a circular chain (boundary of a > triangle). > > Which can be notated [(1,2),(3,1), (2,3)] > > OTOH [(1,2), (1,3), (2,3)] represents two parallel chains, starting and > ending at the same vertices. This will have different homology. > > These conventions make sense to me because all we need to do is order > the facets (left entry is most significant) and then alternate the sign. > > This is what concerns me about your proposal, for changing the VertexSet > structure, the user interface could then loose this ordering information. > > So is this Cyclic? > [(a,b),-(a,c), (b,c)] > > I would say yes, but only if a<b<c or a>b>c, but the user can't know > this because they can't see the underlying index ordering. > > Martin B > -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.