On 19/09/16 11:17, Waldek Hebisch wrote:
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.


Are sure this is buggy?
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

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