AFAICS there is serious confusion in in the code. I have fixed
several problems, but some go beyond "fixing". In particular
DeltaComplex contains coerce to SimplicialComplex. AFAICS
DeltaComplex contains too little information to build
simplicial complex from it. The problem is already visible
at level of fundamental group (however here can be worked
around). Namely, consider delta complex having one 0-dimensonal
simplex (point), two 1 dimensional simplices (edges) and one
two dimensional simplex. The two edges form two loops with
a common point. Boundary of two dimensional is mapped
is mapped to the loops. Using your code it can be
build from the follwing face map:
[[[1, -1],[1, -1]], [1 2 1]]
Now, this fully specifies boundary of two dimensional simplex
as an oriented set. However, we need a mapping. In this case
we can resolve problem because orientation gives us only
one choice of linear map between edges. But in higher
dimensional case to define map we need correspondence
between vertices and all we have is orientation. Note
that knowing boundary as an oriented set is enough to
compute homology, so in fact there are pretty strong
global restrictions on possible maps. But it is
not clear if the map is uniquely determined (probably not),
and even if it is determined it looks hard to compute
it.
--
Waldek Hebisch
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