Re: Picking Generators of Homology
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There are two things at work here. First of all, by default, Dionysus computes generators only for finite bars. So the 1-dimensional cycle, the boundary of [0,1,2] is never computed. If the triangle was in that filtration, then you'd have a pair (5,6) and 6 would store the cycle consisting of the three edges.
The cycles are stored in terms of indices in the filtration, so to translate them into simplices, you need to look them up in the filtration. So, for example, you could change the loop above to:
for i,c in enumerate(m):
print(" + ".join(["%d * %s" % (x.element, f[x.index]) for x in c]))
In other words, the elements of c have members element and index that tell you what the coefficient is and where the simplex is in the filtration.
I hope it helps.
On Wed, Aug 15, 2018 at 7:42 PM, <nukpezah@...> wrote: