Hi all.
There is an example in the official Reference Manual about
SimplicialComplex and Betti Numbers and Euler Characteristic.
S = SimplicialComplex(3, [[0,1], [1,2], [0,2]]) # circle
T = S.product(S) # torus
T
Simplicial complex with 16 vertices and 18 facets
and
T.euler_characteristic()
0
which is correct.
My problem is with the computation of Betti numbers :
T.betti()
{0: 0, 1: 2, 2: 1}
coherent with
T.homology()
{0: 0, 1: Z x Z, 2: Z}
For the torus (correct me if I am wrong), the 0-th Betti number should be 1.
This would agree with the formula given for the Euler Characteristic
in that case : X = B_0 - B_1 + B_2 = 0
Maybe I misunderstood something here...
Thanks for your kind answer...
Best regards
Philippe Saadé
NB : according to the source code of SimplicialComplex, the first
definition should be : S = SimplicialComplex(2, [[0,1], [1,2], [0,2]])
# circle
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