Functionality for computing \xi_2

rivetTDA / rivet

RIVET is a tool for Topological Data Analysis, in particular two-parameter persistent homology.

GNU General Public License v3.0

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Closed mlesnick closed 7 years ago

mlesnick commented 9 years ago

Originally reported by: Matthew Wright (GitHub: mlwright84)

Add functionality for computing \xi_2

mlesnick commented 9 years ago

Original comment by Matthew Wright (GitHub: mlwright84):

done

mlesnick commented 9 years ago

Original comment by M L (GitHub: mlesnick):

dim Mb=\sum{a\leq b} betti_0(M)a - \sum{a\leq b} betti_1(M)a + \sum{a\leq b} betti_2(M)_a.

Hence we can compute betti_2 via a simple dynamic programming algorithm, once we have betti_0 and betti_1.