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Sep 18, 2018 at 16:54 comment added Timothy Chow If you haven't already done so, you might also try asking Francis Sergeraert. www-fourier.ujf-grenoble.fr/~sergerar
Sep 18, 2018 at 16:46 comment added Timothy Chow The following paper does not directly address your question but it might be relevant: "The computation of the Betti numbers of an elliptic space is a NP-hard problem" by Antonio Garvin and Luis Lechuga, Topology and its Applications 131 (2003), 235-238. Note, by the way, that hardness results in complexity theory don't automatically imply that the problems are hard to solve in practice. There are plenty of NP-hard and even #P-hard problems out there that are routinely solved (or approximately solved) in practice.
Sep 18, 2018 at 11:22 history asked Simon Henry CC BY-SA 4.0