Finally in a "book" form -- the long paper of Henri Lombardi, Daniel Perrucci and Marie-Françoise Roy, on the complexity of the Positivstellensatz.
https://bookstore.ams.org/memo-263-1277/?_zs=b8VAN1&_zl=DmiT5 …
#positivstellensatz #sumsofsquares #realalgebraicgeometry
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Is it allowed to dream that someone, someday will improve this bound to match the corresponding effective result in the algebraically closed case -- namely, the singly exponential upper bound on the complexity of Hilbert's Nullstellensatz (by Kollar, Jelonek and others) ?
22:54 - 17. pro 2019.
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