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Feb 16, 2017 at 21:42 comment added Dima Pasechnik something like this (i.e. one can produce explicit small degrees of s.o.s. forms to multiply with) also works for quaternary forms of degree 4, see arxiv.org/abs/1511.03473
Sep 23, 2014 at 19:24 comment added Dima Pasechnik for more variables nothing of this sort is known; Hilbert's (1893) paper substantially uses quite tricky algebraic geometry of complex plane curves (something that nowadays one would explain using en.wikipedia.org/wiki/Theta_characteristic)
Sep 23, 2014 at 19:17 comment added Igor Rivin Cool! Does this only work for ternary?
Sep 22, 2014 at 19:56 history edited Dima Pasechnik CC BY-SA 3.0
more references, and an explanation
Sep 22, 2014 at 19:36 history answered Dima Pasechnik CC BY-SA 3.0