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Oct 13 at 1:09 comment added user82261 The exact form the polynomials take in my application might differ a bit but that's besides the point for now.
Oct 13 at 1:09 comment added user82261 I agree. This is a polynomial in $\mathbb R^{2d}$ at the end of the day. This is essentially one approach suggested here: mathoverflow.net/questions/66842/… I still want to compute bounds on the number of connected components. I am not sure if anything changes in this case.
Oct 13 at 0:46 comment added Ryan Budney You could think of these as polynomials on $(S^1)^d$, i.e. plain old polynomials on $\mathbb R^{2d}$, then restricted so that each variable is unit length. From this perspective, what tools are you missing?
Oct 12 at 23:25 history edited YCor CC BY-SA 4.0
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Oct 12 at 20:56 history asked user82261 CC BY-SA 4.0