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Aug
8
awarded  Editor
Aug
8
comment Finding regions where multi-variate polynomials are positive
Thank you for pointing this out. Sorry, yes, it was a typo. I meant P_j to map to $\mathbb Z$ and not just to $\mathbb N$. I changed it in the question above.
Aug
8
revised Finding regions where multi-variate polynomials are positive
edited body; edited title
Aug
8
awarded  Scholar
Aug
8
accepted Finding regions where multi-variate polynomials are positive
Aug
8
comment Finding regions where multi-variate polynomials are positive
THANK YOU! This looks like a correct proof to me.
Aug
8
comment Finding regions where multi-variate polynomials are positive
Thank you for your answer! Unfortunately, my issue is not to test which polynomials are the same. I need the conjecture above in another proof, which would use the existence of the above S_i to show that some other polynomials are the same. Besides the probabilistic Schwartz-Zippel lemma, there is a decision procedure to test whether two multi-variate polynomials are the same. The procedure just extends the fact that a polynomial of degree n has at most n roots to the multi-variate case. [N. Alon and M. Tarsi. Colorings and orientations of graphs. Combinatorica, 12(2):125­134, 1992.]
Aug
6
awarded  Student
Aug
5
asked Finding regions where multi-variate polynomials are positive