Do you know any bound on f(D,k)?

As Terry mentioned, one cannot get the same bound as in the complex case, but I just wonder if one can get something in that neighborhood. ]]>

Is there a version of Theorem 5 that says that for some function f,

either V < f(D,k), where D is the max degree of the m polynomials,

or V_0 is infinite? Is there a polynomial bound for f? ]]>

Hi,

I am not sure if I understand the comment right but isn’t the mixed volume bounds of Bersntein’s theorem a big gain over Bezout?

It depends the Newton polytope which is some what sparsity.

]]>Sorry to bother you much, but it seems that the post doesn’t reflect the correction :-)

*[Oops; should be visible now. -T.]*

*[Corrected, thanks – T.]*

Thanks ! I am guessing you may assume that the infinite union of isolated points must be a 0 dimensional cycle , therefore a contradiction with a finite degree ,right? But i am confused that why it must be 0 dimensional ? Thanks!

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