All Questions

Say we have two polynomials $$ f = \sum d_n x^n, \quad g = \sum_n b_n x^n $$ that tropicalize to $$ F = \max(d_n + nx), \quad G = \max(b_n + nx). $$ Can we say $f\circ g$ tropicalizes to $F\circ G$? ...

I realize that this problem is extremely generic, so I am pessimistic that there may be concrete solutions, but let me try... Consider a multi-variate polynomial $P(x)$, is it possible to find ...

The field of Puiseux series over an algebraically closed field of characteristic zero is also an algebraically closed field, and furthermore it has a valuation so that our Puiseux series can be ...