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5
votes
1answer
147 views

Is there an algorithm to find out the number of small solutions to a polynomial equation, when we vary all the coefficients?

Let $\Phi (z,t)$ be a polynomial given by $$ \Phi(z,t) := z^n + A_{n-1}(t) z^{n-1} + \ldots + A_1(t) z + A_0(t).$$ Assume that $\Phi(0,0) =0$. It is a fact that a solution $z(t)$ of the equation $$ ...
2
votes
2answers
391 views

What is the closure of space of polynomials in a dense subspace along with a marked point equal to?

EDIT Let $\mathbb{C}^{m*}$ be the space of non zero polynomials of degree at most $d$ in two variables. So an element of this space is essentially $$ f:=f_{00} + f_{10} x + f_{01} y + \ldots ...