Wilkinson polynomial

The Wilkinson polynomial of order $n$ is obtained as the product of the terms $(x-i)$ for i from 1 to $n$. Its expanded form is difficult to solve as soon as $n$ is larger than 12. If eq is the polynomial a procedure for solving it is:

 
EQ:=[eq]:
VAR:=[x]:
INIT:=[[-100,100]]:

`ALIAS/fepsilon`:=1e-9:
`ALIAS/epsilon`:=1e-14:
`ALIAS/storage_mode`:=10:
`ALIAS/3B`:=1:
`ALIAS/Max3B`:=10000:
`ALIAS/Delta3B`:=1e-9:
`ALIAS/optimized`:=0:
`ALIAS/rand`:=500:
`ALIAS/eps_inflation`:=1e-10:
`ALIAS/dist`:=1e-16:

Rouche(EQ,"p",VAR,"rouche"):
WeylFilter(EQ,VAR,VAR,["automatic"],["symbolic"],"SimpWeyl");
DeflationUP(eq,x,"F","J","simp_quo_new",debug);

CatSimp("SIMP","rouche","NO_3B","simp_quo_new","SimpWeyl",0.1);

SOL:=GradientSolve(EQ,VAR,INIT,"SIMP");

To filter the boxes we use WeylFilter, DeflationUP and to find the solutions we use Rouche.