[例1]f0,f1,f2,f3のガロア群

_<x>:=PolynomialAlgebra(Rationals());

f0:=x^5+1;
f1:=x^5-10*x^3+5*x^2+10*x+1;
f2:=x^5-5*x+12;
f3:=x^5+15*x+12;

f0,GaloisGroup(f0);
f1,GaloisGroup(f1);
f2,GaloisGroup(f2);
f3,GaloisGroup(f3);


[例2]f(x)=x^5+ax^3+bx^2+cx+d(-1<a,b,c<3, 0<d<5)のガロア群

_<x>:=PolynomialAlgebra(Rationals());

for i in {0..3} do
 for j in {0..3} do
  for k in {0..3} do
   for m in {1..5} do
     f:=x^5+i*x^3+j*x^2+k*x+m;
     g:=GaloisGroup(f);
     if Order(g) le 60 then 
       print f, g;
     end if;
   end for;
  end for;
 end for;
end for;


[例3]f(x)=x^5+ax^3+bx^2+cx+d([a,b,c,d]=
{[0,10,-10,6],[5,-5,5,3],[5,1,9,5],[9,5,3,9],[8,-11,8,3]}のガロア群

_<x>:=PolynomialAlgebra(Rationals());
t:=[[0,10,-10,6],[5,-5,5,3],[5,1,9,5],[9,5,3,9],[8,-11,8,3]];

for i in {1..#(a)} do
  f:=x^5+t[i,1]*x^3+t[i,2]*x^2+t[i,3]*x+t[i,4];
  g:=GaloisGroup(f);
    if Order(g) le 60 then 
      print f, g;
    end if;
end for;