"Source: Text/Ring/FldFunG.text";
"Line: 9052";
"Date: Fri Sep 26 13:15:42 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/FldFunG.text, line: 9052
// Example: H46E53 ()
print "Example: H46E53";
ei := GetEchoInput();
SetEchoInput(true);
k := GF(13);
A<t> := PolynomialRing(k);
Ax<x> := PolynomialRing(A);
f := x^5 + (t^2 + 2*t + 1)*x^4 + (t^4 + 4*t^3 + 6*t^2 + 4*t + 1)*x^3 + (t^3
+ 3*t^2 + 3*t + 1)*x^2 + (t^4 + 4*t^3 + 6*t^2 + 4*t + 1)*x + t;
L := FunctionField(f);
p := t+1;
Montes(L,p);
P := L`PrimeIdeals[p,1];
P`Type[#P`Type]`slope;
P`Type[#P`Type]`Phi; // the approximation
SFL(~P,10:update := true);
P`Type[#P`Type]`slope;
P`Type[#P`Type]`Phi; // the approximation
SetEchoInput(ei);
