"Source: Text/Ring/RngOrd.text";
"Line: 8611";
"Date: Fri Sep 26 14:51:59 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/RngOrd.text, line: 8611
// Example: H39E37 ()
print "Example: H39E37";
ei := GetEchoInput();
SetEchoInput(true);
Ax<x> := PolynomialRing(Integers());
f := x^5 + 343*x^4 + 49*x^3 + 343*x^2 + 7*x + 6;
L := NumberField(f);
p := 7;
Montes(L,p);
P := L`PrimeIdeals[p,1];
P`Type[#P`Type]`slope;
P`Type[#P`Type]`Phi; // the approximation
slope := 50;                                  
SFL(~P,slope:update := true);            
P`Type[#P`Type]`slope;                   
P`Type[#P`Type]`Phi; // the approximation
SetEchoInput(ei);
