// Magma code for working with p-adic field 3.4.5.16a1.1.


// Define the p-adic field: 
Prec := 100;  // Default precision of 100
Q3 := pAdicField(3, Prec);
K := LocalField(Q3, Polynomial(Q3, [32, 3, 0, 160, 80, 0, 320, 320, 80, 320, 480, 240, 200, 320, 240, 112, 90, 80, 40, 10, 1]));

// Defining polynomial: 
DefiningPolynomial(K);

// Base field Qp: 
Q3;

// Degree over Qp: 
Degree(K);

// Ramification index: 
RamificationIndex(K);

// Residue field degree (Inertia degree): 
InertiaDegree(K);

// Discriminant exponent: 
Valuation(Discriminant(K));