// Magma code for working with p-adic field 3.5.4.15a1.1.


// Define the p-adic field: 
Prec := 100;  // Default precision of 100
Q3 := pAdicField(3, Prec);
K := LocalField(Q3, Polynomial(Q3, [1, 11, 24, 32, 16, 4, 24, 48, 32, 0, 6, 24, 24, 0, 0, 4, 8, 0, 0, 0, 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));