// Magma code for working with p-adic field 17.3.4.9a1.4.


// Define the p-adic field: 
Prec := 100;  // Default precision of 100
Q17 := pAdicField(17, Prec);
K := LocalField(Q17, Polynomial(Q17, [38467, 11248, 1176, 11032, 2353, 168, 1180, 168, 6, 56, 4, 0, 1]));

// Defining polynomial: 
DefiningPolynomial(K);

// Base field Qp: 
Q17;

// Degree over Qp: 
Degree(K);

// Ramification index: 
RamificationIndex(K);

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

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