// Magma code for working with p-adic field 19.3.3.6a1.3.


// Define the p-adic field: 
Prec := 100;  // Default precision of 100
Q19 := pAdicField(19, Prec);
K := LocalField(Q19, Polynomial(Q19, [4932, 3468, 816, 931, 408, 48, 51, 12, 0, 1]));

// Defining polynomial: 
DefiningPolynomial(K);

// Base field Qp: 
Q19;

// Degree over Qp: 
Degree(K);

// Ramification index: 
RamificationIndex(K);

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

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