// Magma code for working with p-adic field 167.2.3.4a1.1.


// Define the p-adic field: 
Prec := 100;  // Default precision of 100
Q167 := pAdicField(167, Prec);
K := LocalField(Q167, Polynomial(Q167, [125, 12617, 413415, 4579276, 82683, 498, 1]));

// Defining polynomial: 
DefiningPolynomial(K);

// Base field Qp: 
Q167;

// Degree over Qp: 
Degree(K);

// Ramification index: 
RamificationIndex(K);

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

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