// Magma code for working with p-adic field 7.4.4.12a1.3.


// Define the p-adic field: 
Prec := 100;  // Default precision of 100
Q7 := pAdicField(7, Prec);
K := LocalField(Q7, Polynomial(Q7, [88, 432, 1404, 2928, 4594, 5312, 5016, 3696, 2539, 1344, 776, 240, 162, 16, 20, 0, 1]));

// Defining polynomial: 
DefiningPolynomial(K);

// Base field Qp: 
Q7;

// Degree over Qp: 
Degree(K);

// Ramification index: 
RamificationIndex(K);

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

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