// Magma code for working with p-adic field 7.2.9.16a1.2.


// Define the p-adic field: 
Prec := 100;  // Default precision of 100
Q7 := pAdicField(7, Prec);
K := LocalField(Q7, Polynomial(Q7, [19690, 354294, 2893401, 14171760, 46373148, 106918056, 178625412, 219294864, 198960138, 133555716, 66320046, 24366096, 6615756, 1319976, 190836, 19440, 1323, 54, 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));