// Magma code for working with p-adic field 197.2.6.10a1.4.


// Define the p-adic field: 
Prec := 100;  // Default precision of 100
Q197 := pAdicField(197, Prec);
K := LocalField(Q197, Polynomial(Q197, [38479, 37849, 8847552, 1132554240, 81554964720, 3132729944064, 50178049081504, 1566364972032, 20388741180, 141569280, 552972, 1152, 1]));

// Defining polynomial: 
DefiningPolynomial(K);

// Base field Qp: 
Q197;

// Degree over Qp: 
Degree(K);

// Ramification index: 
RamificationIndex(K);

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

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