// Magma code for working with p-adic field 179.2.6.10a1.4.


// Define the p-adic field: 
Prec := 100;  // Default precision of 100
Q179 := pAdicField(179, Prec);
K := LocalField(Q179, Polynomial(Q179, [31747, 34277, 7100352, 814234240, 52526983920, 1807661057664, 25944826482464, 903830528832, 13131745980, 101779280, 443772, 1032, 1]));

// Defining polynomial: 
DefiningPolynomial(K);

// Base field Qp: 
Q179;

// Degree over Qp: 
Degree(K);

// Ramification index: 
RamificationIndex(K);

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

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