// Magma code for working with p-adic field 7.12.1.0a1.1.


// Define the p-adic field: 
Prec := 100;  // Default precision of 100
Q7 := pAdicField(7, Prec);
K := LocalField(Q7, Polynomial(Q7, [3, 0, 5, 0, 4, 2, 3, 5, 2, 0, 0, 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));