// Magma code for working with p-adic field 7.3.6.15a1.4.


// Define the p-adic field: 
Prec := 100;  // Default precision of 100
Q7 := pAdicField(7, Prec);
K := LocalField(Q7, Polynomial(Q7, [4117, 0, 36871, 6144, 138240, 46080, 280320, 138240, 334080, 208640, 238464, 161280, 98736, 55296, 20160, 4344, 540, 36, 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));