// Magma code for working with p-adic field 7.3.7.21a15.1.


// Define the p-adic field: 
Prec := 100;  // Default precision of 100
Q7 := pAdicField(7, Prec);
K := LocalField(Q7, Polynomial(Q7, [16391, 112, 172032, 28840, 774172, 258048, 1956864, 967680, 3064320, 1944320, 3096576, 2231040, 2034368, 1427328, 834336, 447888, 178416, 46368, 7588, 756, 42, 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));