// Magma code for working with p-adic field 89.1.20.19a1.3.


// Define the p-adic field: 
Prec := 100;  // Default precision of 100
Q89 := pAdicField(89, Prec);
K := LocalField(Q89, Polynomial(Q89, [801, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]));

// Defining polynomial: 
DefiningPolynomial(K);

// Base field Qp: 
Q89;

// Degree over Qp: 
Degree(K);

// Ramification index: 
RamificationIndex(K);

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

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