Return a basis for the maximal order of the local field L.
Return whether the local field element a lies in the maximal order of its
parent L and a sequence giving the coordinates of a with respect to the
integral basis of L if so.
We construct a local field and compute an integral basis for it.
> P<x> := PolynomialRing(Integers());
> L := LocalField(pAdicField(7, 50), x^6 - 49*x^2 + 686);
> IntegralBasis(L);
[ 1 + O(7^50), (7^-1 + O(7^49))*$.1^2 + O(7^49)*$.1 + O(7^49), (7^-2 +
O(7^48))*$.1^4 + O(7^48)*$.1^3 + O(7^48)*$.1^2 + O(7^50)*$.1 + O(7^50), $.1
+ O(7^50), (7^-1 + O(7^49))*$.1^3 + O(7^49)*$.1^2 + O(7^49)*$.1 + O(7^99),
(7^-2 + O(7^48))*$.1^5 + O(7^48)*$.1^4 + O(7^48)*$.1^3 + O(7^50)*$.1^2 +
O(7^50)*$.1 + O(7^50) ]
V2.28, 13 July 2023