[Next][Prev] [Right] [Left] [Up] [Index] [Root]

Maximal Order

IntegralBasis(L) : RngLocA -> SeqEnum
Return a basis for the maximal order of the local field L.
IsIntegral(a) : RngLocAElt -> BoolElt, SeqEnum
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.

Example RngLocA_max-order (H51E5)

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) ]

 [Next][Prev] [Right] [Left] [Up] [Index] [Root]

Version: V2.19 of Wed Apr 24 15:09:57 EST 2013