Function: nfmodprlift
Section: number_fields
C-Name: nfmodprlift
Prototype: GGG
Help: nfmodprlift(nf,x,pr): lift x from residue field mod pr to nf.
Doc: lift the \typ{FFELT} $x$ (from \tet{nfmodpr}) in the residue field
modulo \var{pr} to the ring of integers. Vectors and matrices are also
supported. For polynomials, use \kbd{apply} and the present function.
The argument \var{pr} is either a maximal ideal in \kbd{idealprimedec}
format or, preferably, a \var{modpr} structure from \tet{nfmodprinit}.
There are no compatibility checks to try and decide whether $x$ is attached
the same residue field as defined by \var{pr}: the result is undefined
if not.
The function \tet{nfmodpr} allows to reduce to the residue field.
\bprog
? K = nfinit(y^3-250);
? P = idealprimedec(K, 5)[2];
? modP = nfmodprinit(K,P);
? K.zk
%4 = [1, 1/5*y, 1/25*y^2]
? apply(t->nfmodpr(K,t,modP), K.zk)
%5 = [1, y, 2*y + 1]
? nfmodprlift(K, %, modP)
%6 = [1, 1/5*y, 2/5*y + 1]
? nfeltval(K, %[3] - K.zk[3], P)
%7 = 1
@eprog