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 an element $x$ from in the residue field modulo \var{pr} to the ring
 of integers; $x$ is a \typ{INTMOD} or \typ{FFELT} from \tet{nfmodpr}.
 Vectors and matrices of such elements 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
