Function: centerlift
Section: conversions
C-Name: centerlift0
Prototype: GDn
Help: centerlift(x,{v}): centered lift of x. Same as lift except for
 intmod and padic components.
Description:
 (pol):pol        centerlift($1)
 (vec):vec        centerlift($1)
 (gen):gen        centerlift($1)
 (pol, var):pol        centerlift0($1, $2)
 (vec, var):vec        centerlift0($1, $2)
 (gen, var):gen        centerlift0($1, $2)
Doc: Same as \tet{lift}, except that \typ{INTMOD} and \typ{PADIC} components
 are lifted using centered residues:

 \item for a \typ{INTMOD} $x\in \Z/n\Z$, the lift $y$ is such that
 $-n/2<y\le n/2$.

 \item  a \typ{PADIC} $x$ is lifted in the same way as above (modulo
 $p^\kbd{padicprec(x)}$) if its valuation $v$ is nonnegative; if not, returns
 the fraction $p^v$ \kbd{centerlift}$(x p^{-v})$; in particular, rational
 reconstruction is not attempted. Use \tet{bestappr} for this.

 For backward compatibility, \kbd{centerlift(x,'v)} is allowed as an alias
 for \kbd{lift(x,'v)}.

 \synt{centerlift}{GEN x}.