Function: centerlift
Section: conversions
C-Name: centerlift0
Prototype: GDn
Help: centerlift(x,{v}): centered lift of x. Same as lift except for
 integermods.
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:
 lifts an element $x=a \bmod n$ of $\Z/n\Z$
 to $a$ in $\Z$, and similarly lifts a polmod to a polynomial. This is the
 same as \tet{lift} except that in the particular case of elements of
 $\Z/n\Z$, the lift $y$ is such that $-n/2<y\le n/2$.  A \typ{PADIC} is lifted
 as above if its valuation $v$ is non-negative; if not, returns the fraction
 $p^v$ \kbd{centerlift}$(x^{-v})$; in particular, note that rational
 reconstruction is not attempted.

 If $x$ is of type fraction, complex, quadratic, polynomial, power series,
 rational function, vector or matrix, the lift is done for each coefficient.
 Reals are forbidden.

Variant: Also available is \fun{GEN}{centerlift}{GEN x} corresponding to
 \kbd{centerlift0(x,-1)}.
