Function: polrootspadic
Section: polynomials
C-Name: rootpadic
Prototype: GGL
Help: polrootspadic(x,p,r): p-adic roots of the polynomial x to precision r.
Doc: vector of $p$-adic roots of the polynomial \var{pol}, given to
 $p$-adic precision $r$ $p$ is assumed to be a prime. Multiple roots are
 \emph{not} repeated. Note that this is not the same as the roots in
 $\Z/p^r\Z$, rather it gives approximations in $\Z/p^r\Z$ of the true roots
 living in $\Q_p$.
 \bprog
 ? polrootspadic(x^3 - x^2 + 64, 2, 5)
 %1 = [2^3 + O(2^5), 2^3 + 2^4 + O(2^5), 1 + O(2^5)]~
 @eprog
 If \var{pol} has inexact \typ{PADIC} coefficients, this is not always
 well-defined; in this case, the polynomial is first made integral by dividing
 out the $p$-adic content, then lifted
 to $\Z$ using \tet{truncate} coefficientwise. Hence the roots given are
 approximations of the roots of an exact polynomial which is $p$-adically
 close to the input. To avoid pitfalls, we advise to only factor polynomials
 with eact rational coefficients.