Function: lfunrootres
Section: l_functions
C-Name: lfunrootres
Prototype: Gb
Help: lfunrootres(data): given the Ldata associated to an L-function (or the
 output of lfunthetainit), compute the root number and the
 residues. In the present implementation, if the polar part is not already
 known completely, at most a single pole is allowed.
 The output is a 3-component vector [r,R,w], where r is the residue of L(s)
 at the unique pole (0 if no pole), R is the residue of Lambda(s), and w is
 the root number.
Doc: Given the \kbd{Ldata} associated to an $L$-function (or the output of
 \kbd{lfunthetainit}), compute the root number and the residues.
 The output is a 3-component vector $[r,R,w]$, where $r$ is the
 residue of $L(s)$ at the unique pole, $R$ is the residue of $\Lambda(s)$,
 and $w$ is the root number. In the present implementation,

 \item either the polar part must be completely known (and is then arbitrary):
 the function determines the root number,

 \bprog
 ? L = lfunmul(1,1); \\ zeta^2
 ? [r,R,w] = lfunrootres(L);
 ? r  \\ single pole at 1, double
 %3 = [[1, 1.[...]*x^-2 + 1.1544[...]*x^-1 + O(x^0)]]
 ? w
 %4 = 1
 ? R \\ double pole at 0 and 1
 %5 = [[1,[...]], [0,[...]]
 @eprog

 \item or at most a single pole is allowed: the function computes both
 the root number and the residue ($0$ if no pole).
