lfunorderzero

Function: lfunorderzero
Section: l_functions
C-Name: lfunorderzero
Prototype: lGD-1,L,b
Help: lfunorderzero(L, {m = -1}): computes the order of the possible zero
 of the L-function at the center k/2 of the critical strip. If m is
 given and has a nonnegative value, assumes the order is at most m.
Doc: Computes the order of the possible zero of the $L$-function at the
 center $k/2$ of the critical strip; return $0$ if $L(k/2)$ does not vanish.

 If $m$ is given and has a nonnegative value, assumes the order is at most $m$.
 Otherwise, the algorithm chooses a sensible default:

 \item if the $L$ argument is an \kbd{Linit}, assume that a multiple zero at
 $s = k / 2$ has order less than or equal to the maximal allowed derivation
 order.

 \item else assume the order is less than $4$.

 You may explicitly increase this value using optional argument~$m$; this
 overrides the default value above. (Possibly forcing a recomputation
 of the \kbd{Linit}.)