lfunthetacost

Function: lfunthetacost
Section: l_functions
C-Name: lfunthetacost0
Prototype: lGDGD0,L,b
Help: lfunthetacost(L,{tdom},{m=0}): estimates the cost of running
 lfunthetainit(L,tdom,m) at current bit precision. Returns the number of
 coefficients an that would be computed. Subsequent evaluation of lfuntheta
 computes that many values of gammamellininv.
 If L is already an Linit, then tdom and m are ignored.
Doc: This function estimates the cost of running
 \kbd{lfunthetainit(L,tdom,m)} at current bit precision. Returns the number of
 coefficients $a_n$ that would be computed. This also estimates the
 cost of a subsequent evaluation \kbd{lfuntheta}, which must compute
 that many values of \kbd{gammamellininv} at the current bit precision.
 If $L$ is already an \kbd{Linit}, then \var{tdom} and $m$ are ignored
 and are best left omitted: we get an estimate of the cost of using that
 particular \kbd{Linit}.

 \bprog
 ? \pb 1000
 ? L = lfuncreate(1); \\ Riemann zeta
 ? lfunthetacost(L); \\ cost for theta(t), t real >= 1
 %1 = 15
 ? lfunthetacost(L, 1 + I); \\ cost for theta(1+I). Domain error !
  ***   at top-level: lfunthetacost(1,1+I)
  ***                 ^--------------------
  *** lfunthetacost: domain error in lfunthetaneed: arg t > 0.785
 ? lfunthetacost(L, 1 + I/2) \\ for theta(1+I/2).
 %2 = 23
 ? lfunthetacost(L, 1 + I/2, 10) \\ for theta^((10))(1+I/2).
 %3 = 24
 ? lfunthetacost(L, [2, 1/10]) \\ cost for theta(t), |t| >= 2, |arg(t)| < 1/10
 %4 = 8

 ? L = lfuncreate( ellinit([1,1]) );
 ? lfunthetacost(L)  \\ for t >= 1
 %6 = 2471
 @eprog