Function: ellwp
Section: elliptic_curves
C-Name: ellwp0
Prototype: GDGD0,L,p
Help: ellwp(w,{z='x},{flag=0}): computes the value at z of the Weierstrass P
 function attached to the lattice w, as given by ellperiods. Optional flag
 means 0 (default), compute only P(z), 1 compute [P(z),P'(z)].
Doc: Computes the value at $z$ of the Weierstrass $\wp$ function attached to
 the lattice $w$ as given by \tet{ellperiods}. It is also possible to
 directly input $w = [\omega_1,\omega_2]$, or an elliptic curve $E$ as given
 by \kbd{ellinit} ($w = \kbd{E.omega}$).
 \bprog
 ? w = ellperiods([1,I]);
 ? ellwp(w, 1/2)
 %2 = 6.8751858180203728274900957798105571978
 ? E = ellinit([1,1]);
 ? ellwp(E, 1/2)
 %4 = 3.9413112427016474646048282462709151389
 @eprog\noindent One can also compute the series expansion around $z = 0$:
 \bprog
 ? E = ellinit([1,0]);
 ? ellwp(E)              \\ 'x implicitly at default seriesprecision
 %5 = x^-2 - 1/5*x^2 + 1/75*x^6 - 2/4875*x^10 + O(x^14)
 ? ellwp(E, x + O(x^12)) \\ explicit precision
 %6 = x^-2 - 1/5*x^2 + 1/75*x^6 + O(x^9)
 @eprog

 Optional \fl\ means 0 (default): compute only $\wp(z)$, 1: compute
 $[\wp(z),\wp'(z)]$.

Variant: For $\fl = 0$, we also have
 \fun{GEN}{ellwp}{GEN w, GEN z, long prec}, and
 \fun{GEN}{ellwpseries}{GEN E, long v, long precdl} for the power series in
 variable $v$.