On calculating values of WeierstrassP function

[Zhibin Liang]

Dear all,

I have a question to ask you.

I want to calculate the approximate value of WeierstrassP function. For example,

E: y^2=4x^3-4x,

\cL is the complex lattice of E, and  \wp(z,\cL) is the WeierstrassP function.

I want to calculate \wp(1,\cL) and want to calculate an approximate value of it of precision 10. How to realize it in Sage?

--

Very best wishes
Zhibin Liang






Building 104 Room 103
Nanhudongyuanyiqu
Wangjing, Chaoyang District
Beijing China,
100102

[John Cremona]

sage: E = EllipticCurve([0,0,0,-1,0]); E
Elliptic Curve defined by y^2 = x^3 - x over Rational Field
sage: L = E.period_lattice()
sage: L.elliptic_exponential(1, to_curve=False)
(1.21375598633877, -0.757861263970861)
sage: L.elliptic_exponential(ComplexField(100)(1), to_curve=False)
(1.2137559863387746413172077160, -0.75786126397086095513491263067)

Look at the documentation in
sage/schemes/elliptic_curves/ell_period_lattice and in particular the
documentation for the elliptic_exponential function which computes the
map from C/L to E.

John

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