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Evaluating values of the Weierstrass $\wp$-function

asked 2013-08-06 11:39:19 +0200

Blackadder gravatar image

I would like to know how can we evaluate the Weierstrass $\wp$-functions. That is, I would like to find $\wp(\theta,\omega,i\omega)$ for some $\theta,\omega\in\mathbb{R}$.

I'm only able to find a function which outputs the Laurent series of the Weierstrass $\wp$-function when an elliptic curve has been entered. Should I evaluate that laurent series?

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answered 2013-08-07 11:29:35 +0200

Luca gravatar image

The function weierstrass_p() of EllipticCurve returns the Laurent expansion of $\wp$ at the origin, hence evaluating it only gives a reasonable approximation near it.

Nothing comes to my mind to do this kind of numerical evaluation straightforwardly in Sage. If you have access to Maple, you could give a shot at the NumGFun package, part of the AlgoLib library It has support for the numerical evaluation of functions satisfying linear differential equations with polynomial coefficients.

The author of NumGFun gave a talk on it at Sage Days 49 As you can read in the slides, nothing of it is already in Sage, but there are plans for the close future. See, for example,, which will add functionality similar to what you need.

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The Jacobi elliptic functions in #14996 are already in Sage, the patch just improves them.

Eviatar Bach gravatar imageEviatar Bach ( 2013-08-08 02:45:41 +0200 )edit

Nice, I didn't know that. Then you may try using the formulas given here: <></p<>>

Luca gravatar imageLuca ( 2013-08-09 12:04:27 +0200 )edit

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Asked: 2013-08-06 11:39:19 +0200

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Last updated: Aug 07 '13