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InverseWeierstrassP

Usage

InverseWeierstrassP[p,   ,   ] 给出Weierstrass函数  等于   的值。


Notes

• 数学函数(参见 节 A.3.10).
• 返回的  的值位于由复半周期   定义的基本周期平行四边形。
InverseWeierstrassP[ p, q ,   ,   ] 的唯一值,其中   .对如此一个值,  必须由  相联系。
• 参见3.2.11节 对椭圆函数的自变量约定的讨论。
• 参见 Mathematica 全书: 3.2.11.
Further Examples

InverseWeierstrassP and related functions take as a second argument the coefficients  of the equation of the elliptic curve under consideration (in Weierstrass normal form). If instead we know the periods of the curve, we start by using WeierstrassInvariants.

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InverseWeierstrassP can take as its first argument either the complex number  whose inverse image under WeierstrassP we seek, or a point  on the curve  . If the numbers  and  are not so related, the result is meaningless.

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This design was chosen because WeierstrassP is two-to-one in its fundamental period parallelogram, so its inverse is not unique. Giving the value of  removes the ambiguity. If  and  for some complex number  , the pair  satisfies the defining equation  .

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The two points mapped by WeierstrassP to  in this case are  and  .

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InverseWeierstrassP is closely related to EllipticLog; see the Further Examples for EllipticExp.