] gives a value of for which the Weierstrass function is equal to .
Mathematical function (see Section A.3.10).
The value of returned always lies in the fundamental period parallelogram defined by the complex half-periods and .
] finds the unique value of for which and . For such a value to exist, and must be related by .
See Section 3.2.11 for a discussion of argument conventions for elliptic functions.
See the Mathematica book: Section 3.2.11.
See also: WeierstrassP, WeierstrassPPrime, WeierstrassHalfPeriods.
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.
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.
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 .
The two points mapped by WeierstrassP to in this case are and .
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