EllipticExp
EllipticExp[u,{a,b}]
is the inverse for EllipticLog. It produces a list {x,y} such that u==EllipticLog[{x,y},{a,b}].
Details

- Mathematical function, suitable for both symbolic and numerical manipulation.
- EllipticExp gives the generalized exponential associated with the elliptic curve
.
- For certain special arguments, EllipticExp automatically evaluates to exact values.
- EllipticExp can be evaluated to arbitrary numerical precision.
Examples
open allclose allBasic Examples (2)
Check relation with the inverse function:
Plot coordinates of the elliptic curve over several real periods of EllipticExp:
Scope (10)
Numerical Evaluation (4)
Visualization (2)
Plot the EllipticExp function for various parameters:
Applications (3)
Define multiplication on the elliptic curve :
Use multiplication on the elliptic curve to add rational numbers:
Compare with EllipticLog:
Properties & Relations (3)
Differentiation:
The point returned by EllipticExp[u,{a,b}] satisfies
:
EllipticExp is closely related to the WeierstrassP function and its derivative:
Possible Issues (1)
EllipticExp is a doubly periodic complex function, so the inverse relation does not always hold:
Text
Wolfram Research (1988), EllipticExp, Wolfram Language function, https://reference.wolfram.com/language/ref/EllipticExp.html.
CMS
Wolfram Language. 1988. "EllipticExp." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/EllipticExp.html.
APA
Wolfram Language. (1988). EllipticExp. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/EllipticExp.html