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BUILT-IN MATHEMATICA SYMBOL

EllipticExp

is the inverse for EllipticLog. It produces a list

such that u==EllipticLog[{x, y}, {a, b}].

EllipticExp gives the generalized exponential associated with the elliptic curve .

For certain special arguments, EllipticExp automatically evaluates to exact values.

Evaluate numerically:

Check relation with the inverse function:

Evaluate numerically:

Out[1]=

Check relation with the inverse function:

Out[2]=

Out[1]=

Evaluate for complex arguments:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

Define multiplication on the elliptic curve

Use multiplication on the elliptic curve to add rational numbers:

Compare with EllipticLog:

Map integers on an elliptic curve:

Differentiation:

EllipticExp is a multivalued complex function, so the inverse relation does not always hold: