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EllipticLog

EllipticLog[{x, y}, {a, b}]
gives the generalized logarithm associated with the elliptic curve y^2=x^3+a x^2+b x.
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • EllipticLog[{x, y}, {a, b}] is defined as the value of the integral , where the sign of the square root is specified by giving the value of y such that .
  • EllipticLog can be evaluated to arbitrary numerical precision.
EXAMPLESCLOSE ALL
Scope   (3)
Evaluate for complex arguments and parameters:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Applications   (1)
Define multiplication on the elliptic curve y^2=x^3+a x^2+b x:
Use multiplication on the elliptic curve to add rational numbers:
Compare with EllipticLog:
Properties & Relations   (2)
Differentiation:
EllipticExp and EllipticLog are inverse functions of one another:
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