Learn R Programming

elliptic (version 0.4-13)

e1e2e3: Calculate e1, e2, e3 from the invariants

Description

Calculates e1, e2, e3 from the invariants using either polyroot or Cardano's method.

Usage

e1e2e3(g, use.laurent=TRUE, AnS=is.real(g), Omega=NULL, tol=1e-6)
eee.cardano(g)

Arguments

g
Two-element vector with g=c(g2,g3)
use.laurent
Boolean, with default TRUE meaning to use P.laurent() to determine the correct ordering for the $e$: $P(\omega_1)$, $P(\omega_2)$, $P(\omega_3)$. Setting to FALSE means to return the solutions of th
AnS
Boolean, with default TRUE meaning to define $\omega_3$ as per ams-55, and FALSE meaning to follow Whittaker and Watson, and define $\omega_1$ and $\omega_2$ as the primitive half periods, and $\omega_3=-\omeg
Omega
A pair of primitive half periods, if known. If supplied, the function uses them to calculate approximate values for the three $e$s (but supplies values calculated by polyroot(), which are much more accurate). The function needs
tol
Real, relative tolerance criterion for terminating Laurent summation

Value

  • Returns a three-element vector.

References

Mathematica

Examples

Run this code
print("e1e2e3")

Run the code above in your browser using DataLab