kleinj {jacobi}

Klein j-function and its inverse

Description

Evaluation of the Klein j-invariant function and its inverse.

Usage

kleinj(tau, transfo = FALSE)

kleinjinv(j)

Arguments

tau

a complex number with strictly positive imaginary part, or a vector or matrix of such complex numbers; missing values allowed

transfo

Boolean, whether to use a transformation of the values of tau close to the real line; using this option can fix some failures of the computation (at the cost of speed), e.g. when the algorithm reaches the maximal number of iterations

j

a complex number

Value

A complex number, vector or matrix.

Note

The Klein-j function is the one with the factor 1728.

Examples

( j <- kleinj(2i) )
66^3
kleinjinv(j)