Problem Statement

The Jacobi symbol is a multiplicative function that generalizes the Legendre symbol. Specifically, the Jacobi symbol (a | n) equals the product of the Legendre symbols (a | p_i)^(k_i), where n = p_1^(k_1)p_2^(k_2)...*p_i^(k_i) and the Legendre symbol (a | p) denotes the value of a ^ ((p-1)/2) (mod p) If n is prime, then the Jacobi symbol (a | n) equals the Legendre symbol (a | n). Calculate the Jacobi symbol (a | n).

Let's start with the solution:

NB. functionally equivalent translation of the Lua program found
NB. at https://en.wikipedia.org/wiki/Jacobi_symbol
jacobi=: {{
  assert. (0<x) * 1=2|x
  y=. x|y
  t=. 1
  while. y do.
    e=. (|.#:y) i.1
    y=. <.y%2^e
    t=. t*_1^(*/3 = 4|x,y)+(2|e)*(8|x) e.3 5
    'x y'=. y, y|x
  end.
  t*x=1
}}"0