code: def migcdex(*x: int) -> tuple[tuple[int, ...], int]:
      r"""Compute extended gcd for multiple integers.
  
      Explanation
      ===========
  
      Given the integers $x_1, \cdots, x_n$ and
      an extended gcd for multiple arguments are defined as a solution
      $(y_1, \cdots, y_n), g$ for the diophantine equation
      $x_1 y_1 + \cdots + x_n y_n = g$ such that
      $g = \gcd(x_1, \cdots, x_n)$.
  
      Examples
      ========
  
      >>> from sympy.functions.elementary._trigonometric_special import migcdex
      >>> migcdex()
      ((), 0)
      >>> migcdex(4)
      ((1,), 4)
      >>> migcdex(4, 6)
      ((-1, 1), 2)
      >>> migcdex(6, 10, 15)
      ((1, 1, -1), 1)
      """
      if not x:
          return (), 0
  
      if len(x) == 1:
          return (1,), x[0]
  
      if len(x) == 2:
          u, v, h = igcdex(x[0], x[1])
          return (u, v), h
  
      y, g = migcdex(*x[1:])
      u, v, h = igcdex(x[0], g)
      return (u, *(v * i for i in y)), h
  
file_path: sympy/sympy/functions/elementary/_trigonometric_special.py
imports: from __future__ import annotations
  from typing import Callable
  from functools import reduce
  from sympy.core.expr import Expr
  from sympy.core.singleton import S
  from sympy.core.intfunc import igcdex
  from sympy.core.numbers import Integer
  from sympy.functions.elementary.miscellaneous import sqrt
  from sympy.core.cache import cacheit
label_desc: Use image node_id 1 for calling a global function with example usage: migcdex() and returns: u,  unknown,  h, ,  int, int,  x, u,  v,  h