code: def polydiv(
      u: ArrayLike, v: ArrayLike, *, trim_leading_zeros: bool = False
  ) -> tuple[Array, Array]:
      check_arraylike("polydiv", u, v)
      u_arr, v_arr = promote_dtypes_inexact(u, v)
      m = len(u_arr) - 1
      n = len(v_arr) - 1
      scale = 1.0 / v_arr[0]
      q: Array = zeros(
          max(m - n + 1, 1), dtype=u_arr.dtype
      )  # force same dtype
      for k in range(0, m - n + 1):
          d = scale * u_arr[k]
          q = q.at[k].set(d)
          u_arr = u_arr.at[k : k + n + 1].add(-d * v_arr)
      if trim_leading_zeros:
          # use the square root of finfo(dtype) to approximate the absolute tolerance used in numpy
          u_arr = trim_zeros_tol(
              u_arr, tol=sqrt(finfo(u_arr.dtype).eps), trim="f"
          )
      return q, u_arr
  
imports: from __future__ import annotations
  from functools import partial
  import operator
  import numpy
  from jax import jit
  from jax import lax
  from jax._src import dtypes
  from jax._src import core
  from jax._src.numpy.lax_numpy import arange, argmin, array, asarray, atleast_1d, concatenate, convolve, diag, dot, finfo, full, ones, outer, roll, trim_zeros, trim_zeros_tol, vander, zeros
  from jax._src.numpy.ufuncs import maximum, true_divide, sqrt
  from jax._src.numpy.reductions import all
  from jax._src.numpy import linalg
  from jax._src.numpy.util import check_arraylike, promote_dtypes, promote_dtypes_inexact, _where, _wraps
  from jax._src.typing import Array, ArrayLike
label_desc: Use image node_id 11 for calling a global function with example usage: polydiv(u, v) and returns: q,  u_arr