code: def coeff_search(m, R):
      r"""
      Generate coefficients for searching through polynomials.
  
      Explanation
      ===========
  
      Lead coeff is always non-negative. Explore all combinations with coeffs
      bounded in absolute value before increasing the bound. Skip the all-zero
      list, and skip any repeats. See examples.
  
      Examples
      ========
  
      >>> from sympy.polys.numberfields.utilities import coeff_search
      >>> cs = coeff_search(2, 1)
      >>> C = [next(cs) for i in range(13)]
      >>> print(C)
      [[1, 1], [1, 0], [1, -1], [0, 1], [2, 2], [2, 1], [2, 0], [2, -1], [2, -2],
       [1, 2], [1, -2], [0, 2], [3, 3]]
  
      Parameters
      ==========
  
      m : int
          Length of coeff list.
      R : int
          Initial max abs val for coeffs (will increase as search proceeds).
  
      Returns
      =======
  
      generator
          Infinite generator of lists of coefficients.
  
      """
      R0 = R
      c = [R] * m
      while True:
          if R == R0 or R in c or -R in c:
              yield c[:]
          j = m - 1
          while c[j] == -R:
              j -= 1
          c[j] -= 1
          for i in range(j + 1, m):
              c[i] = R
          for j in range(m):
              if c[j] != 0:
                  break
          else:
              R += 1
              c = [R] * m
  
imports: from sympy.core.sympify import sympify
  from sympy.ntheory.factor_ import factorint
  from sympy.polys.domains.rationalfield import QQ
  from sympy.polys.domains.integerring import ZZ
  from sympy.polys.matrices.exceptions import DMRankError
  from sympy.polys.numberfields.minpoly import minpoly
  from sympy.printing.lambdarepr import IntervalPrinter
  from sympy.utilities.decorator import public
  from sympy.utilities.lambdify import lambdify
  from mpmath import mp
label_desc: Use image node_id 5 for calling a global function with example usage: coeff_search(m, R) without return types