code: def rs_series_from_list(p, c, x, prec, concur=1):
      """
      Return a series `sum c[n]*p**n` modulo `O(x**prec)`.
  
      It reduces the number of multiplications by summing concurrently.
  
      `ax = [1, p, p**2, .., p**(J - 1)]`
      `s = sum(c[i]*ax[i]` for i in `range(r, (r + 1)*J))*p**((K - 1)*J)`
      with `K >= (n + 1)/J`
  
      Examples
      ========
  
      >>> from sympy.polys.domains import QQ
      >>> from sympy.polys.rings import ring
      >>> from sympy.polys.ring_series import rs_series_from_list, rs_trunc
      >>> R, x = ring('x', QQ)
      >>> p = x**2 + x + 1
      >>> c = [1, 2, 3]
      >>> rs_series_from_list(p, c, x, 4)
      6*x**3 + 11*x**2 + 8*x + 6
      >>> rs_trunc(1 + 2*p + 3*p**2, x, 4)
      6*x**3 + 11*x**2 + 8*x + 6
      >>> pc = R.from_list(list(reversed(c)))
      >>> rs_trunc(pc.compose(x, p), x, 4)
      6*x**3 + 11*x**2 + 8*x + 6
  
      """
  
      # TODO: Add this when it is documented in Sphinx
      """
      See Also
      ========
  
      sympy.polys.rings.PolyRing.compose
  
      """
      R = p.ring
      n = len(c)
      if not concur:
          q = R(1)
          s = c[0] * q
          for i in range(1, n):
              q = rs_mul(q, p, x, prec)
              s += c[i] * q
          return s
      J = int(math.sqrt(n) + 1)
      K, r = divmod(n, J)
      if r:
          K += 1
      ax = [R(1)]
      q = R(1)
      if len(p) < 20:
          for i in range(1, J):
              q = rs_mul(q, p, x, prec)
              ax.append(q)
      else:
          for i in range(1, J):
              if i % 2 == 0:
                  q = rs_square(ax[i // 2], x, prec)
              else:
                  q = rs_mul(q, p, x, prec)
              ax.append(q)
      # optimize using rs_square
      pj = rs_mul(ax[-1], p, x, prec)
      b = R(1)
      s = R(0)
      for k in range(K - 1):
          r = J * k
          s1 = c[r]
          for j in range(1, J):
              s1 += c[r + j] * ax[j]
          s1 = rs_mul(s1, b, x, prec)
          s += s1
          b = rs_mul(b, pj, x, prec)
          if not b:
              break
      k = K - 1
      r = J * k
      if r < n:
          s1 = c[r] * R(1)
          for j in range(1, J):
              if r + j >= n:
                  break
              s1 += c[r + j] * ax[j]
          s1 = rs_mul(s1, b, x, prec)
          s += s1
      return s
  
imports: from sympy.polys.domains import QQ, EX
  from sympy.polys.rings import PolyElement, ring, sring
  from sympy.polys.polyerrors import DomainError
  from sympy.polys.monomials import monomial_min, monomial_mul, monomial_div, monomial_ldiv
  from mpmath.libmp.libintmath import ifac
  from sympy.core import PoleError, Function, Expr
  from sympy.core.numbers import Rational
  from sympy.core.intfunc import igcd
  from sympy.functions import sin, cos, tan, atan, exp, atanh, tanh, log, ceiling
  from sympy.utilities.misc import as_int
  from mpmath.libmp.libintmath import giant_steps
  import math
label_desc: Use image node_id 18 for calling a global function with example usage: rs_series_from_list(p, c, x, prec, concur) and returns: s, s