code: def dup_sqr(f, K):
      """
      Square dense polynomials in ``K[x]``.
  
      Examples
      ========
  
      >>> from sympy.polys import ring, ZZ
      >>> R, x = ring("x", ZZ)
  
      >>> R.dup_sqr(x**2 + 1)
      x**4 + 2*x**2 + 1
  
      """
      df, h = len(f) - 1, []
  
      for i in range(0, 2 * df + 1):
          c = K.zero
  
          jmin = max(0, i - df)
          jmax = min(i, df)
  
          n = jmax - jmin + 1
  
          jmax = jmin + n // 2 - 1
  
          for j in range(jmin, jmax + 1):
              c += f[j] * f[i - j]
  
          c += c
  
          if n & 1:
              elem = f[jmax + 1]
              c += elem**2
  
          h.append(c)
  
      return dup_strip(h)
  
imports: from sympy.polys.densebasic import dup_slice, dup_LC, dmp_LC, dup_degree, dmp_degree, dup_strip, dmp_strip, dmp_zero_p, dmp_zero, dmp_one_p, dmp_one, dmp_ground, dmp_zeros
  from sympy.polys.polyerrors import ExactQuotientFailed, PolynomialDivisionFailed
label_desc: Use image node_id 33 for calling a global function with example usage: dup_sqr(f, K) and returns: dup_strip