code: def dmp_sqr(f, u, K):
      """
      Square dense polynomials in ``K[X]``.
  
      Examples
      ========
  
      >>> from sympy.polys import ring, ZZ
      >>> R, x,y = ring("x,y", ZZ)
  
      >>> R.dmp_sqr(x**2 + x*y + y**2)
      x**4 + 2*x**3*y + 3*x**2*y**2 + 2*x*y**3 + y**4
  
      """
      if not u:
          return dup_sqr(f, K)
  
      df = dmp_degree(f, u)
  
      if df < 0:
          return f
  
      h, v = [], u - 1
  
      for i in range(0, 2 * df + 1):
          c = dmp_zero(v)
  
          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 = dmp_add(c, dmp_mul(f[j], f[i - j], v, K), v, K)
  
          c = dmp_mul_ground(c, K(2), v, K)
  
          if n & 1:
              elem = dmp_sqr(f[jmax + 1], v, K)
              c = dmp_add(c, elem, v, K)
  
          h.append(c)
  
      return dmp_strip(h, u)
  
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 34 for calling a global function with example usage: dmp_sqr(f, u, K) and returns: dmp_strip, dup_sqr, f