code: def rs_tanh(p, x, prec):
      """
      Hyperbolic tangent of a series
  
      Return the series expansion of the tanh of ``p``, about 0.
  
      Examples
      ========
  
      >>> from sympy.polys.domains import QQ
      >>> from sympy.polys.rings import ring
      >>> from sympy.polys.ring_series import rs_tanh
      >>> R, x, y = ring('x, y', QQ)
      >>> rs_tanh(x + x*y, x, 4)
      -1/3*x**3*y**3 - x**3*y**2 - x**3*y - 1/3*x**3 + x*y + x
  
      See Also
      ========
  
      tanh
      """
      if rs_is_puiseux(p, x):
          return rs_puiseux(rs_tanh, p, x, prec)
      R = p.ring
      const = 0
      if _has_constant_term(p, x):
          zm = R.zero_monom
          c = p[zm]
          if R.domain is EX:
              c_expr = c.as_expr()
              const = tanh(c_expr)
          elif isinstance(c, PolyElement):
              try:
                  c_expr = c.as_expr()
                  const = R(tanh(c_expr))
              except ValueError:
                  raise DomainError(
                      "The given series cannot be expanded in "
                      "this domain."
                  )
          else:
              try:
                  const = R(tanh(c))
              except ValueError:
                  raise DomainError(
                      "The given series cannot be expanded in "
                      "this domain."
                  )
          p1 = p - c
          t1 = rs_tanh(p1, x, prec)
          t = rs_series_inversion(1 + const * t1, x, prec)
          return rs_mul(const + t1, t, x, prec)
  
      if R.ngens == 1:
          return _tanh(p, x, prec)
      else:
          return rs_fun(p, _tanh, x, prec)
  
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 44 for calling a global function with example usage: rs_tanh(p, x, prec) and returns: rs_puiseux, rs_mul, _tanh, rs_fun