code: def _switch_domain(g, K):
      # An algebraic relation f(a, b) = 0 over Q can also be written
      # g(b) = 0 where g is in Q(a)[x] and h(a) = 0 where h is in Q(b)[x].
      # This function transforms g into h where Q(b) = K.
      frep = g.rep.inject()
      hrep = frep.eject(K, front=True)
  
      return g.new(hrep, g.gens[0])
  
imports: from sympy.core.add import Add
  from sympy.core.numbers import AlgebraicNumber
  from sympy.core.singleton import S
  from sympy.core.symbol import Dummy
  from sympy.core.sympify import sympify, _sympify
  from sympy.ntheory import sieve
  from sympy.polys.densetools import dup_eval
  from sympy.polys.domains import QQ
  from sympy.polys.numberfields.minpoly import _choose_factor, minimal_polynomial
  from sympy.polys.polyerrors import IsomorphismFailed
  from sympy.polys.polytools import Poly, PurePoly, factor_list
  from sympy.utilities import public
  from mpmath import MPContext
label_desc: Use image node_id 5 for calling a global function with example usage: _switch_domain(g, K) and returns: g