code: def test_is_log_deriv_k_t_radical():
      DE = DifferentialExtension(
          extension={
              "D": [Poly(1, x)],
              "exts": [None],
              "extargs": [None],
          }
      )
      assert (
          is_log_deriv_k_t_radical(Poly(2 * x, x), Poly(1, x), DE)
          is None
      )
  
      DE = DifferentialExtension(
          extension={
              "D": [Poly(1, x), Poly(2 * t1, t1), Poly(1 / x, t2)],
              "exts": [None, "exp", "log"],
              "extargs": [None, 2 * x, x],
          }
      )
      assert is_log_deriv_k_t_radical(
          Poly(x + t2 / 2, t2), Poly(1, t2), DE
      ) == ([(t1, 1), (x, 1)], t1 * x, 2, 0)
      # TODO: Add more tests
  
      DE = DifferentialExtension(
          extension={
              "D": [Poly(1, x), Poly(t0, t0), Poly(1 / x, t)],
              "exts": [None, "exp", "log"],
              "extargs": [None, x, x],
          }
      )
      assert is_log_deriv_k_t_radical(
          Poly(x + t / 2 + 3, t), Poly(1, t), DE
      ) == ([(t0, 2), (x, 1)], x * t0**2, 2, 3)
  
imports: from sympy.integrals.risch import DifferentialExtension, derivation
  from sympy.integrals.prde import prde_normal_denom, prde_special_denom, prde_linear_constraints, constant_system, prde_spde, prde_no_cancel_b_large, prde_no_cancel_b_small, limited_integrate_reduce, limited_integrate, is_deriv_k, is_log_deriv_k_t_radical, parametric_log_deriv_heu, is_log_deriv_k_t_radical_in_field, param_poly_rischDE, param_rischDE, prde_cancel_liouvillian
  from sympy.polys.polymatrix import PolyMatrix
  from sympy.core.numbers import Rational
  from sympy.core.singleton import S
  from sympy.core.symbol import symbols
  from sympy.polys.domains.rationalfield import QQ
  from sympy.polys.polytools import Poly
  from sympy.abc import x, t, n
label_desc: Use image node_id 12 for calling a global function with example usage: test_is_log_deriv_k_t_radical() without return types