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```    This constitutes step 3 of the outline given in the rde.py docstring.
"""
from sympy.integrals.prde import (parametric_log_deriv, limited_integrate,
# TODO: finish writing this and write tests
```
```                    # if beta == m*Dt + Dw for w in k and m in ZZ:
# n = max(n, m)
if A is not None:
aa, z = A
```
```    this equation with deg(q) <= n.
"""

with DecrementLevel(DE):
ba, bd = frac_in(b, DE.t)
```

```    This constitutes step 3 of the outline given in the rde.py docstring.
"""
from sympy.integrals.prde import (parametric_log_deriv, limited_integrate,
# TODO: finish writing this and write tests
```
```                    # if beta == m*Dt + Dw for w in k and m in ZZ:
# n = max(n, m)
if A is not None:
aa, z = A
```
```    this equation with deg(q) <= n.
"""

with DecrementLevel(DE):
ba, bd = frac_in(b, DE.t)
```

```"""Most of these tests come from the examples in Bronstein's book."""
from sympy import Poly, Matrix, S, symbols, I
from sympy.integrals.risch import DifferentialExtension
from sympy.integrals.prde import (prde_normal_denom, prde_special_denom,
prde_linear_constraints, constant_system, prde_spde, prde_no_cancel_b_large,
```
```def test_is_log_deriv_k_t_radical_in_field():
# NOTE: any potential constant factor in the second element of the result
# doesn't matter, because it cancels in Da/a.
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t)]})
assert is_log_deriv_k_t_radical_in_field(Poly(5*t + 1, t), Poly(2*t*x, t), DE) == \
(2, t*x**5)
assert is_log_deriv_k_t_radical_in_field(Poly(2 + 3*t, t), Poly(5*x*t, t), DE) == \
```
```
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(-t/x**2, t)]})
Poly(2*x**2 + 2*x**2*t, t), DE) == \
(2, t + t**2)
assert is_log_deriv_k_t_radical_in_field(Poly(-1, t), Poly(x**2, t), DE) == \
```

```"""Most of these tests come from the examples in Bronstein's book."""
from sympy import Poly, Matrix, S, symbols, I
from sympy.integrals.risch import DifferentialExtension
from sympy.integrals.prde import (prde_normal_denom, prde_special_denom,
prde_linear_constraints, constant_system, prde_spde, prde_no_cancel_b_large,
```
```def test_is_log_deriv_k_t_radical_in_field():
# NOTE: any potential constant factor in the second element of the result
# doesn't matter, because it cancels in Da/a.
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t)]})
assert is_log_deriv_k_t_radical_in_field(Poly(5*t + 1, t), Poly(2*t*x, t), DE) == \
(2, t*x**5)
assert is_log_deriv_k_t_radical_in_field(Poly(2 + 3*t, t), Poly(5*x*t, t), DE) == \
```
```
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(-t/x**2, t)]})