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# sympy.integrals.risch.recognize_derivative

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```"""Most of these tests come from the examples in Bronstein's book."""
from sympy import (Poly, I, S, Function, log, symbols, exp, tan, sqrt,
Symbol, Lambda, sin, cos, Eq, Piecewise, factor)
from sympy.integrals.risch import (gcdex_diophantine, frac_in, as_poly_1t,
derivation, splitfactor, splitfactor_sqf, canonical_representation,
```
```def test_recognize_derivative():
DE = DifferentialExtension(extension={'D': [Poly(1, t)]})
a = Poly(36, t)
d = Poly((t - 2)*(t**2 - 1)**2, t)
assert recognize_derivative(a, d, DE) == False
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t)]})
a = Poly(2, t)
d = Poly(t**2 - 1, t)
assert recognize_derivative(a, d, DE) == False
assert recognize_derivative(Poly(x*t, t), Poly(1, t), DE) == True
```
```    assert recognize_derivative(Poly(x*t, t), Poly(1, t), DE) == True
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t**2 + 1, t)]})
assert recognize_derivative(Poly(t, t), Poly(1, t), DE) == True

```

```"""Most of these tests come from the examples in Bronstein's book."""
from sympy import (Poly, I, S, Function, log, symbols, exp, tan, sqrt,
Symbol, Lambda, sin, cos, Eq, Piecewise, factor)
from sympy.integrals.risch import (gcdex_diophantine, frac_in, as_poly_1t,
derivation, splitfactor, splitfactor_sqf, canonical_representation,
```
```def test_recognize_derivative():
DE = DifferentialExtension(extension={'D': [Poly(1, t)]})
a = Poly(36, t)
d = Poly((t - 2)*(t**2 - 1)**2, t)
assert recognize_derivative(a, d, DE) == False
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t)]})
a = Poly(2, t)
d = Poly(t**2 - 1, t)
assert recognize_derivative(a, d, DE) == False
assert recognize_derivative(Poly(x*t, t), Poly(1, t), DE) == True
```
```    assert recognize_derivative(Poly(x*t, t), Poly(1, t), DE) == True
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t**2 + 1, t)]})
assert recognize_derivative(Poly(t, t), Poly(1, t), DE) == True

```