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# sympy.integrals.risch.canonical_representation

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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_canonical_representation():
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1 + t**2, t)]})
assert canonical_representation(Poly(x - t, t), Poly(t**2, t), DE) == \
(Poly(0, t), (Poly(0, t),
Poly(1, t)), (Poly(-t + x, t),
Poly(t**2, t)))
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t**2 + 1, t)]})
assert canonical_representation(Poly(t**5 + t**3 + x**2*t + 1, t),
```

```"""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_canonical_representation():
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1 + t**2, t)]})
assert canonical_representation(Poly(x - t, t), Poly(t**2, t), DE) == \
(Poly(0, t), (Poly(0, t),
Poly(1, t)), (Poly(-t + x, t),
Poly(t**2, t)))
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t**2 + 1, t)]})
assert canonical_representation(Poly(t**5 + t**3 + x**2*t + 1, t),
```