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# sympy.integrals.rde.spde

All Samples(18)  |  Call(14)  |  Derive(0)  |  Import(4)

```    NonElementaryIntegralException, residue_reduce, splitfactor,
residue_reduce_derivation, DecrementLevel, recognize_log_derivative)
from sympy.integrals.rde import (order_at, order_at_oo, weak_normalizer,
bound_degree, spde, solve_poly_rde)
from sympy.core.compatibility import reduce, xrange
```
```            # Custom version of rischDE() that uses the already computed
# denominator and degree bound from above.
B, C, m, alpha, beta = spde(A, B, C, N, DE)
y = solve_poly_rde(B, C, m, DE)

```

```    NonElementaryIntegralException, residue_reduce, splitfactor,
residue_reduce_derivation, DecrementLevel, recognize_log_derivative)
from sympy.integrals.rde import (order_at, order_at_oo, weak_normalizer,
bound_degree, spde, solve_poly_rde)
from sympy.core.compatibility import reduce, xrange
```
```            # Custom version of rischDE() that uses the already computed
# denominator and degree bound from above.
B, C, m, alpha, beta = spde(A, B, C, N, DE)
y = solve_poly_rde(B, C, m, DE)

```

```"""Most of these tests come from the examples in Bronstein's book."""
from sympy import Poly, S, symbols, oo, I
from sympy.integrals.risch import (DifferentialExtension,
NonElementaryIntegralException)
from sympy.integrals.rde import (order_at, order_at_oo, weak_normalizer,
```
```def test_spde():
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t**2 + 1, t)]})
raises(NonElementaryIntegralException, lambda: spde(Poly(t, t), Poly((t - 1)*(t**2 + 1), t), Poly(1, t), 0, DE))
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)]})
assert spde(Poly(t**2 + x*t*2 + x**2, t), Poly(t**2/x**2 + (2/x - 1)*t, t),
Poly(t**2/x**2 + (2/x - 1)*t, t), 0, DE) == \
(Poly(0, t), Poly(0, t), 0, Poly(0, t), Poly(1, t))
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t0/x**2, t0), Poly(1/x, t)]})
assert spde(Poly(t**2, t), Poly(-t**2/x**2 - 1/x, t),
```
```        Poly(t0*t**2/2 + x**2*t**2 - x**2*t, t))
DE = DifferentialExtension(extension={'D': [Poly(1, x)]})
assert spde(Poly(x**2 + x + 1, x), Poly(-2*x - 1, x), Poly(x**5/2 +
3*x**4/4 + x**3 - x**2 + 1, x), 4, DE) == \
(Poly(0, x), Poly(x/2 - S(1)/4, x), 2, Poly(x**2 + x + 1, x), Poly(5*x/4, x))
```

```"""Most of these tests come from the examples in Bronstein's book."""
from sympy import Poly, S, symbols, oo, I
from sympy.integrals.risch import (DifferentialExtension,
NonElementaryIntegralException)
from sympy.integrals.rde import (order_at, order_at_oo, weak_normalizer,
```
```def test_spde():
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t**2 + 1, t)]})
raises(NonElementaryIntegralException, lambda: spde(Poly(t, t), Poly((t - 1)*(t**2 + 1), t), Poly(1, t), 0, DE))
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)]})
assert spde(Poly(t**2 + x*t*2 + x**2, t), Poly(t**2/x**2 + (2/x - 1)*t, t),
Poly(t**2/x**2 + (2/x - 1)*t, t), 0, DE) == \
(Poly(0, t), Poly(0, t), 0, Poly(0, t), Poly(1, t))
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t0/x**2, t0), Poly(1/x, t)]})
assert spde(Poly(t**2, t), Poly(-t**2/x**2 - 1/x, t),
```
```        Poly(t0*t**2/2 + x**2*t**2 - x**2*t, t))
DE = DifferentialExtension(extension={'D': [Poly(1, x)]})
assert spde(Poly(x**2 + x + 1, x), Poly(-2*x - 1, x), Poly(x**5/2 +
3*x**4/4 + x**3 - x**2 + 1, x), 4, DE) == \
(Poly(0, x), Poly(x/2 - S(1)/4, x), 2, Poly(x**2 + x + 1, x), Poly(5*x/4, x))
```