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# sympy.integrals.risch.hermite_reduce

All Samples(14)  |  Call(12)  |  Derive(0)  |  Import(2)

src/s/y/sympy-0.7.5/sympy/integrals/tests/test_risch.py   sympy(Download)
```"""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_hermite_reduce():
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t**2 + 1, t)]})

assert hermite_reduce(Poly(x - t, t), Poly(t**2, t), DE) == \
((Poly(-x, t), Poly(t, t)), (Poly(0, t), Poly(1, t)), (Poly(-x, t), Poly(1, t)))

DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(-t**2 - t/x - (1 - nu**2/x**2), t)]})

assert hermite_reduce(
Poly(x**2*t**5 + x*t**4 - nu**2*t**3 - x*(x**2 + 1)*t**2 - (x**2 - nu**2)*t - x**5/4, t),
```
```    d = Poly(x*t**6 - 4*x**2*t**5 + 6*x**3*t**4 - 4*x**4*t**3 + x**5*t**2, t)

assert hermite_reduce(a, d, DE) == \
((Poly(3*t**2 + t + 3*x, t), Poly(3*t**4 - 9*x*t**3 + 9*x**2*t**2 - 3*x**3*t, t)),
(Poly(0, t), Poly(1, t)),
(Poly(0, t), Poly(1, t)))

assert hermite_reduce(
Poly(-t**2 + 2*t + 2, t),
```

src/s/y/sympy-HEAD/sympy/integrals/tests/test_risch.py   sympy(Download)
```"""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_hermite_reduce():
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t**2 + 1, t)]})

assert hermite_reduce(Poly(x - t, t), Poly(t**2, t), DE) == \
((Poly(-x, t), Poly(t, t)), (Poly(0, t), Poly(1, t)), (Poly(-x, t), Poly(1, t)))

DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(-t**2 - t/x - (1 - nu**2/x**2), t)]})

assert hermite_reduce(
Poly(x**2*t**5 + x*t**4 - nu**2*t**3 - x*(x**2 + 1)*t**2 - (x**2 - nu**2)*t - x**5/4, t),
```
```    d = Poly(x*t**6 - 4*x**2*t**5 + 6*x**3*t**4 - 4*x**4*t**3 + x**5*t**2, t)

assert hermite_reduce(a, d, DE) == \
((Poly(3*t**2 + t + 3*x, t), Poly(3*t**4 - 9*x*t**3 + 9*x**2*t**2 - 3*x**3*t, t)),
(Poly(0, t), Poly(1, t)),
(Poly(0, t), Poly(1, t)))

assert hermite_reduce(
Poly(-t**2 + 2*t + 2, t),
```