def test_ring_series1(): R, x = ring('x', QQ) p = x**4 + 2 * x**3 + 3 * x + 4 assert _invert_monoms(p) == 4 * x**4 + 3 * x**3 + 2 * x + 1 assert rs_hadamard_exp(p) == x**4 / 24 + x**3 / 3 + 3 * x + 4 R, x = ring('x', QQ) p = x**4 + 2 * x**3 + 3 * x + 4 assert rs_integrate(p, x) == x**5 / 5 + x**4 / 2 + 3 * x**2 / 2 + 4 * x R, x, y = ring('x, y', QQ) p = x**2 * y**2 + x + 1 assert rs_integrate(p, x) == x**3 * y**2 / 3 + x**2 / 2 + x assert rs_integrate(p, y) == x**2 * y**3 / 3 + x * y + y
def test_ring_series1(): R, x = ring('x', QQ) p = x**4 + 2*x**3 + 3*x + 4 assert _invert_monoms(p) == 4*x**4 + 3*x**3 + 2*x + 1 assert rs_hadamard_exp(p) == x**4/24 + x**3/3 + 3*x + 4 R, x = ring('x', QQ) p = x**4 + 2*x**3 + 3*x + 4 assert rs_integrate(p, x) == x**5/5 + x**4/2 + 3*x**2/2 + 4*x R, x, y = ring('x, y', QQ) p = x**2*y**2 + x + 1 assert rs_integrate(p, x) == x**3*y**2/3 + x**2/2 + x assert rs_integrate(p, y) == x**2*y**3/3 + x*y + y