def test_prde_special_denom(): a = Poly(t + 1, t) ba = Poly(t**2, t) bd = Poly(1, t) G = [(Poly(t, t), Poly(1, t)), (Poly(t**2, t), Poly(1, t)), (Poly(t**3, t), Poly(1, t))] DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)]}) assert prde_special_denom(a, ba, bd, G, DE) == \ (Poly(t + 1, t), Poly(t**2, t), [(Poly(t, t), Poly(1, t)), (Poly(t**2, t), Poly(1, t)), (Poly(t**3, t), Poly(1, t))], Poly(1, t)) G = [(Poly(t, t), Poly(1, t)), (Poly(1, t), Poly(t, t))] assert prde_special_denom(Poly(1, t), Poly(t**2, t), Poly(1, t), G, DE) == \ (Poly(1, t), Poly(t**2 - 1, t), [(Poly(t**2, t), Poly(1, t)), (Poly(1, t), Poly(1, t))], Poly(t, t)) DE = DifferentialExtension( extension={'D': [Poly(1, x), Poly(-2 * x * t0, t0)]}) DE.decrement_level() G = [(Poly(t, t), Poly(t**2, t)), (Poly(2 * t, t), Poly(t, t))] assert prde_special_denom(Poly(5*x*t + 1, t), Poly(t**2 + 2*x**3*t, t), Poly(t**3 + 2, t), G, DE) == \ (Poly(5*x*t + 1, t), Poly(0, t), [(Poly(t, t), Poly(t**2, t)), (Poly(2*t, t), Poly(t, t))], Poly(1, x)) DE = DifferentialExtension( extension={'D': [Poly(1, x), Poly((t**2 + 1) * 2 * x, t)]}) G = [(Poly(t + x, t), Poly(t * x, t)), (Poly(2 * t, t), Poly(x**2, x))] assert prde_special_denom(Poly(5*x*t + 1, t), Poly(t**2 + 2*x**3*t, t), Poly(t**3, t), G, DE) == \ (Poly(5*x*t + 1, t), Poly(0, t), [(Poly(t + x, t), Poly(x*t, t)), (Poly(2*t, t, x), Poly(x**2, t, x))], Poly(1, t)) assert prde_special_denom(Poly(t + 1, t), Poly(t**2, t), Poly(t**3, t), G, DE) == \ (Poly(t + 1, t), Poly(0, t), [(Poly(t + x, t), Poly(x*t, t)), (Poly(2*t, t, x), Poly(x**2, t, x))], Poly(1, t))
def test_prde_special_denom(): a = Poly(t + 1, t) ba = Poly(t**2, t) bd = Poly(1, t) G = [(Poly(t, t), Poly(1, t)), (Poly(t**2, t), Poly(1, t)), (Poly(t**3, t), Poly(1, t))] DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)]}) assert prde_special_denom(a, ba, bd, G, DE) == \ (Poly(t + 1, t), Poly(t**2, t), [(Poly(t, t), Poly(1, t)), (Poly(t**2, t), Poly(1, t)), (Poly(t**3, t), Poly(1, t))], Poly(1, t)) G = [(Poly(t, t), Poly(1, t)), (Poly(1, t), Poly(t, t))] assert prde_special_denom(Poly(1, t), Poly(t**2, t), Poly(1, t), G, DE) == \ (Poly(1, t), Poly(t**2 - 1, t), [(Poly(t**2, t), Poly(1, t)), (Poly(1, t), Poly(1, t))], Poly(t, t)) DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(-2*x*t0, t0)]}) DE.decrement_level() G = [(Poly(t, t), Poly(t**2, t)), (Poly(2*t, t), Poly(t, t))] assert prde_special_denom(Poly(5*x*t + 1, t), Poly(t**2 + 2*x**3*t, t), Poly(t**3 + 2, t), G, DE) == \ (Poly(5*x*t + 1, t), Poly(0, t), [(Poly(t, t), Poly(t**2, t)), (Poly(2*t, t), Poly(t, t))], Poly(1, x)) DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly((t**2 + 1)*2*x, t)]}) G = [(Poly(t + x, t), Poly(t*x, t)), (Poly(2*t, t), Poly(x**2, x))] assert prde_special_denom(Poly(5*x*t + 1, t), Poly(t**2 + 2*x**3*t, t), Poly(t**3, t), G, DE) == \ (Poly(5*x*t + 1, t), Poly(0, t), [(Poly(t + x, t), Poly(x*t, t)), (Poly(2*t, t, x), Poly(x**2, t, x))], Poly(1, t)) assert prde_special_denom(Poly(t + 1, t), Poly(t**2, t), Poly(t**3, t), G, DE) == \ (Poly(t + 1, t), Poly(0, t), [(Poly(t + x, t), Poly(x*t, t)), (Poly(2*t, t, x), Poly(x**2, t, x))], Poly(1, t))
def test_prde_special_denom(): a = Poly(t + 1, t) ba = Poly(t**2, t) bd = Poly(1, t) G = [(Poly(t, t), Poly(1, t)), (Poly(t**2, t), Poly(1, t)), (Poly(t**3, t), Poly(1, t))] DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)]}) assert prde_special_denom(a, ba, bd, G, DE) == \ (Poly(t + 1, t), Poly(t**2, t), [(Poly(t, t), Poly(1, t)), (Poly(t**2, t), Poly(1, t)), (Poly(t**3, t), Poly(1, t))], Poly(1, t)) G = [(Poly(t, t), Poly(1, t)), (Poly(1, t), Poly(t, t))] assert prde_special_denom(Poly(1, t), Poly(t**2, t), Poly(1, t), G, DE) == \ (Poly(1, t), Poly(t**2 - 1, t), [(Poly(t**2, t), Poly(1, t)), (Poly(1, t), Poly(1, t))], Poly(t, t))