def test_to_Sequence(): x = symbols('x') R, Dx = DifferentialOperators(ZZ.old_poly_ring(x), 'Dx') n = symbols('n', integer=True) _, Sn = RecurrenceOperators(ZZ.old_poly_ring(n), 'Sn') p = HolonomicFunction(x**2 * Dx**4 + x + Dx, x).to_sequence() q = [(HolonomicSequence(1 + (n + 2) * Sn**2 + (n**4 + 6 * n**3 + 11 * n**2 + 6 * n) * Sn**3), 0, 1)] assert p == q p = HolonomicFunction(x**2 * Dx**4 + x**3 + Dx**2, x).to_sequence() q = [ (HolonomicSequence(1 + (n**4 + 14 * n**3 + 72 * n**2 + 163 * n + 140) * Sn**5), 0, 0) ] assert p == q p = HolonomicFunction(x**3 * Dx**4 + 1 + Dx**2, x).to_sequence() q = [(HolonomicSequence(1 + (n**4 - 2 * n**3 - n**2 + 2 * n) * Sn + (n**2 + 3 * n + 2) * Sn**2), 0, 0)] assert p == q p = HolonomicFunction(3 * x**3 * Dx**4 + 2 * x * Dx + x * Dx**3, x).to_sequence() q = [(HolonomicSequence(2 * n + (3 * n**4 - 6 * n**3 - 3 * n**2 + 6 * n) * Sn + (n**3 + 3 * n**2 + 2 * n) * Sn**2), 0, 1)] assert p == q
def test_to_Sequence_Initial_Coniditons(): x = symbols('x') R, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx') n = symbols('n', integer=True) _, Sn = RecurrenceOperators(QQ.old_poly_ring(n), 'Sn') p = HolonomicFunction(Dx - 1, x, 0, 1).to_sequence() q = HolonomicSequence(-1 + (n + 1)*Sn, 1) assert p == q p = HolonomicFunction(Dx**2 + 1, x, 0, [0, 1]).to_sequence() q = HolonomicSequence(1 + (n**2 + 3*n + 2)*Sn**2, [0, 1]) assert p == q p = HolonomicFunction(Dx**2 + 1 + x**3*Dx, x, 0, [2, 3]).to_sequence() q = HolonomicSequence(n + Sn**2 + (n**2 + 7*n + 12)*Sn**4, [2, 3, -1, -1/2]) assert p == q p = HolonomicFunction(x**3*Dx**5 + 1 + Dx, x).to_sequence() q = HolonomicSequence(1 + (n + 1)*Sn + (n**5 - 5*n**3 + 4*n)*Sn**2) assert p == q
def test_to_Sequence_Initial_Coniditons(): x = symbols('x') R, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx') n = symbols('n', integer=True) _, Sn = RecurrenceOperators(QQ.old_poly_ring(n), 'Sn') p = HolonomicFunction(Dx - 1, x, 0, 1).to_sequence() q = [(HolonomicSequence(-1 + (n + 1) * Sn, 1), 0)] assert p == q p = HolonomicFunction(Dx**2 + 1, x, 0, [0, 1]).to_sequence() q = [(HolonomicSequence(1 + (n**2 + 3 * n + 2) * Sn**2, [0, 1]), 0)] assert p == q p = HolonomicFunction(Dx**2 + 1 + x**3 * Dx, x, 0, [2, 3]).to_sequence() q = [(HolonomicSequence(n + Sn**2 + (n**2 + 7 * n + 12) * Sn**4, [2, 3, -1, -1 / 2, 1 / 12]), 1)] assert p == q p = HolonomicFunction(x**3 * Dx**5 + 1 + Dx, x).to_sequence() q = [(HolonomicSequence(1 + (n + 1) * Sn + (n**5 - 5 * n**3 + 4 * n) * Sn**2), 0, 3)] assert p == q C_0, C_1, C_2, C_3 = symbols('C_0, C_1, C_2, C_3') p = expr_to_holonomic(log(1 + x**2)) q = [(HolonomicSequence(n**2 + (n**2 + 2 * n) * Sn**2, [0, 0, C_2]), 0, 1)] assert p.to_sequence() == q p = p.diff() q = [(HolonomicSequence((n + 2) + (n + 2) * Sn**2, [C_0, 0]), 1, 0)] assert p.to_sequence() == q p = expr_to_holonomic(erf(x) + x).to_sequence() q = [(HolonomicSequence( (2 * n**2 - 2 * n) + (n**3 + 2 * n**2 - n - 2) * Sn**2, [0, 1 + 2 / sqrt(pi), 0, C_3]), 0, 2)] assert p == q