コード例 #1
0
def test_laguerre():
    alpha = Symbol("alpha")

    # generalized Laguerre polynomials:
    assert laguerre_l(0, alpha, x) == 1
    assert laguerre_l(1, alpha, x) == -x + alpha + 1
    assert laguerre_l(2, alpha,
                      x).expand() == (x**2 / 2 - (alpha + 2) * x +
                                      (alpha + 2) * (alpha + 1) / 2).expand()
    assert laguerre_l(
        3, alpha,
        x).expand() == (-x**3 / 6 + (alpha + 3) * x**2 / 2 - (alpha + 2) *
                        (alpha + 3) * x / 2 + (alpha + 1) * (alpha + 2) *
                        (alpha + 3) / 6).expand()

    # Laguerre polynomials:
    assert laguerre_l(0, 0, x) == 1
    assert laguerre_l(1, 0, x) == 1 - x
    assert laguerre_l(2, 0, x).expand() == 1 - 2 * x + x**2 / 2
    assert laguerre_l(3, 0, x).expand() == 1 - 3 * x + 3 * x**2 / 2 - x**3 / 6

    # Test the lowest 10 polynomials with laguerre_poly, to make sure that it
    # works:
    for i in range(10):
        assert laguerre_l(i, 0, x).expand() == laguerre_poly(i, x)
コード例 #2
0
def test_assoc_laguerre():
    n = Symbol("n")
    m = Symbol("m")
    alpha = Symbol("alpha")

    # generalized Laguerre polynomials:
    assert assoc_laguerre(0, alpha, x) == 1
    assert assoc_laguerre(1, alpha, x) == -x + alpha + 1
    assert assoc_laguerre(2, alpha, x).expand() == \
        (x**2/2 - (alpha + 2)*x + (alpha + 2)*(alpha + 1)/2).expand()
    assert assoc_laguerre(3, alpha, x).expand() == \
        (-x**3/6 + (alpha + 3)*x**2/2 - (alpha + 2)*(alpha + 3)*x/2 +
        (alpha + 1)*(alpha + 2)*(alpha + 3)/6).expand()

    # Test the lowest 10 polynomials with laguerre_poly, to make sure it works:
    for i in range(10):
        assert assoc_laguerre(i, 0, x).expand() == laguerre_poly(i, x)

    X = assoc_laguerre(n, m, x)
    assert isinstance(X, assoc_laguerre)

    assert assoc_laguerre(n, 0, x) == laguerre(n, x)
    assert assoc_laguerre(n, alpha, 0) == binomial(alpha + n, alpha)

    assert diff(assoc_laguerre(n, alpha, x), x) == \
        -assoc_laguerre(n - 1, alpha + 1, x)

    assert conjugate(assoc_laguerre(n, alpha, x)) == \
        assoc_laguerre(n, conjugate(alpha), conjugate(x))

    raises(ValueError, lambda: assoc_laguerre(-2.1, alpha, x))
コード例 #3
0
def test_assoc_laguerre():
    n = Symbol("n")
    m = Symbol("m")
    alpha = Symbol("alpha")

    # generalized Laguerre polynomials:
    assert assoc_laguerre(0, alpha, x) == 1
    assert assoc_laguerre(1, alpha, x) == -x + alpha + 1
    assert assoc_laguerre(2, alpha, x).expand() == \
        (x**2/2 - (alpha + 2)*x + (alpha + 2)*(alpha + 1)/2).expand()
    assert assoc_laguerre(3, alpha, x).expand() == \
        (-x**3/6 + (alpha + 3)*x**2/2 - (alpha + 2)*(alpha + 3)*x/2 +
        (alpha + 1)*(alpha + 2)*(alpha + 3)/6).expand()

    # Test the lowest 10 polynomials with laguerre_poly, to make sure it works:
    for i in range(10):
        assert assoc_laguerre(i, 0, x).expand() == laguerre_poly(i, x)

    X = assoc_laguerre(n, m, x)
    assert isinstance(X, assoc_laguerre)

    assert assoc_laguerre(n, 0, x) == laguerre(n, x)
    assert assoc_laguerre(n, alpha, 0) == binomial(alpha + n, alpha)

    assert diff(assoc_laguerre(n, alpha, x), x) == \
        -assoc_laguerre(n - 1, alpha + 1, x)

    assert conjugate(assoc_laguerre(n, alpha, x)) == \
        assoc_laguerre(n, conjugate(alpha), conjugate(x))

    raises(ValueError, lambda: assoc_laguerre(-2.1, alpha, x))
コード例 #4
0
def test_assoc_laguerre():
    n = Symbol("n")
    m = Symbol("m")
    alpha = Symbol("alpha")

    # generalized Laguerre polynomials:
    assert assoc_laguerre(0, alpha, x) == 1
    assert assoc_laguerre(1, alpha, x) == -x + alpha + 1
    assert (assoc_laguerre(
        2, alpha, x).expand() == (x**2 / 2 - (alpha + 2) * x + (alpha + 2) *
                                  (alpha + 1) / 2).expand())
    assert (assoc_laguerre(
        3, alpha,
        x).expand() == (-(x**3) / 6 + (alpha + 3) * x**2 / 2 - (alpha + 2) *
                        (alpha + 3) * x / 2 + (alpha + 1) * (alpha + 2) *
                        (alpha + 3) / 6).expand())

    # Test the lowest 10 polynomials with laguerre_poly, to make sure it works:
    for i in range(10):
        assert assoc_laguerre(i, 0, x).expand() == laguerre_poly(i, x)

    X = assoc_laguerre(n, m, x)
    assert isinstance(X, assoc_laguerre)

    assert assoc_laguerre(n, 0, x) == laguerre(n, x)
    assert assoc_laguerre(n, alpha, 0) == binomial(alpha + n, alpha)
    p = Symbol("p", positive=True)
    assert assoc_laguerre(p, alpha, oo) == (-1)**p * oo
    assert assoc_laguerre(p, alpha, -oo) is oo

    assert diff(assoc_laguerre(n, alpha, x),
                x) == -assoc_laguerre(n - 1, alpha + 1, x)
    _k = Dummy("k")
    assert diff(assoc_laguerre(n, alpha, x), alpha).dummy_eq(
        Sum(assoc_laguerre(_k, alpha, x) / (-alpha + n), (_k, 0, n - 1)))

    assert conjugate(assoc_laguerre(n, alpha, x)) == assoc_laguerre(
        n, conjugate(alpha), conjugate(x))

    assert (assoc_laguerre(n, alpha, x).rewrite("polynomial").dummy_eq(
        gamma(alpha + n + 1) * Sum(
            x**_k * RisingFactorial(-n, _k) /
            (factorial(_k) * gamma(_k + alpha + 1)),
            (_k, 0, n),
        ) / factorial(n)))
    raises(ValueError, lambda: assoc_laguerre(-2.1, alpha, x))
    raises(ArgumentIndexError, lambda: assoc_laguerre(n, alpha, x).fdiff(1))
    raises(ArgumentIndexError, lambda: assoc_laguerre(n, alpha, x).fdiff(4))
コード例 #5
0
def test_laguerre():
    alpha = Symbol("alpha")

    # generalized Laguerre polynomials:
    assert assoc_laguerre(0, alpha, x) == 1
    assert assoc_laguerre(1, alpha, x) == -x + alpha + 1
    assert assoc_laguerre(
        2, alpha, x).expand() == (x**2 / 2 - (alpha + 2) * x + (alpha + 2) *
                                  (alpha + 1) / 2).expand()
    assert assoc_laguerre(
        3, alpha,
        x).expand() == (-x**3 / 6 + (alpha + 3) * x**2 / 2 - (alpha + 2) *
                        (alpha + 3) * x / 2 + (alpha + 1) * (alpha + 2) *
                        (alpha + 3) / 6).expand()

    # Laguerre polynomials:
    assert assoc_laguerre(0, 0, x) == 1
    assert assoc_laguerre(1, 0, x) == 1 - x
    assert assoc_laguerre(2, 0, x).expand() == 1 - 2 * x + x**2 / 2
    assert assoc_laguerre(3, 0,
                          x).expand() == 1 - 3 * x + 3 * x**2 / 2 - x**3 / 6

    # Test the lowest 10 polynomials with laguerre_poly, to make sure that it
    # works:
    for i in range(10):
        assert assoc_laguerre(i, 0, x).expand() == laguerre_poly(i, x)

    n = Symbol("n")
    X = laguerre(n, x)
    assert isinstance(X, laguerre)

    assert laguerre(n, 0) == 1

    assert diff(laguerre(n, x), x) == -assoc_laguerre(n - 1, 1, x)

    m = Symbol("m")
    X = assoc_laguerre(n, m, x)
    assert isinstance(X, assoc_laguerre)

    assert assoc_laguerre(n, 0, x) == laguerre(n, x)
    assert assoc_laguerre(n, alpha, 0) == binomial(alpha + n, alpha)

    assert diff(assoc_laguerre(n, alpha, x),
                x) == -assoc_laguerre(n - 1, alpha + 1, x)
コード例 #6
0
def test_laguerre():
    alpha = Symbol("alpha")

    # generalized Laguerre polynomials:
    assert laguerre_l(0, alpha, x) == 1
    assert laguerre_l(1, alpha, x) == -x + alpha + 1
    assert laguerre_l(2, alpha, x).expand() == (x**2/2 - (alpha+2)*x + (alpha+2)*(alpha+1)/2).expand()
    assert laguerre_l(3, alpha, x).expand() == (-x**3/6 + (alpha+3)*x**2/2 - (alpha+2)*(alpha+3)*x/2 + (alpha+1)*(alpha+2)*(alpha+3)/6).expand()

    # Laguerre polynomials:
    assert laguerre_l(0, 0, x) == 1
    assert laguerre_l(1, 0, x) == 1 - x
    assert laguerre_l(2, 0, x).expand() == 1 - 2*x + x**2/2
    assert laguerre_l(3, 0, x).expand() == 1 - 3*x + 3*x**2/2 - x**3/6

    # Test the lowest 10 polynomials with laguerre_poly, to make sure that it
    # works:
    for i in range(10):
        assert laguerre_l(i, 0, x).expand() == laguerre_poly(i, x)
コード例 #7
0
ファイル: test_spec_polynomials.py プロジェクト: Maihj/sympy
def test_laguerre():
    alpha = Symbol("alpha")

    # generalized Laguerre polynomials:
    assert assoc_laguerre(0, alpha, x) == 1
    assert assoc_laguerre(1, alpha, x) == -x + alpha + 1
    assert assoc_laguerre(2, alpha, x).expand() == \
        (x**2/2 - (alpha + 2)*x + (alpha + 2)*(alpha + 1)/2).expand()
    assert assoc_laguerre(3, alpha, x).expand() == \
        (-x**3/6 + (alpha + 3)*x**2/2 - (alpha + 2)*(alpha + 3)*x/2 +
        (alpha + 1)*(alpha + 2)*(alpha + 3)/6).expand()

    # Laguerre polynomials:
    assert assoc_laguerre(0, 0, x) == 1
    assert assoc_laguerre(1, 0, x) == 1 - x
    assert assoc_laguerre(2, 0, x).expand() == 1 - 2*x + x**2/2
    assert assoc_laguerre(3, 0, x).expand() == 1 - 3*x + 3*x**2/2 - x**3/6

    # Test the lowest 10 polynomials with laguerre_poly, to make sure that it
    # works:
    for i in range(10):
        assert assoc_laguerre(i, 0, x).expand() == laguerre_poly(i, x)

    n = Symbol("n")
    X = laguerre(n, x)
    assert isinstance(X, laguerre)

    assert laguerre(n, 0) == 1

    assert diff(laguerre(n, x), x) == -assoc_laguerre(n - 1, 1, x)

    m = Symbol("m")
    X = assoc_laguerre(n, m, x)
    assert isinstance(X, assoc_laguerre)

    assert assoc_laguerre(n, 0, x) == laguerre(n, x)
    assert assoc_laguerre(n, alpha, 0) == binomial(alpha + n, alpha)

    assert diff(assoc_laguerre(n, alpha, x), x) == \
        -assoc_laguerre(n - 1, alpha + 1, x)