Python rs_sinh Examples

Example #1

File: test_ring_series.py Project: asmeurer/sympy

def test_sinh():
    R, x, y = ring('x, y', QQ)
    assert rs_sinh(x, x, 9)/x**5 == S(1)/5040*x**2 + S(1)/120 + S(1)/6*x**(-2) + x**(-4)
    assert rs_sinh(x*y + x**2*y**3, x, 9) == x**8*y**11/12 + \
        x**8*y**9/720 + x**7*y**9/12 + x**7*y**7/5040 + x**6*y**9/6 + \
        x**6*y**7/24 + x**5*y**7/2 + x**5*y**5/120 + x**4*y**5/2 + \
        x**3*y**3/6 + x**2*y**3 + x*y

Example #2

File: test_ring_series.py Project: helpin/sympy

def test_sinh():
    R, x, y = ring('x, y', QQ)
    assert rs_sinh(x, x, 9) == 1/5040*x**7 + 1/120*x**5 + 1/6*x**3 + x
    assert rs_sinh(x*y + x**2*y**3, x, 9) == 1/12*x**8*y**11 + \
        1/720*x**8*y**9 + 1/12*x**7*y**9 + 1/5040*x**7*y**7 + 1/6*x**6*y**9 + \
        1/24*x**6*y**7 + 1/2*x**5*y**7 + 1/120*x**5*y**5 + 1/2*x**4*y**5 + \
        1/6*x**3*y**3 + x**2*y**3 + x*y

Example #3

File: test_ring_series.py Project: z-campbell/sympy

def test_sinh():
    R, x, y = ring('x, y', QQ)
    assert rs_sinh(x, x, 9) == x**7 / 5040 + x**5 / 120 + x**3 / 6 + x
    assert rs_sinh(x*y + x**2*y**3, x, 9) == x**8*y**11/12 + \
        x**8*y**9/720 + x**7*y**9/12 + x**7*y**7/5040 + x**6*y**9/6 + \
        x**6*y**7/24 + x**5*y**7/2 + x**5*y**5/120 + x**4*y**5/2 + \
        x**3*y**3/6 + x**2*y**3 + x*y

Example #4

File: test_ring_series.py Project: kumarkrishna/sympy

def test_sinh():
    R, x, y = ring('x, y', QQ)
    assert rs_sinh(x, x, 9) == x**7/5040 + x**5/120 + x**3/6 + x
    assert rs_sinh(x*y + x**2*y**3, x, 9) == x**8*y**11/12 + \
        x**8*y**9/720 + x**7*y**9/12 + x**7*y**7/5040 + x**6*y**9/6 + \
        x**6*y**7/24 + x**5*y**7/2 + x**5*y**5/120 + x**4*y**5/2 + \
        x**3*y**3/6 + x**2*y**3 + x*y

Example #5

File: test_ring_series.py Project: mayou36/sympy

def test_sinh():
    R, x, y = ring('x, y', QQ)
    assert rs_sinh(x, x, 9) / x**5 == Rational(1, 5040) * x**2 + Rational(
        1, 120) + Rational(1, 6) * x**(-2) + x**(-4)
    assert rs_sinh(x*y + x**2*y**3, x, 9) == x**8*y**11/12 + \
        x**8*y**9/720 + x**7*y**9/12 + x**7*y**7/5040 + x**6*y**9/6 + \
        x**6*y**7/24 + x**5*y**7/2 + x**5*y**5/120 + x**4*y**5/2 + \
        x**3*y**3/6 + x**2*y**3 + x*y

Example #6

def test_sinh():
    R, x, y = ring('x, y', QQ)
    assert rs_sinh(x, x,
                   9) == 1 / 5040 * x**7 + 1 / 120 * x**5 + 1 / 6 * x**3 + x
    assert rs_sinh(x*y + x**2*y**3, x, 9) == 1/12*x**8*y**11 + \
        1/720*x**8*y**9 + 1/12*x**7*y**9 + 1/5040*x**7*y**7 + 1/6*x**6*y**9 + \
        1/24*x**6*y**7 + 1/2*x**5*y**7 + 1/120*x**5*y**5 + 1/2*x**4*y**5 + \
        1/6*x**3*y**3 + x**2*y**3 + x*y

Example #7

File: test_ring_series.py Project: Azatik1000/Massey-Omura-Cryptosystem

def test_sinh():
    R, x, y = ring('x, y', QQ)
    assert rs_sinh(x, x, 9) / x**5 == S(1) / 5040 * x**2 + S(1) / 120 + S(
        1) / 6 * x**(-2) + x**(-4)
    assert rs_sinh(x*y + x**2*y**3, x, 9) == x**8*y**11/12 + \
        x**8*y**9/720 + x**7*y**9/12 + x**7*y**7/5040 + x**6*y**9/6 + \
        x**6*y**7/24 + x**5*y**7/2 + x**5*y**5/120 + x**4*y**5/2 + \
        x**3*y**3/6 + x**2*y**3 + x*y

Example #8

File: test_ring_series.py Project: mayou36/sympy

def test_puiseux():
    R, x, y = ring('x, y', QQ)
    p = x**QQ(2, 5) + x**QQ(2, 3) + x

    r = rs_series_inversion(p, x, 1)
    r1 = -x**QQ(14,15) + x**QQ(4,5) - 3*x**QQ(11,15) + x**QQ(2,3) + \
        2*x**QQ(7,15) - x**QQ(2,5) - x**QQ(1,5) + x**QQ(2,15) - x**QQ(-2,15) \
        + x**QQ(-2,5)
    assert r == r1

    r = rs_nth_root(1 + p, 3, x, 1)
    assert r == -x**QQ(4, 5) / 9 + x**QQ(2, 3) / 3 + x**QQ(2, 5) / 3 + 1

    r = rs_log(1 + p, x, 1)
    assert r == -x**QQ(4, 5) / 2 + x**QQ(2, 3) + x**QQ(2, 5)

    r = rs_LambertW(p, x, 1)
    assert r == -x**QQ(4, 5) + x**QQ(2, 3) + x**QQ(2, 5)

    p1 = x + x**QQ(1, 5) * y
    r = rs_exp(p1, x, 1)
    assert r == x**QQ(4,5)*y**4/24 + x**QQ(3,5)*y**3/6 + x**QQ(2,5)*y**2/2 + \
        x**QQ(1,5)*y + 1

    r = rs_atan(p, x, 2)
    assert r ==  -x**QQ(9,5) - x**QQ(26,15) - x**QQ(22,15) - x**QQ(6,5)/3 + \
        x + x**QQ(2,3) + x**QQ(2,5)

    r = rs_atan(p1, x, 2)
    assert r ==  x**QQ(9,5)*y**9/9 + x**QQ(9,5)*y**4 - x**QQ(7,5)*y**7/7 - \
        x**QQ(7,5)*y**2 + x*y**5/5 + x - x**QQ(3,5)*y**3/3 + x**QQ(1,5)*y

    r = rs_asin(p, x, 2)
    assert r == x**QQ(9,5)/2 + x**QQ(26,15)/2 + x**QQ(22,15)/2 + \
        x**QQ(6,5)/6 + x + x**QQ(2,3) + x**QQ(2,5)

    r = rs_cot(p, x, 1)
    assert r == -x**QQ(14,15) + x**QQ(4,5) - 3*x**QQ(11,15) + \
        2*x**QQ(2,3)/3 + 2*x**QQ(7,15) - 4*x**QQ(2,5)/3 - x**QQ(1,5) + \
        x**QQ(2,15) - x**QQ(-2,15) + x**QQ(-2,5)

    r = rs_cos_sin(p, x, 2)
    assert r[0] == x**QQ(28,15)/6 - x**QQ(5,3) + x**QQ(8,5)/24 - x**QQ(7,5) - \
        x**QQ(4,3)/2 - x**QQ(16,15) - x**QQ(4,5)/2 + 1
    assert r[1] == -x**QQ(9,5)/2 - x**QQ(26,15)/2 - x**QQ(22,15)/2 - \
        x**QQ(6,5)/6 + x + x**QQ(2,3) + x**QQ(2,5)

    r = rs_atanh(p, x, 2)
    assert r == x**QQ(9,5) + x**QQ(26,15) + x**QQ(22,15) + x**QQ(6,5)/3 + x + \
        x**QQ(2,3) + x**QQ(2,5)

    r = rs_sinh(p, x, 2)
    assert r == x**QQ(9,5)/2 + x**QQ(26,15)/2 + x**QQ(22,15)/2 + \
        x**QQ(6,5)/6 + x + x**QQ(2,3) + x**QQ(2,5)

    r = rs_cosh(p, x, 2)
    assert r == x**QQ(28,15)/6 + x**QQ(5,3) + x**QQ(8,5)/24 + x**QQ(7,5) + \
        x**QQ(4,3)/2 + x**QQ(16,15) + x**QQ(4,5)/2 + 1

    r = rs_tanh(p, x, 2)
    assert r == -x**QQ(9,5) - x**QQ(26,15) - x**QQ(22,15) - x**QQ(6,5)/3 + \
        x + x**QQ(2,3) + x**QQ(2,5)

Example #9

File: test_ring_series.py Project: asmeurer/sympy

def test_puiseux():
    R, x, y = ring('x, y', QQ)
    p = x**QQ(2,5) + x**QQ(2,3) + x

    r = rs_series_inversion(p, x, 1)
    r1 = -x**QQ(14,15) + x**QQ(4,5) - 3*x**QQ(11,15) + x**QQ(2,3) + \
        2*x**QQ(7,15) - x**QQ(2,5) - x**QQ(1,5) + x**QQ(2,15) - x**QQ(-2,15) \
        + x**QQ(-2,5)
    assert r == r1

    r = rs_nth_root(1 + p, 3, x, 1)
    assert r == -x**QQ(4,5)/9 + x**QQ(2,3)/3 + x**QQ(2,5)/3 + 1

    r = rs_log(1 + p, x, 1)
    assert r == -x**QQ(4,5)/2 + x**QQ(2,3) + x**QQ(2,5)

    r = rs_LambertW(p, x, 1)
    assert r == -x**QQ(4,5) + x**QQ(2,3) + x**QQ(2,5)

    p1 = x + x**QQ(1,5)*y
    r = rs_exp(p1, x, 1)
    assert r == x**QQ(4,5)*y**4/24 + x**QQ(3,5)*y**3/6 + x**QQ(2,5)*y**2/2 + \
        x**QQ(1,5)*y + 1

    r = rs_atan(p, x, 2)
    assert r ==  -x**QQ(9,5) - x**QQ(26,15) - x**QQ(22,15) - x**QQ(6,5)/3 + \
        x + x**QQ(2,3) + x**QQ(2,5)

    r = rs_atan(p1, x, 2)
    assert r ==  x**QQ(9,5)*y**9/9 + x**QQ(9,5)*y**4 - x**QQ(7,5)*y**7/7 - \
        x**QQ(7,5)*y**2 + x*y**5/5 + x - x**QQ(3,5)*y**3/3 + x**QQ(1,5)*y

    r = rs_asin(p, x, 2)
    assert r == x**QQ(9,5)/2 + x**QQ(26,15)/2 + x**QQ(22,15)/2 + \
        x**QQ(6,5)/6 + x + x**QQ(2,3) + x**QQ(2,5)

    r = rs_cot(p, x, 1)
    assert r == -x**QQ(14,15) + x**QQ(4,5) - 3*x**QQ(11,15) + \
        2*x**QQ(2,3)/3 + 2*x**QQ(7,15) - 4*x**QQ(2,5)/3 - x**QQ(1,5) + \
        x**QQ(2,15) - x**QQ(-2,15) + x**QQ(-2,5)

    r = rs_cos_sin(p, x, 2)
    assert r[0] == x**QQ(28,15)/6 - x**QQ(5,3) + x**QQ(8,5)/24 - x**QQ(7,5) - \
        x**QQ(4,3)/2 - x**QQ(16,15) - x**QQ(4,5)/2 + 1
    assert r[1] == -x**QQ(9,5)/2 - x**QQ(26,15)/2 - x**QQ(22,15)/2 - \
        x**QQ(6,5)/6 + x + x**QQ(2,3) + x**QQ(2,5)

    r = rs_atanh(p, x, 2)
    assert r == x**QQ(9,5) + x**QQ(26,15) + x**QQ(22,15) + x**QQ(6,5)/3 + x + \
        x**QQ(2,3) + x**QQ(2,5)

    r = rs_sinh(p, x, 2)
    assert r == x**QQ(9,5)/2 + x**QQ(26,15)/2 + x**QQ(22,15)/2 + \
        x**QQ(6,5)/6 + x + x**QQ(2,3) + x**QQ(2,5)

    r = rs_cosh(p, x, 2)
    assert r == x**QQ(28,15)/6 + x**QQ(5,3) + x**QQ(8,5)/24 + x**QQ(7,5) + \
        x**QQ(4,3)/2 + x**QQ(16,15) + x**QQ(4,5)/2 + 1

    r = rs_tanh(p, x, 2)
    assert r == -x**QQ(9,5) - x**QQ(26,15) - x**QQ(22,15) - x**QQ(6,5)/3 + \
        x + x**QQ(2,3) + x**QQ(2,5)