Python roots_cyclotomic示例

示例#1

文件： test_polyroots.py 项目： NalinG/sympy

def test_roots_cyclotomic():
    assert roots_cyclotomic(cyclotomic_poly(1, x, polys=True)) == [1]
    assert roots_cyclotomic(cyclotomic_poly(2, x, polys=True)) == [-1]
    assert roots_cyclotomic(cyclotomic_poly(
        3, x, polys=True)) == [-S(1)/2 - I*sqrt(3)/2, -S(1)/2 + I*sqrt(3)/2]
    assert roots_cyclotomic(cyclotomic_poly(4, x, polys=True)) == [-I, I]
    assert roots_cyclotomic(cyclotomic_poly(
        6, x, polys=True)) == [S(1)/2 - I*sqrt(3)/2, S(1)/2 + I*sqrt(3)/2]

    assert roots_cyclotomic(cyclotomic_poly(7, x, polys=True)) == [
        -cos(pi/7) - I*sin(pi/7),
        -cos(pi/7) + I*sin(pi/7),
        -cos(3*pi/7) - I*sin(3*pi/7),
        -cos(3*pi/7) + I*sin(3*pi/7),
        cos(2*pi/7) - I*sin(2*pi/7),
        cos(2*pi/7) + I*sin(2*pi/7),
    ]

    assert roots_cyclotomic(cyclotomic_poly(8, x, polys=True)) == [
        -sqrt(2)/2 - I*sqrt(2)/2,
        -sqrt(2)/2 + I*sqrt(2)/2,
        sqrt(2)/2 - I*sqrt(2)/2,
        sqrt(2)/2 + I*sqrt(2)/2,
    ]

    assert roots_cyclotomic(cyclotomic_poly(12, x, polys=True)) == [
        -sqrt(3)/2 - I/2,
        -sqrt(3)/2 + I/2,
        sqrt(3)/2 - I/2,
        sqrt(3)/2 + I/2,
    ]

    assert roots_cyclotomic(
        cyclotomic_poly(1, x, polys=True), factor=True) == [1]
    assert roots_cyclotomic(
        cyclotomic_poly(2, x, polys=True), factor=True) == [-1]

    assert roots_cyclotomic(cyclotomic_poly(3, x, polys=True), factor=True) == \
        [-root(-1, 3), -1 + root(-1, 3)]
    assert roots_cyclotomic(cyclotomic_poly(4, x, polys=True), factor=True) == \
        [-I, I]
    assert roots_cyclotomic(cyclotomic_poly(5, x, polys=True), factor=True) == \
        [-root(-1, 5), -root(-1, 5)**3, root(-1, 5)**2, -1 - root(-1, 5)**2 + root(-1, 5) + root(-1, 5)**3]

    assert roots_cyclotomic(cyclotomic_poly(6, x, polys=True), factor=True) == \
        [1 - root(-1, 3), root(-1, 3)]

示例#2

文件： test_polyroots.py 项目： stefanv/sympy

def test_roots_cyclotomic():
    assert roots_cyclotomic(cyclotomic_poly(1, x, polys=True)) == [1]
    assert roots_cyclotomic(cyclotomic_poly(2, x, polys=True)) == [-1]
    assert roots_cyclotomic(cyclotomic_poly(3, x, polys=True)) == [
        -S(1) / 2 - I * sqrt(3) / 2, -S(1) / 2 + I * sqrt(3) / 2
    ]
    assert roots_cyclotomic(cyclotomic_poly(4, x, polys=True)) == [-I, I]
    assert roots_cyclotomic(cyclotomic_poly(6, x, polys=True)) == [
        S(1) / 2 - I * sqrt(3) / 2,
        S(1) / 2 + I * sqrt(3) / 2
    ]

    assert roots_cyclotomic(cyclotomic_poly(7, x, polys=True)) == [
        -cos(pi / 7) - I * sin(pi / 7),
        -cos(pi / 7) + I * sin(pi / 7),
        cos(2 * pi / 7) - I * sin(2 * pi / 7),
        cos(2 * pi / 7) + I * sin(2 * pi / 7),
        -cos(3 * pi / 7) - I * sin(3 * pi / 7),
        -cos(3 * pi / 7) + I * sin(3 * pi / 7),
    ]

    assert roots_cyclotomic(cyclotomic_poly(8, x, polys=True)) == [
        -sqrt(2) / 2 - I * sqrt(2) / 2,
        -sqrt(2) / 2 + I * sqrt(2) / 2,
        sqrt(2) / 2 - I * sqrt(2) / 2,
        sqrt(2) / 2 + I * sqrt(2) / 2,
    ]

    assert roots_cyclotomic(cyclotomic_poly(12, x, polys=True)) == [
        -sqrt(3) / 2 - I / 2,
        -sqrt(3) / 2 + I / 2,
        sqrt(3) / 2 - I / 2,
        sqrt(3) / 2 + I / 2,
    ]

    assert roots_cyclotomic(cyclotomic_poly(1, x, polys=True),
                            factor=True) == [1]
    assert roots_cyclotomic(cyclotomic_poly(2, x, polys=True),
                            factor=True) == [-1]

    assert roots_cyclotomic(cyclotomic_poly(3, x, polys=True), factor=True) == \
        [-(-1)**(S(1)/3), -1 + (-1)**(S(1)/3)]
    assert roots_cyclotomic(cyclotomic_poly(4, x, polys=True), factor=True) == \
        [-I, I]
    assert roots_cyclotomic(cyclotomic_poly(5, x, polys=True), factor=True) == \
        [-(-1)**(S(1)/5), (-1)**(S(2)/5), -(-1)**(S(3)/5),
         -1 + (-1)**(S(1)/5) - (-1)**(S(2)/5) + (-1)**(S(3)/5)]
    assert roots_cyclotomic(cyclotomic_poly(6, x, polys=True), factor=True) == \
        [(-1)**(S(1)/3), 1 - (-1)**(S(1)/3)]

示例#3

文件： test_polyroots.py 项目： qmattpap/sympy

def test_roots_cyclotomic():
    assert roots_cyclotomic(cyclotomic_poly(1, x, polys=True)) == [1]
    assert roots_cyclotomic(cyclotomic_poly(2, x, polys=True)) == [-1]
    assert roots_cyclotomic(cyclotomic_poly(3, x, polys=True)) == [-S(1)/2 - I*3**(S(1)/2)/2, -S(1)/2 + I*3**(S(1)/2)/2]
    assert roots_cyclotomic(cyclotomic_poly(4, x, polys=True)) == [-I, I]
    assert roots_cyclotomic(cyclotomic_poly(6, x, polys=True)) == [S(1)/2 - I*3**(S(1)/2)/2, S(1)/2 + I*3**(S(1)/2)/2]

    assert roots_cyclotomic(cyclotomic_poly(7, x, polys=True)) == [
        -cos(pi/7)   - I*sin(pi/7),
        -cos(pi/7)   + I*sin(pi/7),
         cos(2*pi/7) - I*sin(2*pi/7),
         cos(2*pi/7) + I*sin(2*pi/7),
        -cos(3*pi/7) - I*sin(3*pi/7),
        -cos(3*pi/7) + I*sin(3*pi/7),
    ]

    assert roots_cyclotomic(cyclotomic_poly(8, x, polys=True)) == [
        -2**(S(1)/2)/2 - I*2**(S(1)/2)/2,
        -2**(S(1)/2)/2 + I*2**(S(1)/2)/2,
         2**(S(1)/2)/2 - I*2**(S(1)/2)/2,
         2**(S(1)/2)/2 + I*2**(S(1)/2)/2,
    ]

    assert roots_cyclotomic(cyclotomic_poly(12, x, polys=True)) == [
        -3**(S(1)/2)/2 - I/2,
        -3**(S(1)/2)/2 + I/2,
         3**(S(1)/2)/2 - I/2,
         3**(S(1)/2)/2 + I/2,
    ]

    assert roots_cyclotomic(cyclotomic_poly(1, x, polys=True), factor=True) == [1]
    assert roots_cyclotomic(cyclotomic_poly(2, x, polys=True), factor=True) == [-1]

    assert roots_cyclotomic(cyclotomic_poly(3, x, polys=True), factor=True) == \
        [-(-1)**(S(1)/3), -1 + (-1)**(S(1)/3)]
    assert roots_cyclotomic(cyclotomic_poly(4, x, polys=True), factor=True) == \
        [-I, I]
    assert roots_cyclotomic(cyclotomic_poly(5, x, polys=True), factor=True) == \
        [-(-1)**(S(1)/5), (-1)**(S(2)/5), -(-1)**(S(3)/5), -1 + (-1)**(S(1)/5) - (-1)**(S(2)/5) + (-1)**(S(3)/5)]
    assert roots_cyclotomic(cyclotomic_poly(6, x, polys=True), factor=True) == \
        [(-1)**(S(1)/3), 1 - (-1)**(S(1)/3)]

示例#4

文件： test_polyroots.py 项目： sylee957/sympy

def test_roots_cyclotomic():
    assert roots_cyclotomic(cyclotomic_poly(1, x, polys=True)) == [1]
    assert roots_cyclotomic(cyclotomic_poly(2, x, polys=True)) == [-1]
    assert roots_cyclotomic(cyclotomic_poly(3, x, polys=True)) == [
        Rational(-1, 2) - I * sqrt(3) / 2,
        Rational(-1, 2) + I * sqrt(3) / 2
    ]
    assert roots_cyclotomic(cyclotomic_poly(4, x, polys=True)) == [-I, I]
    assert roots_cyclotomic(cyclotomic_poly(6, x, polys=True)) == [
        S.Half - I * sqrt(3) / 2, S.Half + I * sqrt(3) / 2
    ]

    assert roots_cyclotomic(cyclotomic_poly(7, x, polys=True)) == [
        -cos(pi / 7) - I * sin(pi / 7),
        -cos(pi / 7) + I * sin(pi / 7),
        -cos(pi * Rational(3, 7)) - I * sin(pi * Rational(3, 7)),
        -cos(pi * Rational(3, 7)) + I * sin(pi * Rational(3, 7)),
        cos(pi * Rational(2, 7)) - I * sin(pi * Rational(2, 7)),
        cos(pi * Rational(2, 7)) + I * sin(pi * Rational(2, 7)),
    ]

    assert roots_cyclotomic(cyclotomic_poly(8, x, polys=True)) == [
        -sqrt(2) / 2 - I * sqrt(2) / 2,
        -sqrt(2) / 2 + I * sqrt(2) / 2,
        sqrt(2) / 2 - I * sqrt(2) / 2,
        sqrt(2) / 2 + I * sqrt(2) / 2,
    ]

    assert roots_cyclotomic(cyclotomic_poly(12, x, polys=True)) == [
        -sqrt(3) / 2 - I / 2,
        -sqrt(3) / 2 + I / 2,
        sqrt(3) / 2 - I / 2,
        sqrt(3) / 2 + I / 2,
    ]

    assert roots_cyclotomic(cyclotomic_poly(1, x, polys=True),
                            factor=True) == [1]
    assert roots_cyclotomic(cyclotomic_poly(2, x, polys=True),
                            factor=True) == [-1]

    assert roots_cyclotomic(cyclotomic_poly(3, x, polys=True), factor=True) == \
        [-root(-1, 3), -1 + root(-1, 3)]
    assert roots_cyclotomic(cyclotomic_poly(4, x, polys=True), factor=True) == \
        [-I, I]
    assert roots_cyclotomic(cyclotomic_poly(5, x, polys=True), factor=True) == \
        [-root(-1, 5), -root(-1, 5)**3, root(-1, 5)**2, -1 - root(-1, 5)**2 + root(-1, 5) + root(-1, 5)**3]

    assert roots_cyclotomic(cyclotomic_poly(6, x, polys=True), factor=True) == \
        [1 - root(-1, 3), root(-1, 3)]

示例#5

def test_roots_cyclotomic():
    assert roots_cyclotomic(cyclotomic_poly(1, x, polys=True)) == [1]
    assert roots_cyclotomic(cyclotomic_poly(2, x, polys=True)) == [-1]
    assert roots_cyclotomic(cyclotomic_poly(
        3, x, polys=True)) == [-S(1)/2 - I*sqrt(3)/2, -S(1)/2 + I*sqrt(3)/2]
    assert roots_cyclotomic(cyclotomic_poly(4, x, polys=True)) == [-I, I]
    assert roots_cyclotomic(cyclotomic_poly(
        6, x, polys=True)) == [S(1)/2 - I*sqrt(3)/2, S(1)/2 + I*sqrt(3)/2]

    assert roots_cyclotomic(cyclotomic_poly(7, x, polys=True)) == [
        -cos(pi/7) - I*sin(pi/7),
        -cos(pi/7) + I*sin(pi/7),
        -cos(3*pi/7) - I*sin(3*pi/7),
        -cos(3*pi/7) + I*sin(3*pi/7),
        cos(2*pi/7) - I*sin(2*pi/7),
        cos(2*pi/7) + I*sin(2*pi/7),
    ]

    assert roots_cyclotomic(cyclotomic_poly(8, x, polys=True)) == [
        -sqrt(2)/2 - I*sqrt(2)/2,
        -sqrt(2)/2 + I*sqrt(2)/2,
        sqrt(2)/2 - I*sqrt(2)/2,
        sqrt(2)/2 + I*sqrt(2)/2,
    ]

    assert roots_cyclotomic(cyclotomic_poly(12, x, polys=True)) == [
        -sqrt(3)/2 - I/2,
        -sqrt(3)/2 + I/2,
        sqrt(3)/2 - I/2,
        sqrt(3)/2 + I/2,
    ]

    assert roots_cyclotomic(
        cyclotomic_poly(1, x, polys=True), factor=True) == [1]
    assert roots_cyclotomic(
        cyclotomic_poly(2, x, polys=True), factor=True) == [-1]

    assert roots_cyclotomic(cyclotomic_poly(3, x, polys=True), factor=True) == \
        [-root(-1, 3), -1 + root(-1, 3)]
    assert roots_cyclotomic(cyclotomic_poly(4, x, polys=True), factor=True) == \
        [-I, I]
    assert roots_cyclotomic(cyclotomic_poly(5, x, polys=True), factor=True) == \
        [-root(-1, 5), -root(-1, 5)**3, root(-1, 5)**2, -1 - root(-1, 5)**2 + root(-1, 5) + root(-1, 5)**3]

    assert roots_cyclotomic(cyclotomic_poly(6, x, polys=True), factor=True) == \
        [1 - root(-1, 3), root(-1, 3)]

示例#6

文件： test_polyroots.py 项目： robotment/sympy

def test_roots_cyclotomic():
    assert roots_cyclotomic(cyclotomic_poly(1, x, polys=True)) == [1]
    assert roots_cyclotomic(cyclotomic_poly(2, x, polys=True)) == [-1]
    assert roots_cyclotomic(cyclotomic_poly(3, x, polys=True)) == [-S(1)/2 + I*3**(S(1)/2)/2, -S(1)/2 - I*3**(S(1)/2)/2]
    assert roots_cyclotomic(cyclotomic_poly(4, x, polys=True)) == [I, -I]
    assert roots_cyclotomic(cyclotomic_poly(6, x, polys=True)) == [S(1)/2 + I*3**(S(1)/2)/2, S(1)/2 - I*3**(S(1)/2)/2]

    assert roots_cyclotomic(cyclotomic_poly(7, x, polys=True)) == [
         I*sin(2*pi/7) + cos(2*pi/7),
         I*sin(3*pi/7) - cos(3*pi/7),
         I*sin(pi/7)   - cos(pi/7),
        -I*sin(pi/7)   - cos(pi/7),
        -I*sin(3*pi/7) - cos(3*pi/7),
        -I*sin(2*pi/7) + cos(2*pi/7),
    ]

    assert roots_cyclotomic(cyclotomic_poly(8, x, polys=True)) == [
         2**(S(1)/2)/2 + I*2**(S(1)/2)/2,
        -2**(S(1)/2)/2 + I*2**(S(1)/2)/2,
        -2**(S(1)/2)/2 - I*2**(S(1)/2)/2,
         2**(S(1)/2)/2 - I*2**(S(1)/2)/2,
    ]

    assert roots_cyclotomic(cyclotomic_poly(12, x, polys=True)) == [
         I/2 + 3**(S(1)/2)/2,
         I/2 - 3**(S(1)/2)/2,
        -I/2 - 3**(S(1)/2)/2,
        -I/2 + 3**(S(1)/2)/2,
    ]

    assert roots_cyclotomic(cyclotomic_poly(1, x, polys=True), factor=True) == [1]
    assert roots_cyclotomic(cyclotomic_poly(2, x, polys=True), factor=True) == [-1]

    assert roots_cyclotomic(cyclotomic_poly(3, x, polys=True), factor=True) == \
        [-1 + (-1)**(S(1)/3), -(-1)**(S(1)/3)]
    assert roots_cyclotomic(cyclotomic_poly(4, x, polys=True), factor=True) == \
        [I, -I]
    assert roots_cyclotomic(cyclotomic_poly(5, x, polys=True), factor=True) == \
        [-(-1)**(S(1)/5), (-1)**(S(2)/5), -1 + (-1)**(S(1)/5) - (-1)**(S(2)/5) + (-1)**(S(3)/5), -(-1)**(S(3)/5)]
    assert roots_cyclotomic(cyclotomic_poly(6, x, polys=True), factor=True) == \
        [(-1)**(S(1)/3), 1 - (-1)**(S(1)/3)]