test_subresultants_qq_zz.py 文件源码

def test_sylvester():
    x = var('x')

    assert sylvester(x**3 -7, 0, x) == sylvester(x**3 -7, 0, x, 1) == Matrix([[0]])
    assert sylvester(0, x**3 -7, x) == sylvester(0, x**3 -7, x, 1) == Matrix([[0]])
    assert sylvester(x**3 -7, 0, x, 2) == Matrix([[0]])
    assert sylvester(0, x**3 -7, x, 2) == Matrix([[0]])

    assert sylvester(x**3 -7, 7, x).det() == sylvester(x**3 -7, 7, x, 1).det() == 343
    assert sylvester(7, x**3 -7, x).det() == sylvester(7, x**3 -7, x, 1).det() == 343
    assert sylvester(x**3 -7, 7, x, 2).det() == -343
    assert sylvester(7, x**3 -7, x, 2).det() == 343

    assert sylvester(3, 7, x).det() == sylvester(3, 7, x, 1).det() == sylvester(3, 7, x, 2).det() == 1

    assert sylvester(3, 0, x).det() == sylvester(3, 0, x, 1).det() == sylvester(3, 0, x, 2).det() == 1

    assert sylvester(x - 3, x - 8, x) == sylvester(x - 3, x - 8, x, 1) == sylvester(x - 3, x - 8, x, 2) == Matrix([[1, -3], [1, -8]])

    assert sylvester(x**3 - 7*x + 7, 3*x**2 - 7, x) == sylvester(x**3 - 7*x + 7, 3*x**2 - 7, x, 1) == Matrix([[1, 0, -7,  7,  0], [0, 1,  0, -7,  7], [3, 0, -7,  0,  0], [0, 3,  0, -7,  0], [0, 0,  3,  0, -7]])

    assert sylvester(x**3 - 7*x + 7, 3*x**2 - 7, x, 2) == Matrix([
[1, 0, -7,  7,  0,  0], [0, 3,  0, -7,  0,  0], [0, 1,  0, -7,  7,  0], [0, 0,  3,  0, -7,  0], [0, 0,  1,  0, -7,  7], [0, 0,  0,  3,  0, -7]])