test_subresultants_qq_zz.py 文件源码

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

    p = x**8 + x**6 - 3*x**4 - 3*x**3 + 8*x**2 + 2*x - 5
    q = 3*x**6 + 5*x**4 - 4*x**2 - 9*x + 21
    assert sturm_pg(p, q, x)[-1] != sylvester(p, q, x, 2).det()
    sam_factors = [1, 1, -1, -1, 1, 1]
    assert sturm_pg(p, q, x) == [i*j for i,j in zip(sam_factors, euclid_pg(p, q, x))]

    p = -9*x**5 - 5*x**3 - 9
    q = -45*x**4 - 15*x**2
    assert sturm_pg(p, q, x, 1)[-1] == sylvester(p, q, x, 1).det()
    assert sturm_pg(p, q, x)[-1] != sylvester(p, q, x, 2).det()
    assert sturm_pg(-p, q, x)[-1] == sylvester(-p, q, x, 2).det()
    assert sturm_pg(-p, q, x) == modified_subresultants_pg(-p, q, x)