test_modules.py 文件源码

def test_in_terms_of_generators():
    R = QQ.old_poly_ring(x, order="ilex")
    M = R.free_module(2).submodule([2*x, 0], [1, 2])
    assert M.in_terms_of_generators(
        [x, x]) == [R.convert(S(1)/4), R.convert(x/2)]
    raises(ValueError, lambda: M.in_terms_of_generators([1, 0]))

    M = R.free_module(2) / ([x, 0], [1, 1])
    SM = M.submodule([1, x])
    assert SM.in_terms_of_generators([2, 0]) == [R.convert(-2/(x - 1))]

    R = QQ.old_poly_ring(x, y) / [x**2 - y**2]
    M = R.free_module(2)
    SM = M.submodule([x, 0], [0, y])
    assert SM.in_terms_of_generators(
        [x**2, x**2]) == [R.convert(x), R.convert(y)]