コード例 #1
0
def test_primitive_element():
    assert primitive_element([sqrt(2)]) == (PurePoly(x**2 - 2), [1], [[1, 0]])

    assert (primitive_element([sqrt(2), sqrt(3)]) ==
            (PurePoly(x**4 - 10*x**2 + 1), [1, 1], [[QQ(+1, 2), 0, -QQ(9, 2), 0],
                                                    [QQ(-1, 2), 0, QQ(11, 2), 0]]))
    A = QQ.algebraic_field(sqrt(2))
    assert (primitive_element([sqrt(2), sqrt(3)], domain=A) ==
            (PurePoly(x**2 - 2*sqrt(2)*x - 1, x, domain=A), [1, 1],
             [[A.unit], [1, -A.unit]]))
    assert (primitive_element([sqrt(2), sqrt(2 + sqrt(2))], domain=A) ==
            (PurePoly(x**2 - 2*sqrt(2)*x - sqrt(2), x, domain=A), [1, 1],
             [[A.unit], [1, -A.unit]]))

    A = QQ.algebraic_field(sqrt(2) + sqrt(3))
    assert (primitive_element([sqrt(2), sqrt(3)], domain=A) ==
            (PurePoly(x - sqrt(2) - sqrt(3), x, domain=A), [1, 1],
             [[A([QQ(1, 2), 0, -QQ(9, 2), 0])], [A([-QQ(1, 2), 0, QQ(11, 2), 0])]]))

    pytest.raises(ValueError, lambda: primitive_element([]))

    # issue sympy/sympy#13849
    assert (primitive_element([sqrt(2), sqrt(2) + sqrt(5)]) ==
            (PurePoly(x**4 - 76*x**2 + 4), [1, 2], [[QQ(1, 12), 0, QQ(-37, 6), 0],
                                                    [QQ(-1, 24), 0, QQ(43, 12), 0]]))

    # issue sympy/sympy#14117
    assert (primitive_element([I*sqrt(2*sqrt(2) + 3), I*sqrt(-2*sqrt(2) + 3), I]) ==
            (PurePoly(x**4 + 54*x**2 + 81), [1, 2, 4], [[QQ(1, 3), 0], [QQ(1, 27), 0, 2, 0],
                                                        [QQ(-1, 54), 0, QQ(-5, 6), 0]]))
コード例 #2
0
def test_sympyissue_18874():
    e = [sqrt(2) + sqrt(5), sqrt(2)]

    assert primitive_element(e) == (PurePoly(x**4 - 46 * x**2 + 169),
                                    [1, 2], [[0, QQ(-20, 39), 0,
                                              QQ(1, 39)],
                                             [0, QQ(59, 78), 0,
                                              QQ(-1, 78)]])