isNormal -- determine if a reduced ring is normal

i1 : R = QQ[x,y,z]/ideal(x^6-z^6-y^2*z^4);

i2 : isNormal R

o2 = false

i3 : isNormal(integralClosure R)
            +----------------+
choices are |(1, 1, x)       |
            +----------------+
            |        2     3 |
            |(3, 2, y z + z )|
            +----------------+
            +----------------+
choices are |(1, 1, x)       |
            +----------------+
            |(1, 1, w )      |
            |        0       |
            +----------------+
            |        2     3 |
            |(3, 2, y z + z )|
            +----------------+
            +----------------+
choices are |(1, 1, x)       |
            +----------------+
            |(1, 1, w )      |
            |        2       |
            +----------------+
            |(1, 1, w )      |
            |        1       |
            +----------------+
            |        2     3 |
            |(3, 2, y z + z )|
            +----------------+
            +----------+
choices are |(1, 1, x) |
            +----------+
            |(1, 1, w )|
            |        5 |
            +----------+
            |(1, 1, w )|
            |        4 |
            +----------+
            |(1, 1, w )|
            |        3 |
            +----------+
            +----------+
choices are |(1, 1, x) |
            +----------+
            |(1, 1, w )|
            |        3 |
            +----------+
            |(1, 1, w )|
            |        6 |
            +----------+
            +----------+
choices are |(1, 1, x) |
            +----------+
            |(1, 1, w )|
            |        6 |
            +----------+

o3 = true