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def Vector (x,y,z):

    return (x,y,z)

def Add (a,b):

    return (a[0]+b[0],a[1]+b[1],a[2]+b[2])

def Sub (a,b):

    return (a[0]-b[0],a[1]-b[1],a[2]-b[2])

def Neg (a):

    return (-a[0],-a[1],-a[2])

def Cross(a,b):

    return (a[1]*b[2]-a[2]*b[1], a[2]*b[0]-a[0]*b[2], a[0]*b[1]-a[1]*b[0])

def Scale(a,f):

    return (a[0]*f,a[1]*f,a[2]*f)

def Dot (a,b):

    return a[0]*b[0]+a[1]*b[1]+a[2]*b[2]

def Transform (a,p,q,r):

    return (Dot (a,p),

            Dot (a,q),

            Dot (a,r))

def Mag(a):

    import VS

    return VS.sqrt(Dot(a,a))

def Norm (a):

    return Scale(a,1.0/Mag(a))

def SafeNorm (a):

    mag = Mag(a)

    if (mag):

        return Scale(a,1.0/mag)

    else:

        return Vector(0,0,0)

def ScaledCross (a,b):

    return Norm(Cross(a,b))

def Max(a,b):

    return ((a[0]>b[0])*a[0]+(a[0]<=b[0])*b[0],

            (a[1]>b[1])*a[1]+(a[1]<=b[1])*b[1],

            (a[2]>b[2])*a[2]+(a[2]<=b[2])*b[2])

def Min(a,b):

    return ((a[0]<b[0])*a[0]+(a[0]>=b[0])*b[0],

            (a[1]<b[1])*a[1]+(a[1]>=b[1])*b[1],

            (a[2]<b[2])*a[2]+(a[2]>=b[2])*b[2])