human
I am working on the file "QuadraysJN.ipynb".
The first task is:
Converting to xyz will not work yet, as the Vector class is not yet defined.  That's what's coming.
Can you write Python code for it?
assistant
#Here's coming.

class Vector:

    def __init__(self, arg):
        """Initialize a vector at an (x,y,z)"""
        self.xyz = XYZ(*map(float,arg))

    def __repr__(self):
        return repr(self.xyz)
    
    @property
    def x(self):
        return self.xyz.x

    @property
    def y(self):
        return self.xyz.y

    @property
    def z(self):
        return self.xyz.z
    
    def __mul__(self, scalar):
        """Return vector (self) * scalar."""
        newcoords = [scalar * dim for dim in self.xyz]
        return type(self)(newcoords)

    __rmul__ = __mul__ # allow scalar * vector

    def __truediv__(self,scalar):
        """Return vector (self) * 1/scalar"""        
        return self.__mul__(1.0/scalar)
    
    def __add__(self,v1):
        """Add a vector to this vector, return a vector""" 
        newcoords = map(add, v1.xyz, self.xyz)
        return type(self)(newcoords)
        
    def __sub__(self,v1):
        """Subtract vector from this vector, return a vector"""
        return self.__add__(-v1)
    
    def __neg__(self):      
        """Return a vector, the negative of this one."""
        return type(self)(tuple(map(neg, self.xyz)))

    def unit(self):
        return self.__mul__(1.0/self.length())

    def dot(self,v1):
        """Return scalar dot product of this with another vector."""
        return sum(map(mul , v1.xyz, self.xyz))

    def cross(self,v1):
        """Return the vector cross product of this with another vector"""
        newcoords = (self.y * v1.z - self.z * v1.y, 
                     self.z * v1.x - self.x * v1.z,
                     self.x * v1.y - self.y * v1.x )
        return type(self)(newcoords)
    
    def length(self):
        """Return this vector's length"""
        return self.dot(self) ** 0.5

    def quadray(self):
        """return (a, b, c, d) quadray based on current (x, y, z)"""
        x, y, z = self.xyz
        k = 2/root2
        a = k * ((x >= 0)* ( x) + (y >= 0) * ( y) + (z >= 0) * ( z))
        b = k * ((x <  0)* (-x) + (y <  0) * (-y) + (z >= 0)...