#
import math
#

class ThreeVec:
    "Class for 3 Vector and operations"
    def __init__ ( self, x=0., y=0., z=0.):
        self.x = x
        self.y = y
        self.z = z
    def Add( self, tv ):
        newvec = ThreeVec( self.x+tv.x, self.y+tv.y, self.z+tv.z)
        return newvec
    def __add__( self, tv ):
        "method for overloading the + operator"
        newvec = ThreeVec( self.x+tv.x, self.y+tv.y, self.z+tv.z)
        return newvec
    def __mul__( self, a ):
        "method for overloading the * operator Vec * Zahl"
        newvec = ThreeVec( self.x*a, self.y*a, self.z*a)
        return newvec
    def __rmul__( self, a ):
        "method for overloading the * operator: Zahl * Vec"
        newvec = ThreeVec( self.x*a, self.y*a, self.z*a)
        return newvec
#
    def Angle(self, tv):
        return math.acos(self.SkalProd(tv)/(self.Length()*tv.Length()))
 
    def SkalProd( self, tv ):
        return( self.x*tv.x + self.y*tv.y + self.z*tv.z)
    def Length( self ):
        return math.sqrt( self.x**2 + self.y**2 + self.z**2 )
    def __lt__( self, tv):
        "method for overloading the < operator"
        return self.Length() < tv.Length() 
        
    def __str__( self ) :
        return "( %6.3f, %6.3f, %6.3f )" % ( self.x, self.y, self.z)



# gets only executed when called as main script
#
if __name__ == "__main__" :
    u = ThreeVec (1.,2.,0.)
    print (u.x, u.y, u.z)
    print (u)
    print (u*3.)
    print (1.2*u)

    import random
    
    tvc = []
    for i in range(100):
        u = ThreeVec( random.gauss(0,1), random.gauss(0,1), random.gauss(0,1))
        tvc.append(u)
        
    tvc.sort()
    for tv in tvc:
        print (tv.Length(), tv)