from numpy.lib.scimath import sqrt

class V2D:
    #######GESTIONE-TOLLERANZA#######
    #membro statico della classe
    __tol=1e-6
    
    #metodo della classe
    @classmethod #senza questo cls si riferirebbe all'oggetto e non alla classe (come self)
    def set_tol(cls,t):
        cls.__tol = t
    
    @classmethod#senza questo cls si riferirebbe all'oggetto e non alla classe (come self)
    def get_tol(cls):
        return cls.__tol

    #######METODI#######
    #costruttore
    def __init__(self,x,y):
        self.x=x
        self.y=y

    #conversione a stringa
    def __str__(self):
        return '({0},{1})'.format(self.x , self.y)
        
    #modulo
    def __abs__(self):
        return sqrt(self.x**2+self.y**2)
    
    #uguaglianza 
    def __eq__(self,other):
       return (abs(self.x - other.x) < V2D.get_tol()) and (abs(self.y - other.y) < V2D.get_tol()) 

    #disuguaglianza
    def __ne__(self,other):
        return not self.__eq(other)

    #somma vettoriale
    def __add__(self,other):
        return V2D(self.x + other.x , self.y + other.y)

    #sottrazione vettoriale
    def __sub__(self,other):
        return V2D(self.x - other.x , self.y - other.y)

    #prodotto scalare
    def __mul__(self,other):
        return (self.x * other.x + self.y * other.y)

if __name__=='__main__':

    k=V2D(20,30)
    v=V2D(2,3)
    print('{0} + {1} = {2}'.format(k,v,k+v))
    print('{0} - {1} = {2}'.format(k,v,k-v))
    print('{0} * {1} = {2}'.format(k,v,k*v))
    print('abs(v)  ',abs(v))
    print('v==k  ',v==k)
    print('v==v  ',v==v)

    print('-'*40)
    V2D.set_tol(1e-2)
    print('tolleranza = {0}'.format(V2D.get_tol()))
    v2=V2D(2.0001,3.0001)
    v3=V2D(2.00000001,3.00000001)
    print('v==v2  ',v==v2)
    print('v==v3  ',v==v3)

    print('-'*40)
    V2D.set_tol(1e-5)
    print('tolleranza = {0}'.format(V2D.get_tol()))
    v2=V2D(2.0001,3.0001)
    v3=V2D(2.00000001,3.00000001)
    print('v==v2  ',v==v2)
    print('v==v3  ',v==v3)

    print('-'*40)
    V2D.set_tol(1e-10)
    print('tolleranza = {0}'.format(V2D.get_tol()))
    v2=V2D(2.0001,3.0001)
    v3=V2D(2.00000001,3.00000001)
    print('v==v2  ',v==v2)
    print('v==v3  ',v==v3)