#!/usr/bin/env python
# coding: utf-8

"""  From "COMPUTATIONAL PHYSICS" & "COMPUTER PROBLEMS in PHYSICS",
     by RH Landau, MJ Paez, and CC Bordeianu (deceased).
     Copyright R Landau, Oregon State Unv, MJ Paez, Univ Antioquia,
     C Bordeianu, Univ Bucharest, 2020.
     Please respect copyright & acknowledge our work.""" 
     
# Quarks.py verification of the SU(3) algebre for quarks 
 
from numpy import *
from numpy.linalg import *

L1 = array([[0,1,0],[1,0,0],[0,0,0]])  # eight generators
L2 = array([[0,-1j,0],[1j,0,0],[0,0,0]])
L3 = array([[1,0,0],[0,-1,0],[0,0,0]])
L4 = array([[0,0,1],[0,0,0],[1,0,0]])
L5 = array([[0,0,-1j],[0,0,0],[1j,0,0]])
L6 = array([[0,0,0],[0,0,1],[0,1,0]])
L7 = array([[0,0,0],[0,0,-1j],[0,1j,0]])
L8 = array([[1,0,0],[0,1,0],[0,0,-2]])*1/sqrt(3)
u = array([1,0,0])   # up quark
d = array([0,1,0])   # down quark
s = array([0,0,1])   # strange quark
Ip = 0.5*(L1+1j*L2)  # raising operators   
Up = 0.5*(L6+1j*L7)
Vp = 0.5*(L4+1j*L5)
Im = 0.5*(L1-1j*L2)  # lowering operators   
Um = 0.5*(L6-1j*L7)
Vm = 0.5*(L4-1j*L5)
Ipxd = dot(Ip,d)    # raices d to u
print("Ipxd",Ipxd)
Vpxs = dot(Vp,s)    # raises s to u
print("Vpxs",Vpxs)
Upxs = dot(Up,s)    #  raises s to d
print("Upxs ",Upxs)