from sympy import *
from IPython.display import display

params0, params1, params2, params3= symbols('params0 params1 params2 params3')
E00, E01, E02, E11, E12, E22 = symbols('E00 E01 E02 E11 E12 E22')
W, Q = symbols('W Q')

Q=params0*(E00*E00)+params1*(E11*E11+E22*E22+2*E12*E12)+params2*(2*E01*E01+2*E02*E02)
W=params3*(exp(Q)-1)/2

print("W=",W)
print()

for i in range(0,3):
    for j in range(0,3):
        if i<=j:
            print("result(",i,",",j,")=", end='')
            display(diff(W,'E%d%d' % (i,j)))
    
print()

#Indexes fourth order tensor
A=Matrix(21,4, [ 0 , 0 , 0 , 0, 
                 0 , 0 , 0 , 1, 
                 0 , 0 , 0 , 2, 
                 0 , 0 , 1 , 1, 
                 0 , 0 , 1 , 2, 
                 0 , 0 , 2 , 2, 
                 0 , 1 , 0 , 1, 
                 0 , 1 , 0 , 2, 
                 0 , 1 , 1 , 1, 
                 0 , 1 , 1 , 2, 
                 0 , 1 , 2 , 2, 
                 0 , 2 , 0 , 2, 
                 0 , 2 , 1 , 1, 
                 0 , 2 , 1 , 2, 
                 0 , 2 , 2 , 2, 
                 1 , 1 , 1 , 1, 
                 1 , 1 , 1 , 2, 
                 1 , 1 , 2 , 2, 
                 1 , 2 , 1 , 2, 
                 1 , 2 , 2 , 2, 
                 2 , 2 , 2 , 2 ])

#for l in range(0,21):
#    print(A[l,0],A[l,1],A[l,2],A[l,3])

print()

for l in range(0,21):
    print("result(",A[l,0],",",A[l,1],",",A[l,2],",",A[l,3],")=", end='')
    display(diff(  diff(W,'E%d%d' % (A[l,0],A[l,1]))  ,'E%d%d' % (A[l,2],A[l,3])))