import sympy

r, phi = sympy.symbols('r phi')

gmn= sympy.Matrix([[1,0],[0,r**2]])
gMN= gmn**(-1)
indices = {0:'r', 1:'phi'}

for i in [0,1]:
    for j in [0,1]:
        for k in [0,1]:
            sum = 0
            for l in [0,1]:
                #print (1./2)*gMN[2*1+j]*(sympy.diff(gmn[2*0+j],phi) +sympy.diff(gmn[2*1+j],r) -sympy.diff(gmn[2*0+1],r))
                sum += (1./2)*gMN[2*k+l]*(sympy.diff(gmn[2*j+l],indices[i]) +sympy.diff(gmn[2*i+l],indices[j]) -sympy.diff(gmn[2*i+j],indices[l]))
            #print 'gamma',i,j,k,sum
            print 'gamma','^',indices[k],'_{',indices[i],indices[j],'}',sum

r, theta, phi = sympy.symbols('r theta phi')

gmn= sympy.Matrix([[r**2,0],[0,(r**2)*(sympy.sin(theta)**2)]])
gMN= gmn**(-1)
indices = {0:'theta', 1:'phi'}

for i in [0,1]:
    for j in [0,1]:
        for k in [0,1]:
            sum = 0
            for l in [0,1]:
            #   print (1./2)*gMN[2*1+j]*(sympy.diff(gmn[2*0+j],phi) +sympy.diff(gmn[2*1+j],r) -sympy.diff(gmn[2*0+1],r))
                sum += (1./2)*gMN[2*k+l]*(sympy.diff(gmn[2*j+l],indices[i]) +sympy.diff(gmn[2*i+l],indices[j]) -sympy.diff(gmn[2*i+j],indices[l]))
            #print 'gamma',i,j,k,sum
            print 'gamma','^',indices[k],'_{',indices[i],indices[j],'}',sum