Table of Contents

LeviCivitaSimplify


Description

Examples


Simplify combinations of Levi-Civita tensors in dimension 3 in Euclidean space:

setAntiSymmetric 'e_abc'
println LeviCivitaSimplify.euclidean['e_abc'] >> 'e_abc*e^abd'.t
   > 2*d^d_c
println LeviCivitaSimplify.euclidean['e_abc'] >> 'e_abc*e^abc'.t
   > 6
def t = 'e_abc*e^amd*e_mnk*e^bnk'.t
println LeviCivitaSimplify.euclidean['e_abc'] >> t
   > 4*d_{c}^{d}


Simplify combinations of Levi-Civita tensors in dimension 4 in Euclidean space:

setAntiSymmetric 'e_abcd'
def t = '4*e^h_d^fb*e_abch*e_e^d_gf'.t
println LeviCivitaSimplify.euclidean['e_abcd'] >> t
   > 16*e_{eagc}
Simplify same expression in Minkowski space:
setAntiSymmetric 'e_abcd'
def t = '4*e^h_d^fb*e_abch*e_e^d_gf'.t
println LeviCivitaSimplify.minkowski['e_abcd'] >> t
   > -16*e_{eagc}


Simplify combinations of Levi-Civita tensors in dimension 5 in Minkowski space:

setAntiSymmetric 'e_abcde'
def t = '''e^{m}_{g}^{kci}*e_{pdj}^{l}_{o}*e_{c}^{n}_{mi}^{p}
           *e_{khnef}*e^{g}_{a}^{efd}*e_{l}^{hj}_{b}^{o}'''.t
println LeviCivitaSimplify.minkowski['e_abcde'] >> t
   > 864*g_{ab}


Simplify expression where Levi-Civita is contracted with symmetric tensor:

setAntiSymmetric 'e_abcd'
def t = 'e_abcd*(A^a + C^a)*(A^b + C^b)'.t
println LeviCivitaSimplify.minkowski['e_abcd'] >> t
   > 0


See also