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Contraction of repeated indices, Mathematica
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| dim = 3; | |
| SetAttributes[KD, Orderless] | |
| KD[i_, i_] := dim | |
| ContractDeltas[delta_] := | |
| With[{rule = {KD[x_, y_] f_[w___, x_, z___] -> f[w, y, z], | |
| Power[KD[x_, y_], 2] -> dim}}, Expand[delta] //. rule] | |
| (* A basic example *) | |
| del2 = KD[i, j] KD[i, l] + KD[k, j] KD[i, k] KD[j, f] + KD[i, i] KD[g, f] KD[f, s] + KD[u, v] KD[w, v] KD[w, u]; | |
| ContractDeltas[del2] // TraditionalForm |
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