# simplification rule with symmetry

What rule can you think of to replace the first line by the second?

I have a bunch of expression like these, which I would like to simplify. All dependent cross terms must be written in the same order, using $\epsilon^{i j} A_i \times B_j = \epsilon^{i j} B_i \times A_j$.

The other expressions look like this, but there are a few differences:

• The names of the fields in the crossproduct differ; e.g. $e_{2 i}$ and $\omega_{2 i}$ instead of $e_{1 i}$ and $e_{2 i}$
• The sum can contain more terms. In particular it can contain more cross products
• Terms that are dependent may not appear right after each other in the sum

Which rule would cover all such expressions?

This is the input for the first line.

ϵ^ij*((σ*Cross[Subscript[Subscript[e, 1], i], Subscript[Subscript[ω, 1], j]]*Subscript[M, 1])/4 + (σ*Cross[Subscript[Subscript[ω, 1], i], Subscript[Subscript[e, 1], j]]*Subscript[M, 1])/4)
• The only correct answer is to not use replacement rules and instead do it mathematically. Also, ditch the subscripts. Possible duplicate: mathematica.stackexchange.com/q/3463/5
– rm -rf
Jan 29, 2013 at 18:44
• Perhaps this is of interest.
– Jens
Jan 29, 2013 at 20:37