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I want to define a function, that works like this:

f[3v[1,2,3]] = 1/3 v[1,3,2] + 3^2 v[1,2,3] f[2v[2,2,1]] = 1/2 v[2,1,2] + 2^2 v[2,2,1]

Basically, it should affect coefficients before vectors and also permute indices. I've tried to look through references but was confused. Can you help me with that?

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Mathematica is great for this because you can use any pattern you like when defining a function. This can be used to pick out parts of interest from an expression and use them on the right-hand side to create a new one.

f[c_ v[arg1_, arg2_, arg3_]] := (1/c) v[arg1, arg3, arg2] + c^2 v[arg1, arg2, arg3] f[3 v[1, 2, 3]]

9 v[1, 2, 3] + 1/3 v[1, 3, 2]

f[2 v[2, 2, 1]]

1/2 v[2, 1, 2] + 4 v[2, 2, 1]

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  • $\begingroup$ Can this work when i don't know in advance how many indices are there? Like here we have three indices, but suppose I also want the same function work when there are 4 indices? Like f[2 v [1,2,3,4]] = 1/2 v[1,3,2,4]+4 v[1,2,3,4] ? $\endgroup$ Commented Jan 23, 2019 at 18:29
  • $\begingroup$ @Nicky rest in the pattern v[arg1_, arg2_, arg3_, rest___] matches zero or more parameters of v, perhaps that is what you need. Without knowing more about what you are trying to do it's hard to tell. $\endgroup$ Commented Jan 23, 2019 at 20:02
  • $\begingroup$ Yes, you're right, I should've wrote exactly what I need. Basically, first I fix n - number of indices. I don't know in advance what it will be - 3, 7, or 14. I have linear combinations of vectors with n indices, like v[i_1, i_2, ..., v_n]. Now, I want to perform operations with these vectors and sometimes it involves swapping indices. Like f[k, v[i_1, i_2, ..., i_k, i_{k+1}, v_n]] = c[k] v[i_1, i_2, ..., i_{k+1}, i_k, ...., i_n]. $\endgroup$ Commented Jan 23, 2019 at 22:23

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