#What function is this?

11 messages · Page 1 of 1 (latest)

naive quiverBOT
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violet sphinx
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that would be standard notation, yes

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sigma is one of 3! permutations on 3 elements

thin matrix
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Sigma(1) can be 1,2 or 3 then sigma(2) is one of the two remaining elements that isn’t sigma(1) and sigma(3) is the last element remaining that isn’t sigma(1) or sigma(2) that’s what a permutation is, a bijection from {1,2,3}
To {1,2,3} in this case

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And I’m guessing $(x_i)_{1 \le i \le 3}$ are the roots of the cubic

pulsar vergeBOT
thin matrix
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The only thing that you need to know is that all $\sigma(i)$ are all distinct (by injectivity)

pulsar vergeBOT
thin matrix
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And no, I don’t think it does matter because whichever root you choose in what order because it would be the same as permuting twice the columns each time which will not change the determinant

severe turretBOT
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@coarse mesa has given 1 rep to @thin matrix @violet sphinx