I want to know if there is a way to find the distinct variants of a function such as $\left(x_1-x_2\right)\left(x_1-x_3\right)\left(x_2-x_3\right)$ more efficiently than just writing out and tabulating every permutation of the variables. My intuition tells me that there might be, but I could be wrong. Could anyone point me in the right direction? Thanks for any help.
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What do you mean by "distinct variants" of the function? Are you looking for other expressions that are always equal to the given expression? If so, given there are infinitely many ways to formulate equivalent expressions, are there any rules/restrictions as to which expressions are allowed? Or am I just completely off base here? – user854214 Dec 01 '20 at 02:02
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I am just looking for ways to permute the variables and find the distinct permutations, i e, $x_1x_2+x_3x_4$ can have the variables $x_1,x_2,x_3,x_4$ permuted in 24 ways, and when you write them all out there are exactly three distinct variants. I just want to know if there is a faster way than writing out every permutation and looking for the distinct variants. – Chairman Meow Dec 01 '20 at 02:13