On Thursday, April 23, 2020 at 3:04:46 AM UTC-7, vdelecroix wrote:
>
>
> I think that it would be good to implement this directly of the level of 
> multivariate polynomials. I opened 
>

What would the uptake of such a method be? If I needed to test if a 
polynomial is symmetric, I would probably end up rolling my own because:
 - I wouldn't know or expect such a method to exist on symmetric polynomials
 - I wouldn't know what the particular conditions and assumptions on the 
input would be (and whether the author silently had different definitions 
in mind than I had).
Because it's so easy to program myself, I would probably decide that's 
faster than figuring out if the library version is appropriate (if I knew 
if it existed in the first place).

In terms of use: I think it's very rare in a computational setting to want 
to know if a polynomial is symmetric and not want it expressed in 
(elementary) symmetric polynomials. That's a routine I'd look for -- 
although surprisingly, this is something that routinely gets done poorly in 
computer algebra systems (including magma!), so I'd probably end up 
implementing elimination anyway.

(in this case, it's clear the code is needed in at least one place of the 
library, so it's not really a loss to put it somewhere, but for code 
maintainability, I'd keep it closer to where it's used and then perhaps 
refactor if it shows the demand is there to have it in a more accessible 
spot)

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