On Fri, Apr 24, 2020 at 12:53 AM Nils Bruin <nbr...@sfu.ca> wrote: > > 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).
A natural function to have in the library is to compute the image of a polynomial under a linear transformation. And based on it, a function to compute the orbit of a polynomial under a group G generated by a finite number of the latter. E.g. GAP has the one for permutations (if you like, permutation matrices) only 41.2-13 OnIndeterminates ‣ OnIndeterminates( poly, perm ) ────────────────────────────────────────────────────────────────────────────────────────────────────── function A permutation perm acts on the multivariate polynomial poly by permuting the indeterminates as it permutes points. And it can be used as an "action" in their general machinery for computing orbits. > > 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. I think in a domain like computational group theory and computational invariant theory (and practice :-)) is is not rare at all. I did such computations many times, mostly for various extremal combinatorics problems. Dima > > (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) > > -- > You received this message because you are subscribed to the Google Groups > "sage-devel" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-devel+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-devel/f8462d8f-7dc9-4797-84e4-4f5f131ad367%40googlegroups.com. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAAWYfq3Z%3DrJhnsOWyWvHp5bxNfsU14hyfh_x3at4%3DCuK2N-YpQ%40mail.gmail.com.
