Timeline for Formulas for the structure constants of a field extension basis given by a primitive element
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Mar 26, 2018 at 12:47 | comment | added | M.G. | @OfirGorodetsky: thanks, this is great! | |
| Mar 26, 2018 at 12:26 | comment | added | Ofir Gorodetsky | The polynomials $p_i$, in your notation, are (up to a minus sign) equal to the "complete homogeneous symmetric polynomials" in the roots of $\mu(t)$, usually denoted by $h_i$ in the literature. I suggest looking up Newton's identities, which explain how to compute polynomials such as your $p_i$ using the given $c_i$-s. | |
| Mar 26, 2018 at 12:24 | comment | added | M.G. | Yes, that's a really good idea. I too think there should be some combinatorial structure to them. I was not aware that one can search OEIS for polynomials. What other databases are there for polynomials? | |
| Mar 26, 2018 at 12:20 | comment | added | Dirk | @July As I just wrote in my edit, I would suggest to compute them (and properly check that you have the right ones, e.g. by doing examples with a computer, I just computed them on 2 pages of paper by hand, so no guarantee that there are no errors) and then search databases like OEIS to get an idea. I think that there should be a combinatorial structure in how the coefficients of the $p_i$ get picked, similar to the coefficients in the multiplication of certain polynomials, in the binomial theorem, etc. | |
| Mar 26, 2018 at 12:18 | history | edited | Dirk | CC BY-SA 3.0 |
added 225 characters in body
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| Mar 26, 2018 at 12:17 | comment | added | M.G. | Thanks for typing some of the calculations in. Indeed the question boils down to the polynomials $p_k$. I am hoping someone might already know something about these expressions or find an already known pattern there before I start reinventing the wheel :-) Re your edit: yes, that's a good idea! | |
| Mar 26, 2018 at 11:20 | history | answered | Dirk | CC BY-SA 3.0 |