Timeline for Taking polynomial inverses over a field?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Aug 10, 2023 at 4:20 | comment | added | Gerry Myerson | Question simulposted to m.se, math.stackexchange.com/questions/4750141/… in violation of rules on both sites. | |
| Aug 9, 2023 at 14:17 | comment | added | David E Speyer | It looks like there is a fair bit of literature in this area; the relevant search terms are "permutation polynomial" and "compositional inverse". | |
| Aug 9, 2023 at 14:06 | comment | added | David E Speyer | EG If your polynomial is $x^3$ for $p^{\deg q} \equiv 2 \bmod 3$, then the inverse polynomial is $x^{(2 p^{\deg q} -1)/3}$. | |
| Aug 9, 2023 at 14:04 | comment | added | David E Speyer | What is the source of your knowledge that $f$ is bijective? If this is just given to you as a black box promise, I don't see how you can do better than Lagrange interpolation. But there are only a few known classes of easily recognized permutation polynomials (see en.wikipedia.org/wiki/Permutation_polynomial ), so if your polynomial belongs to one of them, you might be able to do better. | |
| Aug 9, 2023 at 13:47 | history | edited | mtheorylord | CC BY-SA 4.0 |
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| Aug 9, 2023 at 13:14 | comment | added | Jared White | Do you mean that you are looking for an algorithm to find the inverse of $f$, rather than of $g$? Also, to be clear, to you mean you want to find an inverse with respect to composition, rather than with respect to the field operation (which is multiplication)? | |
| Aug 9, 2023 at 12:53 | history | asked | mtheorylord | CC BY-SA 4.0 |