Timeline for Chinese remainder theorem for composition
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 12, 2023 at 6:27 | comment | added | Gerry Myerson | "Narrow down $f$ to one of $p$ elements in $F_{p^6}$." So, you are viewing a polynomial $f$ as an element of the field of $p^6$ elements? | |
| Aug 11, 2023 at 21:25 | answer | added | Will Sawin | timeline score: 3 | |
| Aug 11, 2023 at 21:05 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| Aug 11, 2023 at 18:11 | comment | added | mtheorylord | To be concrete, its like I know how $f$ behaves with $x^2+1$ and $x^3+1$ and I just want to figure out how it behaves with $(x^2+1)^3+1$. Playing around with the system of equations gives some information. In this case (with degrees 2 and 3), I should be able to narrow down $f$ to one of $p$ elements in $F_{p^6}$ | |
| Aug 11, 2023 at 18:02 | comment | added | Gro-Tsen | Think of it this way: knowing $f$ mod $\phi$ essentially means knowing the values of $f$ on the roots of $\phi$ (in an algebraic closure). It seems unlikely you can say anything interesting about the values of $f$ on the roots of $\phi_1\circ\phi_2$ from its values on the roots of $\phi_1$ and of $\phi_2$. Now maybe if you were to ask about $f\circ\phi_2$, of if this were about some different kind of “modulo” or by changing the question in other ways there might be something to say — I don't know. | |
| Aug 11, 2023 at 17:31 | history | asked | mtheorylord | CC BY-SA 4.0 |