Timeline for Discriminant of a composition of binary forms
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| May 23, 2017 at 14:00 | comment | added | Abdelmalek Abdesselam | @Anton: You are right. I just fixed the formula. I think you are also right that there are quite a few typos in the article regarding $d_1\ldots d_n$ instead of $d_1\ldots d_{n-1}$. Unfortunately, these errors are also in the published version link.springer.com/article/10.1007/s11786-014-0188-7 | |
| May 23, 2017 at 13:58 | history | edited | Abdelmalek Abdesselam | CC BY-SA 3.0 |
corrected formula
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| May 23, 2017 at 13:31 | comment | added | Anton | I think there is a mistake in the degree of K w.r.t. A or B. It should be $2d(r-1)$, not $2dr(r-1)$. This matches the example that Stanley Yao Xiao wrote (case d=r=2). Also, I think there is a typo in the paper that is a little bit confusing: sometimes they write a product of $d_i$ from i to n, which is wrong, since $d_i$ are defined only up to $n-1$. Just wanted to confirm with you that my intuition is correct. | |
| May 21, 2017 at 21:36 | comment | added | Anton | Thanks Abdelmalek, this is clearly what I was looking for. What really puzzled me is that K is a polynomial in F,A,B, but then I saw in your answer that it is actually a polynomial in coefficients of F,A,B. | |
| May 21, 2017 at 21:33 | vote | accept | Anton | ||
| May 21, 2017 at 18:43 | comment | added | Abdelmalek Abdesselam | I should also mention that they show that $K$ is irreducible in $char\neq 2$. | |
| May 21, 2017 at 18:13 | comment | added | Abdelmalek Abdesselam | They do not give more info than that. $K$ is some (multi) homegeneous polynomial in $F$ and $(A,B)$. There are nice (base change) formulas for resultants of compositions but the authors say that the discriminant case is "much more involved". | |
| May 21, 2017 at 17:02 | comment | added | Anton | thanks a lot for your respond! I don't quite understand what K is. You say tat it is homogeneous. Homogeneous what? Is this some kind of invariant? | |
| May 21, 2017 at 16:51 | history | answered | Abdelmalek Abdesselam | CC BY-SA 3.0 |