Timeline for On the linear factors of a polynomial obtained from the determinant of a matrix whose entries are related to Binomial expansion
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Sep 25, 2018 at 23:01 | vote | accept | user521337 | ||
| Sep 25, 2018 at 10:59 | history | edited | Somos | CC BY-SA 4.0 |
Light rewording.
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| Sep 24, 2018 at 18:22 | comment | added | Will Jagy | Using $1 + w + w^2 = 0,$ the term I called f3 is $$ (x+y-1)(xw+yw^2-1)(x w^2 + y w - 1) $$ the other terms f5,f7,f9 are products of pairs of complex conjugate terms (assuming x,y real for cosmetic purposes) | |
| Sep 24, 2018 at 18:15 | comment | added | Will Jagy | Took a few tries, I did $n=3$ by combining into real products, once I fixed some errors it was nice , had pari check the product against the determinant // f3 = x^3 + y^3 + 3 * x * y - 1 // f5 = x^2 + 2 * x * y + y^2 + x + y + 1 // f7 = x^2 - x * y + y^2 + x - 2 * y + 1 // f9 = x^2 - x * y + y^2 -2 * x + y + 1 // p = x^9 + (3*y^3 - 3)*x^6 + (3*y^6 + 21*y^3 + 3)*x^3 + (y^9 - 3*y^6 + 3*y^3 - 1) // | |
| Sep 24, 2018 at 11:04 | history | edited | Somos | CC BY-SA 4.0 |
Ciculant --> Toeplitz.
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| Sep 24, 2018 at 6:15 | comment | added | Zach Teitler | Right. The matrix stays the same when $x,y$ are replaced by $zx,wy$. | |
| Sep 24, 2018 at 3:25 | history | edited | Somos | CC BY-SA 4.0 |
Removed last sentence since comment questioning degree was deleted.
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| Sep 24, 2018 at 2:55 | history | undeleted | Somos | ||
| Sep 24, 2018 at 2:55 | history | edited | Somos | CC BY-SA 4.0 |
Added more words.
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| Sep 24, 2018 at 1:58 | history | deleted | Somos | via Vote | |
| Sep 24, 2018 at 1:56 | history | answered | Somos | CC BY-SA 4.0 |