作者Frank000 (Frank000)
看板Math
標題[代數] irreducible
時間Sun Apr 24 08:41:54 2011
證明t^8-t^4+1 irreducilbe over Q
如果沒辦法的話，有沒有別的方法證明exp(i*pi/12)的minimal polynomial是t^8-t^4+1?
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◆ From: 108.65.2.220
1F：→ Sfly :cyclotomic polynomials are irr 04/24 09:24
2F：推 calvin4 :let x = t^4. then the polynomial becomes x^2 - x 04/24 12:13
3F：→ calvin4 :+ 1, which is irreducible over Q. the rest of the 04/24 12:14
4F：→ calvin4 :proof is left to you. 04/24 12:15
5F：推 wickeday :好奇樓上的方法要怎麼做，t^4-1是reducible但x-1是 04/24 14:55
6F：→ wickeday :irreducible說。 04/24 14:56
7F：→ calvin4 :我好像搞錯題型了。你說得對…… 04/25 02:27