純粋・応用数学・数学隣接分野（含むガロア理論）12

[過去ﾛｸﾞ] 純粋・応用数学・数学隣接分野（含むガロア理論）12 (1002ﾚｽ)
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67: 現代数学の彼岸 ◆mrg.0Mu9EdE8  [] 2022/12/26(月) 08:01:02.61 ID:QjvnggET

くだらん計算

B0-B1
= ξ + ξ^4 + ξ^5 + ξ^9 + ξ^3 - ξ^2 - ξ^8 - ξ^10 - ξ^7 - ξ^6

(B0-B1)^2
=(ξ      + ξ^4 + ξ^ 5 + ξ^  9 + ξ^3 - ξ^2 - ξ^8 - ξ^10 - ξ^7 - ξ^  6)^2
= ξ^2  + ξ^5 + ξ^ 6 + ξ^10 + ξ^4 - ξ^3 - ξ^9 - 1       - ξ^8   - ξ^ 7
+ξ^5  + ξ^8 + ξ^ 9 + ξ^  2 + ξ^7 - ξ^6 - ξ     - ξ^  3 - 1       - ξ^10
+ξ^6  + ξ^9 + ξ^10 + ξ^ 3 + ξ^8 - ξ^7 - ξ^2 - ξ^  4 - ξ       - 1
+ξ^10 + ξ^2 + ξ^ 3 + ξ^ 7 + ξ     - 1     - ξ^6 - ξ^  8 - ξ^  5 - ξ^ 4
+ξ^4   + ξ^7 + ξ^ 8 + ξ      + ξ^6 - ξ^5 - 1     - ξ^  2 - ξ^10 - ξ^ 9
- ξ^3   - ξ^6   - ξ^ 7  - 1      -  ξ^5 + ξ^  4 + ξ^10 + ξ     + ξ^9 + ξ^8
- ξ^9   - ξ       - ξ^ 2  - ξ^6   - １  　+ ξ^10 + ξ^ 5 + ξ^7 + ξ^4 + ξ^3
- 1       - ξ^3   - ξ^ 4  - ξ^8   - ξ^2  + ξ       + ξ^ 7 + ξ^9 + ξ^6 + ξ^5
- ξ^8   - 1       - ξ       - ξ^5   - ξ^10 + ξ^ 9 + ξ^ 4 + ξ^6 + ξ^3 + ξ^2
- ξ^7   - ξ ^10 - 1      - ξ^4   - ξ^9   + ξ^ 8 + ξ^ 3 + ξ^5 + ξ^2 + ξ
=10(-1)+ξ+ξ^2+ξ^3+ξ^4+ξ^5+ξ^6+ξ^7+ξ^8+ξ^9+ξ^10
=-11

http://rio2016.5ch.net/test/read.cgi/math/1671460269/67

134: わかるすうがく 近谷蒙 ◆nSGM2Czuyoqf  [sage] 2022/12/30(金) 17:30:50.61 ID:bjNnsn/s

>>133
?^2
=　　(ζ7　-ζ7^6)(ζ7-ζ7^6)+ω^2(ζ7　-ζ7^6)(ζ7^2-ζ7^5)+ω　(ζ7　-ζ7^6)(ζ7^4-ζ7^3)
+ω^2(ζ7^2-ζ7^5)(ζ7-ζ7^6)+ω　(ζ7^2-ζ7^5)(ζ7^2-ζ7^5)+　　(ζ7^2-ζ7^5)(ζ7^4-ζ7^3)
+ω　(ζ7^4-ζ7^3)(ζ7-ζ7^6)+　　(ζ7^4-ζ7^3)(ζ7^2-ζ7^5)+ω^2(ζ7^4-ζ7^3)(ζ7^4-ζ7^3)
=　　((ζ7^2+ζ7^5-2)　　　　　 +(ζ7^6-ζ7^2-ζ7^5+ζ7　) +(ζ7^6-ζ7^5-ζ7^2+ζ7　) )
+ω^2((ζ7^3-ζ7　-ζ7^6+ζ7^4) +(ζ7^3-ζ7^6-ζ7　+ζ7^4) +(ζ7　+ζ7^6-2)　　　　　 )
+ω  ((ζ7^5-ζ7^3-ζ7^4+ζ7^2) +(ζ7^4+ζ7^3-2)           +(ζ7^5-ζ7^4-ζ7^3+ζ7^2) )
=　　(-2+ζ7  +ζ7  +ζ7^6+ζ7^6+ζ7^2+ζ7^5-ζ7^2-ζ7^2-ζ7^5-ζ7^5)
+ω^2(-2+ζ7^4+ζ7^4+ζ7^3+ζ7^3+ζ7　+ζ7^6-ζ7  -ζ7  -ζ7^6-ζ7^6)
+ω  (-2+ζ7^2+ζ7^2+ζ7^5+ζ7^5+ζ7^4+ζ7^3-ζ7^4-ζ7^4-ζ7^3-ζ7^3)
=(2-ω^2)?
=(3+ω)?

??
=　　(ζ7　+ζ7^6)(ζ7-ζ7^6)+ω^2(ζ7　+ζ7^6)(ζ7^2-ζ7^5)+ω　(ζ7　+ζ7^6)(ζ7^4-ζ7^3)
+ω^2(ζ7^3+ζ7^4)(ζ7-ζ7^6)+ω　(ζ7^3+ζ7^4)(ζ7^2-ζ7^5)+　　(ζ7^3+ζ7^4)(ζ7^4-ζ7^3)
+ω　(ζ7^2+ζ7^5)(ζ7-ζ7^6)+　　(ζ7^2+ζ7^5)(ζ7^2-ζ7^5)+ω^2(ζ7^2+ζ7^5)(ζ7^4-ζ7^3)
=　　((ζ7^2-ζ7^5)+(ζ7-ζ7^6)+(ζ7^4-ζ7^3)
+ω　((ζ7^5+ζ7^3-ζ7^4-ζ7^2)+(ζ7^5+ζ7^6-ζ7　-ζ7^2)+(ζ7^3+ζ7^6-ζ7　-ζ7^4))
+ω^2((ζ7^3+ζ7　-ζ7^6-ζ7^4)+(ζ7^4+ζ7^5-ζ7^2-ζ7^3)+(ζ7^6+ζ7^2-ζ7^5-ζ7　))
=(-2ω+1)?

http://rio2016.5ch.net/test/read.cgi/math/1671460269/134

872: 現代数学の系譜 雑談 ◆yH25M02vWFhP  [] 2023/01/17(火) 21:05:34.61 ID:6qoiGrEF

>>858
>Abhyankarさん

ありがとう
勉強不足で、Abhyankarさん、初耳です
検索すると、下記か
うーん、なるほど

https://en.wikipedia.org/wiki/Abhyankar
Abhyankar
Abhyankar is a surname native to the Indian state of Maharashtra. Abhyankar surname is found among Chitpavan Brahmin community.[1][2]

https://upload.wikimedia.org/wikipedia/commons/e/ee/Abhyankar_Grothendieck.jpg
Shreeram Abhyankar (right) with Alexander Grothendieck (left), Michael Artin in the background, at Montreal, Quebec, Canada in 1970.
https://en.wikipedia.org/wiki/Shreeram_Shankar_Abhyankar
Shreeram Shankar Abhyankar
Shreeram Shankar Abhyankar (22 July 1930 ? 2 November 2012)[1][2] was an Indian American mathematician known for his contributions to algebraic geometry. He, at the time of his death, held the Marshall Distinguished Professor of Mathematics Chair at Purdue University, and was also a professor of computer science and industrial engineering. He is known for Abhyankar's conjecture of finite group theory.
His latest research was in the area of computational and algorithmic algebraic geometry.
Contents
1 Career
2 Death
3 Selected publications
4 Honours

Career
Abhyankar was born in a Chitpavan Brahmin family in Ujjain, Madhya Pradesh, India. He earned his B.Sc. from Royal Institute of Science of University of Mumbai in 1951, his M.A. at Harvard University in 1952, and his Ph.D. at Harvard in 1955. His thesis, written under the direction of Oscar Zariski, was titled Local uniformization on algebraic surfaces over modular ground fields.[3][4] Before going to Purdue, he was an associate professor of mathematics at Cornell University and Johns Hopkins University.

http://rio2016.5ch.net/test/read.cgi/math/1671460269/872

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