"Differential Galois theory"의 두 판 사이의 차이
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| 15번째 줄: | 15번째 줄: | ||
| − | <h5 style="line-height: 3.428em | + | <h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">Liouville extension</h5> |
* we can adjoin integrals and exponentials of integrals + algbraic extension | * we can adjoin integrals and exponentials of integrals + algbraic extension | ||
| 37번째 줄: | 37번째 줄: | ||
| − | + | <h5>solution by quadrature</h5> | |
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| + | * [http://ocw.mit.edu/NR/rdonlyres/Mathematics/18-034Spring-2007/Readings/notesqd.pdf QD. SOLUTION BY QUADRATURE] | ||
| 70번째 줄: | 72번째 줄: | ||
* http://gigapedia.info/1/ritt | * http://gigapedia.info/1/ritt | ||
| − | * | + | * [http://gigapedia.info/1/Galois%27+dream http://gigapedia.info/1/Galois'+dream] |
| − | + | * | |
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* http://gigapedia.info/1/ | * http://gigapedia.info/1/ | ||
* http://gigapedia.info/1/ | * http://gigapedia.info/1/ | ||
2009년 8월 31일 (월) 11:31 판
- adele and idele
- differential galois theory
- Liouville
elemetary extension
- using exponential and logarithm
- elementary element
Liouville extension
- we can adjoin integrals and exponentials of integrals + algbraic extension
- an element is said to be representable by a generalized quadrature
Picard-Vessiot extension
- examples
- algebraic extension
- adjoining an integral
- adjoining the exponential of an integral
theorem
If a Picard-Vessiot extension is a Liouville extension, then the Galois group of this extension is solvable.
solution by quadrature
하위페이지
표준적인 도서 및 추천도서
- Abel_s_theorem_by_Arnold.djvu
- arnold book on abel theorem problem 348
- http://gigapedia.info/1/differential+galois+theory
- http://gigapedia.info/1/Kolchin
- http://gigapedia.info/1/ritt
- http://gigapedia.info/1/Galois'+dream
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
- Algebraic Functions (Dover Phoenix Editions)
- Gilbert Ames Bliss
- http://gigapedia.org/v5/item:view_links?id=100873
- Gilbert Ames Bliss
참고할만한 자료
- Determining the Galois Group of a Polynomial
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/Differential_Galois_theory
- http://en.wikipedia.org/wiki/Homotopy_lifting_property
- http://en.wikipedia.org/wiki/covering_space
- http://en.wikipedia.org/wiki/Field_extension
- http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
- http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
- 다음백과사전 http://enc.daum.net/dic100/search.do?q=