"유한체 위의 정수론과 기하학"의 두 판 사이의 차이

수학노트
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잔글 (찾아 바꾸기 – “</h5>” 문자열을 “==” 문자열로)
 
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1번째 줄: 1번째 줄:
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<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%;">이 항목의 수학노트 원문주소==
 
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==개요==
 
==개요==
  
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==코드==
 
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# (*choose the range l for the number of primes*)<br> l := 50<br> (*choose a polynomial to work with*)<br> Pol := x^2 - 5<br> disc := Discriminant[Pol, x]<br> (*choose a modulus*)<br> M := 5<br> Pr[l_] := Table[Prime[n], {n, 1, l}]<br> S := Pr[l]<br> (*output*)<br> Print["discriminant of polynomial", " ", Pol // TraditionalForm]<br> disc<br> (*decomposition of the given polynomial modulo p*)<br> TableForm[Table[{Mod[p, M], Factor[Pol, Modulus -> p]}, {p, S}],<br>  TableHeadings -> {S, {"residue class", "decomposition"}},<br>  TableAlignments -> Center]
 
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==메모==
 
==메모==
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* http://www.science.unitn.it/~degraaf/compalg/polfact.pdf
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* Michel Waldschmidt [http://www.math.jussieu.fr/~miw/articles/pdf/FiniteFieldsKathmanduCIMPA2010.pdf Finite fields]
  
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==관련된 항목들==
 
==관련된 항목들==
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* [[유한체 위의 타원곡선에 대한 가우스 정리]]
 
* [[이차잉여의 상호법칙]]
 
* [[이차잉여의 상호법칙]]
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* [[정수론에서의 상호법칙 (reciprocity laws)|더 일반적인 상호법칙들(reciprocity laws)]]
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* [[정수론에서의 상호법칙 (reciprocity laws)]]
 
* [[체론(field theory)]]
 
* [[체론(field theory)]]
 
* [[타니야마-시무라 추측(정리)]]
 
* [[타니야마-시무라 추측(정리)]]
  
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==매스매티카 파일 및 계산 리소스==
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* https://docs.google.com/file/d/0B8XXo8Tve1cxaWJXREZtdmhOdkE/edit
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==사전 형태의 자료==
  
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==사전 형태의 자료==
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* http://ko.wikipedia.org/wiki/
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* http://en.wikipedia.org/wiki/Factorization_of_polynomials_over_finite_fields
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* http://ko.wikipedia.org/wiki/
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==강의==
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* http://en.wikipedia.org/wiki/
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* Richard Taylor  [http://video.ias.edu/taylor-lecture-2-12 Primes and Equations], Feb 2012
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* [http://eom.springer.de/default.htm The Online Encyclopaedia of Mathematics]
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==리뷰, 에세이, 강의노트==
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* Van der Geer, Gerard. “Counting Curves over Finite Fields.” arXiv:1409.6090 [math], September 22, 2014. http://arxiv.org/abs/1409.6090.
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* Mazur, Barry. 1993. “On the Passage from Local to Global in Number Theory.” arXiv:math/9307231 (June 30). http://arxiv.org/abs/math/9307231.
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* Koblitz, Neal. 1982. Why Study Equations over Finite Fields? Mathematics Magazine 55, no. 3 (May 1): 144-149. doi:[http://dx.doi.org/10.2307/2690080 10.2307/2690080].
  
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==관련논문==
 
==관련논문==
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* Dalalyan, Samuel H. ‘An Algorithm for Determining the Irreducible Polynomials over Finite Fields’. arXiv:1505.00776 [math], 2 May 2015. http://arxiv.org/abs/1505.00776.
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* Narayanan, Anand Kumar. ‘Polynomial Factorization over Finite Fields By Computing Euler-Poincare Characteristics of Drinfeld Modules’. arXiv:1504.07697 [cs, Math], 28 April 2015. http://arxiv.org/abs/1504.07697.
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* Achter, Jeffrey D., Daniel Erman, Kiran S. Kedlaya, Melanie Matchett Wood, and David Zureick-Brown. “A Heuristic for the Distribution of Point Counts for Random Curves over a Finite Field.” arXiv:1410.7373 [math], October 27, 2014. http://arxiv.org/abs/1410.7373.
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[[분류:정수론]]
  
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* Koblitz, Neal. 1982. Why Study Equations over Finite Fields? Mathematics Magazine 55, no. 3 (May 1): 144-149. doi:[http://dx.doi.org/10.2307/2690080 10.2307/2690080]. 
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==메타데이터==
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* http://www.jstor.org/action/doBasicSearch?Query=
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===위키데이터===
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* http://www.ams.org/mathscinet
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* ID : [https://www.wikidata.org/wiki/Q5428743 Q5428743]
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* http://dx.doi.org/
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===Spacy 패턴 목록===
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* [{'LOWER': 'factorization'}, {'LOWER': 'of'}, {'LOWER': 'polynomials'}, {'LOWER': 'over'}, {'LOWER': 'finite'}, {'LEMMA': 'field'}]

2021년 2월 17일 (수) 04:56 기준 최신판

개요

메모



관련된 항목들


매스매티카 파일 및 계산 리소스


사전 형태의 자료


강의


리뷰, 에세이, 강의노트

  • Van der Geer, Gerard. “Counting Curves over Finite Fields.” arXiv:1409.6090 [math], September 22, 2014. http://arxiv.org/abs/1409.6090.
  • Mazur, Barry. 1993. “On the Passage from Local to Global in Number Theory.” arXiv:math/9307231 (June 30). http://arxiv.org/abs/math/9307231.
  • Koblitz, Neal. 1982. Why Study Equations over Finite Fields? Mathematics Magazine 55, no. 3 (May 1): 144-149. doi:10.2307/2690080.


관련논문

  • Dalalyan, Samuel H. ‘An Algorithm for Determining the Irreducible Polynomials over Finite Fields’. arXiv:1505.00776 [math], 2 May 2015. http://arxiv.org/abs/1505.00776.
  • Narayanan, Anand Kumar. ‘Polynomial Factorization over Finite Fields By Computing Euler-Poincare Characteristics of Drinfeld Modules’. arXiv:1504.07697 [cs, Math], 28 April 2015. http://arxiv.org/abs/1504.07697.
  • Achter, Jeffrey D., Daniel Erman, Kiran S. Kedlaya, Melanie Matchett Wood, and David Zureick-Brown. “A Heuristic for the Distribution of Point Counts for Random Curves over a Finite Field.” arXiv:1410.7373 [math], October 27, 2014. http://arxiv.org/abs/1410.7373.

메타데이터

위키데이터

Spacy 패턴 목록

  • [{'LOWER': 'factorization'}, {'LOWER': 'of'}, {'LOWER': 'polynomials'}, {'LOWER': 'over'}, {'LOWER': 'finite'}, {'LEMMA': 'field'}]
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