유한체 위의 정수론과 기하학

 

 

 

 

 

코드

1. (*choose the range l for the number of primes*)
   l := 50
   (*choose a polynomial to work with*)
   Pol := x^2 - 5
   disc := Discriminant[Pol, x]
   (*choose a modulus*)
   M := 5
   Pr[l_] := Table[Prime[n], {n, 1, l}]
   S := Pr[l]
   (*output*)
   Print["discriminant of polynomial", " ", Pol // TraditionalForm]
   disc
   (*decomposition of the given polynomial modulo p*)
   TableForm[Table[{Mod[p, M], Factor[Pol, Modulus -> p]}, {p, S}],
    TableHeadings -> {S, {"residue class", "decomposition"}},
    TableAlignments -> Center]

 

 

 

 

관련된 항목들

• 이차잉여의 상호법칙
• 더 일반적인 상호법칙들(reciprocity laws)
• 체론(field theory)
• 타니야마-시무라 추측(정리)

 

 

사전 형태의 자료

• http://ko.wikipedia.org/wiki/
• http://en.wikipedia.org/wiki/
• The Online Encyclopaedia of Mathematics

 

 

관련논문

• 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.