IUTを読むための用語集資料集スレ

41 名前：現代数学の系譜 雑談 mailto:sage [2020/06/24(水) 23:20:01.80 ID:b5EBywaq.net] >>36 Inter-universal geometry と ABC予想 (応援スレ) 48 https://rio2016.5ch.net/test/read.cgi/math/1592119272/ 62 名前：現代数学の系譜 雑談 ◆yH25M02vWFhP [] 投稿日：2020/06/18(木) 17:18:11.72 ID:LPUPFt8f [3/4] >>61 つづき Contents 1 Notation 2 The algorithm 3 Implementations Notation Assume that all the coefficients of the equation of the curve lie in a complete discrete valuation ring R with perfect residue field and maximal ideal generated by a prime π. The elliptic curve is given by the equation y^2+a1xy+a3y=x^3+a2x^2+a4x+a6. Define: a{i,m}=a_{i}/π^m b2=a1^2+4a2 b4=a1a3+2a4 b6=a3^2+4a6 b8=a1^2a6-a1a3a4+4a2a6+a2a3^2-a4^2 c4=b2^2-24b4 c6=-b2^3+36b2b4-216b6 Δ =-b2^2b8-8b4^3-27b6^2+9b2b4b6 j=c4^3/Δ . Implementations The algorithm is implemented for algebraic number fields in the PARI/GP computer algebra system, available through the function elllocalred. (引用終り) 以上

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