Annotation of OpenXM/src/math-misc/twistedLogCohomology-ja.tex, Revision 1.2
1.2 ! nisitani 1: \documentclass{jarticle}
1.1 nisitani 2:
1.2 ! nisitani 3: \begin{document}
! 4: \begin{center}
! 5: {\bf twistedLogCohomology(List,List) -- 2変数多項式に付随する twisted logarithmic cohomology 群を計算}
! 6: \end{center}
! 7: \begin{flushleft}
! 8:
! 9: {\bf 概要}
! 10:
! 11: \begin{itemize}
! 12: \item 使用方法: twistedLogCohomology(F,A)
! 13: \item 関数名: twistedLogCohomology
! 14: \item 入力:
! 15: \begin{itemize}
! 16: \item F, 2変数多項式のリスト
! 17: \item A, 有理数のリスト
! 18: \end{itemize}
! 19: \item 出力:
! 20: \begin{itemize}
! 21: \item ハッシュテーブル. 次のものを要素として含む: $\{$ Bfunction, CohomologyGroups, LogBasis, OmegaRes, PreCycles, VResolution $\}$
! 22: \end{itemize}
! 23: \end{itemize}
! 24:
! 25: {\bf 説明}
! 26:
! 27: Twisted logarithmic cohomology 群の基底はハッシュテーブル LogBasis に含まれる.
! 28: $H^1$ と $H^2$ の基底は分子のみ出力される.
! 29: 以下の例では $H^1$ の基底は
! 30: $\{ \frac{y^2dx-xydy}{x(x+y)}, \frac{2x^2dx+2xydx}{x(x+y)} \}$,
! 31: $H^2$ の基底は $\{ \frac{ydxdy}{x(x+y)} \}$ である.
! 32:
! 33: {\footnotesize
! 34: \begin{verbatim}
! 35: i1 : loadPackage "Dmodules";
! 36:
! 37: i2 : load "twistedLogCohomology.m2";
! 38:
! 39: i3 : R = QQ[x,y];
! 40:
! 41: i4 : twistedLogCohomology({x,x+y},{-1,0})
! 42: Warning: not a generic weight vector. Could be difficult...
! 43:
! 44: o5 = HashTable{BFunction => (s - 1) }
! 45: 1
! 46: CohomologyGroups => HashTable{0 => QQ }
! 47: 2
! 48: 1 => QQ
! 49: 1
! 50: 2 => QQ
! 51: LogBasis => HashTable{0 => | x | }
! 52: 1 => | y2dx-xydy 2x2dx+2xydx |
! 53: 2 => | ydxdy |
! 54: 1 2 1
! 55: OmegaRes => (QQ[x, y, dx, dy]) <-- (QQ[x, y, dx, dy]) <-- (QQ[x, y, dx, dy]) <-- 0
! 56:
! 57: 0 1 2 3
! 58: PreCycles => HashTable{0 => | -x2-xy |}
! 59: | -x |
! 60: 1 => | 0 -2x |
! 61: | -y 0 |
! 62: | 0 0 |
! 63: 2 => | y |
! 64: 1 3 2
! 65: VResolution => (QQ[x, y, dx, dy]) <-- (QQ[x, y, dx, dy]) <-- (QQ[x, y, dx, dy]) <-- 0
! 66:
! 67: 0 1 2 3
1.1 nisitani 68:
1.2 ! nisitani 69: o5 : HashTable
1.1 nisitani 70:
1.2 ! nisitani 71: \end{verbatim}
! 72: }
1.1 nisitani 73:
1.2 ! nisitani 74: \end{flushleft}
! 75: \end{document}
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