version 1.1, 2012/02/19 01:11:26 |
version 1.2, 2012/03/01 02:27:34 |
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(J\documentclass{jarticle}(B |
\documentclass{jarticle} |
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(J\begin{document}(B |
\begin{document} |
(J\begin{center}(B |
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(J{\bf twistedLogCohomology(List,List) -- 2$@JQ?tB?9`<0$KIU?o$9$k(J twisted logarithmic cohomology $@72$r7W;;(J}(B |
{\bf twistedLogCohomology(List,List) -- 2変数多項式に付随する twisted logarithmic cohomology 群を計算} |
(J\end{center}(B |
\end{center} |
(J\begin{flushleft}(B |
\begin{flushleft} |
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(J{\bf $@35MW(J}(B |
{\bf 概要} |
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(J\begin{itemize}(B |
\begin{itemize} |
(J\item $@;HMQJ}K!(J: twistedLogCohomology(F,A)(B |
\item 使用方法: twistedLogCohomology(F,A) |
(J\item $@4X?tL>(J: twistedLogCohomology(B |
\item 関数名: twistedLogCohomology |
(J\item $@F~NO(J:(B |
\item 入力: |
(J \begin{itemize}(B |
\begin{itemize} |
(J\item F, 2$@JQ?tB?9`<0$N%j%9%H(B |
\item F, 2変数多項式のリスト |
(J\item A, $@M-M}?t$N%j%9%H(B |
\item A, 有理数のリスト |
(J \end{itemize}(B |
\end{itemize} |
(J\item $@=PNO(J:(B |
\item 出力: |
(J \begin{itemize}(B |
\begin{itemize} |
(J\item $@%O%C%7%e%F!<%V%k(J. $@<!$N$b$N$rMWAG$H$7$F4^$`(J: $\{$ Bfunction, CohomologyGroups, LogBasis, OmegaRes, PreCycles, VResolution $\}$(B |
\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 $\}$ |
(J \end{itemize}(B |
\end{itemize} |
(J\end{itemize}(B |
\end{itemize} |
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(J{\bf $@@bL@(J}(B |
{\bf 説明} |
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(JTwisted logarithmic cohomology $@72$N4pDl$O%O%C%7%e%F!<%V%k(J LogBasis $@$K4^$^$l$k(J. (B |
Twisted logarithmic cohomology 群の基底はハッシュテーブル LogBasis に含まれる. |
(J$H^1$ $@$H(J $H^2$ $@$N4pDl$OJ,;R$N$_=PNO$5$l$k(J. (B |
$H^1$ と $H^2$ の基底は分子のみ出力される. |
$@0J2<$NNc$G$O(J $H^1$ $@$N4pDl$O(J (B |
以下の例では $H^1$ の基底は |
(J$\{ \frac{y^2dx-xydy}{x(x+y)}, \frac{2x^2dx+2xydx}{x(x+y)} \}$, (B |
$\{ \frac{y^2dx-xydy}{x(x+y)}, \frac{2x^2dx+2xydx}{x(x+y)} \}$, |
(J$H^2$ $@$N4pDl$O(J $\{ \frac{ydxdy}{x(x+y)} \}$ $@$G$"$k(J. (B |
$H^2$ の基底は $\{ \frac{ydxdy}{x(x+y)} \}$ である. |
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(J{\footnotesize (B |
{\footnotesize |
(J\begin{verbatim}(B |
\begin{verbatim} |
(Ji1 : loadPackage "Dmodules";(B |
i1 : loadPackage "Dmodules"; |
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(Ji2 : load "twistedLogCohomology.m2";(B |
i2 : load "twistedLogCohomology.m2"; |
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(Ji3 : R = QQ[x,y];(B |
i3 : R = QQ[x,y]; |
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(Ji4 : twistedLogCohomology({x,x+y},{-1,0})(B |
i4 : twistedLogCohomology({x,x+y},{-1,0}) |
(JWarning: not a generic weight vector. Could be difficult...(B |
Warning: not a generic weight vector. Could be difficult... |
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(Jo5 = HashTable{BFunction => (s - 1) }(B |
o5 = HashTable{BFunction => (s - 1) } |
(J 1(B |
1 |
(J CohomologyGroups => HashTable{0 => QQ }(B |
CohomologyGroups => HashTable{0 => QQ } |
(J 2(B |
2 |
(J 1 => QQ(B |
1 => QQ |
(J 1(B |
1 |
(J 2 => QQ(B |
2 => QQ |
(J LogBasis => HashTable{0 => | x | }(B |
LogBasis => HashTable{0 => | x | } |
(J 1 => | y2dx-xydy 2x2dx+2xydx |(B |
1 => | y2dx-xydy 2x2dx+2xydx | |
(J 2 => | ydxdy |(B |
2 => | ydxdy | |
(J 1 2 1(B |
1 2 1 |
(J OmegaRes => (QQ[x, y, dx, dy]) <-- (QQ[x, y, dx, dy]) <-- (QQ[x, y, dx, dy]) <-- 0(B |
OmegaRes => (QQ[x, y, dx, dy]) <-- (QQ[x, y, dx, dy]) <-- (QQ[x, y, dx, dy]) <-- 0 |
(J (B |
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(J 0 1 2 3(B |
0 1 2 3 |
(J PreCycles => HashTable{0 => | -x2-xy |}(B |
PreCycles => HashTable{0 => | -x2-xy |} |
(J | -x |(B |
| -x | |
(J 1 => | 0 -2x |(B |
1 => | 0 -2x | |
(J | -y 0 |(B |
| -y 0 | |
(J | 0 0 |(B |
| 0 0 | |
(J 2 => | y |(B |
2 => | y | |
(J 1 3 2(B |
1 3 2 |
(J VResolution => (QQ[x, y, dx, dy]) <-- (QQ[x, y, dx, dy]) <-- (QQ[x, y, dx, dy]) <-- 0(B |
VResolution => (QQ[x, y, dx, dy]) <-- (QQ[x, y, dx, dy]) <-- (QQ[x, y, dx, dy]) <-- 0 |
(J (B |
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(J 0 1 2 3(B |
0 1 2 3 |
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(Jo5 : HashTable(B |
o5 : HashTable |
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(J\end{verbatim}(B |
\end{verbatim} |
(J}(B |
} |
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(J\end{flushleft}(B |
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(J\end{document}(B |
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