(J\documentclass{jarticle}(B

(J\begin{document}(B
(J\begin{center}(B
(J{\bf twistedLogCohomology(List,List) -- 2$@JQ?tB?9`<0$KIU?o$9$k(J twisted logarithmic cohomology $@72$r7W;;(J}(B
(J\end{center}(B
(J\begin{flushleft}(B

(J{\bf $@35MW(J}(B

(J\begin{itemize}(B
(J\item $@;HMQJ}K!(J: twistedLogCohomology(F,A)(B
(J\item $@4X?tL>(J: twistedLogCohomology(B
(J\item $@F~NO(J:(B
(J  \begin{itemize}(B
	(J\item F, 2$@JQ?tB?9`<0$N%j%9%H(B
	(J\item A, $@M-M}?t$N%j%9%H(B
(J  \end{itemize}(B
(J\item $@=PNO(J:(B
(J  \begin{itemize}(B
	(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
(J  \end{itemize}(B
(J\end{itemize}(B

(J{\bf $@@bL@(J}(B

(JTwisted logarithmic cohomology $@72$N4pDl$O%O%C%7%e%F!<%V%k(J LogBasis $@$K4^$^$l$k(J. (B
(J$H^1$ $@$H(J $H^2$ $@$N4pDl$OJ,;R$N$_=PNO$5$l$k(J. (B
$@0J2<$NNc$G$O(J $H^1$ $@$N4pDl$O(J (B
(J$\{ \frac{y^2dx-xydy}{x(x+y)}, \frac{2x^2dx+2xydx}{x(x+y)} \}$, (B
(J$H^2$ $@$N4pDl$O(J $\{ \frac{ydxdy}{x(x+y)} \}$ $@$G$"$k(J. (B

(J{\footnotesize (B
(J\begin{verbatim}(B
(Ji1 : loadPackage "Dmodules";(B

(Ji2 : load "twistedLogCohomology.m2";(B

(Ji3 : R = QQ[x,y];(B

(Ji4 : twistedLogCohomology({x,x+y},{-1,0})(B
(JWarning: not a generic weight vector.  Could be difficult...(B

(Jo5 = HashTable{BFunction => (s - 1)                                                                    }(B
(J                                                    1(B
(J               CohomologyGroups => HashTable{0 => QQ }(B
(J                                                    2(B
(J                                             1 => QQ(B
(J                                                    1(B
(J                                             2 => QQ(B
(J               LogBasis => HashTable{0 => | x |                    }(B
(J                                     1 => | y2dx-xydy 2x2dx+2xydx |(B
(J                                     2 => | ydxdy |(B
(J                                             1                       2                       1(B
(J               OmegaRes => (QQ[x, y, dx, dy])  <-- (QQ[x, y, dx, dy])  <-- (QQ[x, y, dx, dy])  <-- 0(B
(J                                                                                                    (B
(J                           0                       1                       2                       3(B
(J               PreCycles => HashTable{0 => | -x2-xy |}(B
(J                                           | -x     |(B
(J                                      1 => | 0  -2x |(B
(J                                           | -y 0   |(B
(J                                           | 0  0   |(B
(J                                      2 => | y |(B
(J                                                1                       3                       2(B
(J               VResolution => (QQ[x, y, dx, dy])  <-- (QQ[x, y, dx, dy])  <-- (QQ[x, y, dx, dy])  <-- 0(B
(J                                                                                                       (B
(J                              0                       1                       2                       3(B

(Jo5 : HashTable(B

(J\end{verbatim}(B
(J}(B

(J\end{flushleft}(B
(J\end{document}(B