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{\bf twistedLogCohomology(List,List) -- twisted logarithmic cohomology groups in two variables}
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{\bf Synopsis}
\begin{itemize}
\item Usage: twistedLogCohomology(F,A)
\item Function: twistedLogCohomology
\item inputs:
\begin{itemize}
\item F, a list of polynomials in two variables
\item A, a list of rational numbers
\end{itemize}
\item outputs:
\begin{itemize}
\item a hashtable, with entries $\{$ Bfunction, CohomologyGroups, LogBasis, OmegaRes, PreCycles, VResolution $\}$
\end{itemize}
\end{itemize}
{\bf Description}
Bases of twisted logarithmic cohomology groups are contained in a hashtable LogBasis.
Bases of $H^1$ and $H^2$ are outputted only numerators.
In following example, a basis of $H^1$ is
$\{ \frac{y^2dx-xydy}{x(x+y)}, \frac{2x^2dx+2xydx}{x(x+y)} \}$,
a basis of $H^2$ is $\{ \frac{ydxdy}{x(x+y)} \}$.
{\footnotesize
\begin{verbatim}
i1 : loadPackage "Dmodules";
i2 : load "twistedLogCohomology.m2";
i3 : R = QQ[x,y];
i4 : twistedLogCohomology({x,x+y},{-1,0})
Warning: not a generic weight vector. Could be difficult...
o5 = HashTable{BFunction => (s - 1) }
1
CohomologyGroups => HashTable{0 => QQ }
2
1 => QQ
1
2 => QQ
LogBasis => HashTable{0 => | x | }
1 => | y2dx-xydy 2x2dx+2xydx |
2 => | ydxdy |
1 2 1
OmegaRes => (QQ[x, y, dx, dy]) <-- (QQ[x, y, dx, dy]) <-- (QQ[x, y, dx, dy]) <-- 0
0 1 2 3
PreCycles => HashTable{0 => | -x2-xy |}
| -x |
1 => | 0 -2x |
| -y 0 |
| 0 0 |
2 => | y |
1 3 2
VResolution => (QQ[x, y, dx, dy]) <-- (QQ[x, y, dx, dy]) <-- (QQ[x, y, dx, dy]) <-- 0
0 1 2 3
o5 : HashTable
\end{verbatim}
}
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