## Macaulay2 1.1 or later has a command logCohomology

An easy example
of computing the dimensions of logarithmic cohomology groups.
## The case of f = (x^{3}+y^{4}+x y^{3})(x^{2}+y^{2})

This folder contains programs and session logs to find bases
of H^{i}(log f) for

f = (x^3+y^4+x*y^3)*(x^2+y^2)

You can recompute our result with these files.

Reference: Example 4.1 in the paper
"Francisco Jesus Castro-Jimenez and Nobuki Takayama,
The computation of the logarithmic cohomology for plane curves"
arxiv.org/abs/0712.0001 .

Google search of the published version of this paper by doi.

### Files

The output of the free basis of the syzygy of (f,f_x,f_y)
is embedded in the following two programs.
See mysyzz variable in makeTauInputTest in
trans.m2 and
LL in tau.rr .
Macaulay2 1.1 or later contains the codes in trans.m2, but
some functions are hidden. See instructions below to use these hidden
functions.

The free basis is obtained by A.Fabianska by the Maple package
QuillenSuslin. The correctness of the output is checked in trans.m2.
### Macaulay2 1.1 and Risa/Asir logs to find bases of H^1(log f).

Since some functions for our computation are hidden in the Macaulay 2
(1.1 or later)
standard package, download
Dmodules-1-1.tar.gz (right click) and load Dmodules.m2 from this archive.
See the session log below as to details.

Computation of transfers is done in
trans-log-2008-08-26.txt
and computation of tau^{-1} is done in
tau-log-2007-11-22.txt.
### Macaulay2 log to find bases of H^0(log f) and H^2(log f).

trans-log-a.txt
### References

- Talk on this topics (in Japanese) .
- Details on the derivation of the quasi-isomorphism of tau:
Hand written note .

$Id: readme.html,v 1.1 2009/08/24 03:06:10 taka Exp $
in misc-2008/09/LogCohomology