Macaulay2 1.1 or later has a command logCohomology

An easy example of computing the dimensions of logarithmic cohomology groups.

The case of f = (x3+y4+x y3)(x2+y2)

This folder contains programs and session logs to find bases of Hi(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" .
Google search of the published version of this paper by doi.


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).



  1. Talk on this topics (in Japanese) .
  2. 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