Yet Another Cohomology Program

Status: planning

Abstract

Yacop allows to resolve sub Hopf algebras of the Steenrod algebra at small primes. It can compute chain maps and Ext/Tor for small (differential) A-modules. It contains a graphical chart viewer that can also create postscript charts.

Project details

Status:

All the basic stuff is working but a couple of things are still missing:
  • Framework for differential Steenrod algebra modules not finished.
  • Regression test suite needs to be created.
  • Tor/Ext framework is missing

Installation (preview):

The supported platforms are Linux and MacOS. Solaris should also work when Sage eventually supports it.
  • Download and install sage version 4.6.1
  • On Linux make sure you have the file/usr/include/X11/Xlib.h You might have to install the "libx11-dev" package to get this file.
  • Download the files "tcltk8.5.9-decarbon.spkg", "yacop1.0.spkg", "15206.patch" from the links above.
  • Install the sage packages "tcltk8.5.9-decarbon.spkg", "yacop1.0.spkg" via
    ./sage -f -s tcltk8.5.9-decarbon.spkg
    ./sage -f -s yacop1.0.spkg
  • Install the Yacop/Sage patch from the sage prompt via
    sage: hg_sage.patch("15206.patch")
  • Rebuild the sage index and documentation via
    ./sage -b
    ./sage -docbuild reference html
You should then find the documentation of the Yacop features under devel/sage/doc/output/html/en/reference/algebras.html

Example:

Here's a little sample session:
cn@jehova:/waste/cn/sage-4.6.1> ./sage
----------------------------------------------------------------------
| Sage Version 4.6.1, Release Date: 2011-01-11                       |
| Type notebook() for the GUI, and license() for information.        |
----------------------------------------------------------------------
Loading Sage library. Current Mercurial branch is: yacop-release
sage: C=SteenrodAlgebraGroundFieldResolution(SteenrodAlgebra(5))
sage: # compute a resolution
sage: time C.extend(s=30,n=500)
CPU times: user 79.43 s, sys: 6.26 s, total: 85.69 s
Wall time: 90.10 s
sage: # look at some Ext groups
sage: C.generators(n=453)
{g(9,453), g(12,453), g(22,453), g(3,453), g(29,453), g(11,453), g(18,453)}
sage: # open chart viewer
sage: C.gui()
Here's a screenshot of the chart viewer:
yacop chart viewer