From the bottom of this page you can download
Mathematica programs that know many results about the unstable
homotopy groups of spheres up to the 19-stem. Most of the information
is taken from Toda's book "Composition methods in homotopy groups of
spheres"; a few additional facts are proved in an accompanying note or
quoted from elsewhere. The program does not do any serious
calculations for itself, it is merely a convenient way of organizing
and accessing results obtained by traditional methods. One can also
do some automated consistency checking to detect any errors. I have
tried to use a fairly general framework so that other computations in
unstable homotopy can be included later if people are interested.
This program is not really finished, but I think it is already useful,
and I have moved on to other things, so I have decided to release it.
Here are some examples of things one can type, and the program's
TeXToMath.m - used by Toda.m to convert
help messages from LaTeX to Mathematica encoding. (This is rather
crude, and will only handle a limited range of LaTeX constructs.)
LambdaAlgebra.m - definitions
related to the lambda algebra, including lambda algebra
representatives for some of Toda's generators. This program can
calculate the cohomology of the lambda algebra, but it uses a very
naive and inefficient algorithm, and takes a ridiculous amount of
space to represent the result.
TodaChecks.m - some auxiliary
functions for checking the completeness and consistency of the
results encoded in Toda.m. (There are currently numerous failures
of completeness, but none of consistency.)
LambdaData.m - 10MB of data on bases
for the lambda algebra that put the differential in canonical form.
You probably do not want or need to download this file.