From: totaro@appmath.uchicago.edu (Burt Totaro)
Newsgroups: sci.math.research
Subject: Re: Todd-polynomials
Date: Sat, 27 Jul 1996 22:08:35 GMT

>From: psmue@math.unizh.ch (S. Mueller)
>Does anyone know a reference where the higher Todd-polynomials are listed 
>(Hirzebruch gives them up to order 6 in "Topological Methods in Algebraic 
>Geometry", p.14). I need them up to order 8.

There is a very convenient computer program that computes Todd polynomials,
intersection numbers on various kinds of algebraic varieties, and so on:
it's a Maple package called "schubert", written by Sheldon Katz
and Stein Stromme. To get it, ftp to ftp.math.okstate.edu
with user=anonymous, password=<your e-mail address>, then type
cd pub/schubert, and get the README file, which explains which other
files you need.

Here are the Todd polynomials up to order 8, according to schubert:

> DIM:=8: b:=bundle(8,c): t:=todd(b);

t := 1+1/2*c1*t+(1/12*c1^2+1/12*c2)*t^2+1/24*c1*c2*t^3+(1/180*c2*c1^2-1/720*c1^
4+1/240*c2^2+1/720*c1*c3-1/720*c4)*t^4+(-1/1440*c2*c1^3+1/480*c1*c2^2+1/1440*c3
*c1^2-1/1440*c1*c4)*t^5+(1/30240*c6+11/60480*c3*c1*c2+1/30240*c1^6+1/6048*c2^3-
1/30240*c1*c5-1/6720*c4*c2-1/12096*c4*c1^2-1/60480*c3^2+1/12096*c3*c1^3+11/
60480*c2^2*c1^2-1/5040*c2*c1^4)*t^6+(11/120960*c3*c2*c1^2-1/13440*c4*c1*c2+1/
60480*c1*c6-1/60480*c5*c1^2+1/60480*c4*c1^3-1/120960*c1*c3^2-1/60480*c3*c1^4+1/
12096*c1*c2^3-1/12096*c2^2*c1^3+1/60480*c2*c1^5)*t^7+(1/72576*c3*c1*c2^2+13/
1814400*c3*c2*c1^3-19/3628800*c4*c2*c1^2-1/226800*c5*c1*c2-1/1209600*c8-1/
1209600*c1^8+1/172800*c2^4-13/3628800*c4*c1*c3+1/1209600*c1*c7+13/3628800*c6*c2
+1/518400*c6*c1^2+1/1209600*c5*c3-1/518400*c5*c1^3+1/725760*c4^2-17/1814400*c4*
c2^2+1/259200*c4*c1^4-1/453600*c3^2*c2+1/1209600*c3^2*c1^2-1/259200*c3*c1^5+1/
453600*c2^3*c1^2-1/72576*c2^2*c1^4+1/151200*c2*c1^6)*t^8


Burt Totaro