This is a program to compute Thom polynomials of second-order Thom-Boardman singularities \(Sigma^{i,j}(n)\).

The computation is based on the localization method described in the author's PhD thesis: http://renyi.hu/~komuves/phdthesis.pdf.

USAGE:

sigma-ij -h help sigma-ij -i3 -j1 -n7 compute \(Tp(Sigma^{3,1}(7))\) sigma-oj -i3 -j1 -n7 -r compute with coefficients in the given ring sigma-oj -i3 -j1 -n7 -B -b compute the n-th (out of N) part sigma-oj -i3 -j1 -n7 -rZp compute in the (baked-in) prime field Zp sigma-oj -i3 -j1 -n7 -o change the output file

Supported rings:

• rationals
• integers (remark: the division-free determinant algorithm often fails)
• Zp, a baked-in prime field

The -B and -b options are useful to parallelize the computation over many computers.

TODO:

• better (and faster) prime field implementation(s)
• allow arbitrary prime fields instead of just a baked-in one
• pivoting for the Bareiss (division-free) determinant algorithm
• implement explicit formula for j=1