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:
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sigma-ij -h help
sigma-ij -i3 -j1 -n7 compute $Tp(Sigma^{3,1}(7))$
sigma-oj -i3 -j1 -n7 -r<RING> compute with coefficients in the given ring
sigma-oj -i3 -j1 -n7 -B<N> -b<n> 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<FILE> 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:
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- 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
