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