The sigma-ij package

[ Tags: bsd3, library, math, program ] [ Propose Tags ]

A program to compute Thom polynomials of second order Thom-Boardman singularities, using the localization method described in the author's PhD thesis

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Versions 0.2,,
Dependencies array (>=0.5), base (==4.*), combinat (>=0.2.8), containers (>=0.5), optparse-applicative, parsec2, random, sigma-ij (>=, time [details]
License BSD3
Copyright (c) 2010, 2016 Balazs Komuves
Author Balazs Komuves
Maintainer bkomuves (plus) hackage (at) gmail (dot) com
Category Math
Home page
Uploaded Sat Oct 22 19:25:28 UTC 2016 by BalazsKomuves
Distributions NixOS:
Executables sigma-ij
Downloads 121 total (5 in the last 30 days)
Rating 0.0 (0 ratings) [clear rating]
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Status Docs not available [build log]
All reported builds failed as of 2016-11-14 [all 4 reports]
Hackage Matrix CI


  • Math
    • Algebra
      • Math.Algebra.Determinant
      • Math.Algebra.ModP
      • Math.Algebra.Schur
    • FreeModule
      • Math.FreeModule.Class
      • Math.FreeModule.Helper
      • Math.FreeModule.PP
      • Math.FreeModule.Parser
      • Math.FreeModule.PrettyPrint
      • Math.FreeModule.SortedList
      • Math.FreeModule.Symbol
    • ThomPoly
      • Math.ThomPoly.Formulae
      • Math.ThomPoly.Shared
      • Math.ThomPoly.SigmaI
      • Math.ThomPoly.SigmaIJ
      • Math.ThomPoly.Subs


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Readme for sigma-ij-

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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: <>.


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.


 - 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