## JGD_G5/IG5-6

Decomposable subspaces at degree d of the invariant ring of G5, Nicolas Thiery.
Name IG5-6 JGD_G5 1965 30 77 251 251 Combinatorial Problem No 2008 N. Thiery J.-G. Dumas
Structural Rank 30 true 1 35 0 0% 0% no no integer
SVD Statistics
Matrix Norm 2.838675e+01
Minimum Singular Value 1.814446e-01
Condition Number 1.564485e+02
Rank 30
sprank(A)-rank(A) 0
Null Space Dimension 0
Full Numerical Rank? yes
Download ```Decomposable subspaces at degree d of the invariant ring of G5, Nicolas Thiery. Univ. Paris Sud. From Jean-Guillaume Dumas' Sparse Integer Matrix Collection, http://ljk.imag.fr/membres/Jean-Guillaume.Dumas/simc.html http://www.lapcs.univ-lyon1.fr/~nthiery/LinearAlgebra/ Linear Algebra for combinatorics Abstract: Computations in algebraic combinatorics often boils down to sparse linear algebra over some exact field. Such computations are usually done in high level computer algebra systems like MuPAD or Maple, which are reasonnably efficient when the ground field requires symbolic computations. However, when the ground field is, say Q or Z/pZ, the use of external specialized libraries becomes necessary. This document, geared toward developpers of such libraries, present a brief overview of my needs, which seems to be fairly typical in the community. IG5-6: 30 x 77 : rang = 30 (Iteratif: 0.01 s, Gauss: 0.01 s) IG5-7: 62 x 150 : rang = 62 (Iteratif: 0.02 s, Gauss: 0.01 s) IG5-8: 156 x 292 : rang = 154 (Iteratif: 0.08 s, Gauss: 0.01 s) IG5-9: 342 x 540 : rang = 308 (Iteratif: 0.46 s, Gauss: 0.02 s) IG5-10: 652 x 976 : rang = 527 (Iteratif: 2.1 s, Gauss: 0.07 s) IG5-11: 1227 x 1692 : rang = 902 (Iteratif: 7.5 s, Gauss: 0.22 s) IG5-12: 2296 x 2875 : rang = 1578 (Iteratif: 26 s, Gauss: 0.93 s) IG5-13: 3994 x 4731 : rang = 2532 (Iteratif: 80 s, Gauss: 3.35 s) IG5-14: 6727 x 7621 : rang = 3906 (Iteratif: 244 s, Gauss: 10.06 s) IG5-15: 11358 x 11987 : rang = 6146 (Iteratif: s, Gauss: 29.74 s) IG5-16: 18485 x 18829 : rang = 9519 (Iteratif: s, Gauss: 621.97 s) IG5-17: 27944 x 30131 : rang = 14060 (Iteratif: s, Gauss: 1973.8 s) Filename in JGD collection: G5/IG5-6.txt2```