I need to calculate vast numbers of determinants of integer matrices (size around 30x30 to 50x50) and would like to know the fastest software for this.

It must use exact integer arithmetic as the determinants get large.

Mathematica does this of course, but quite slowly. Magma is much faster. Any recommendations?

  • $\begingroup$ Have you tried PARI/GP? And to be pre-emptive: not MATLAB; it's meant for inexact arithmetic... $\endgroup$ – J. M. is a poor mathematician Oct 21 '11 at 0:24
  • $\begingroup$ Maple does exact calculations. I loaded the "with(LinearAlgebra):" package and then generated a random 100x100 matrix of integers. Maple computed it's determinant using "Determinant" in just a second or two. It'll handle 30x30 and 50x50 matrices with ease. $\endgroup$ – Bill Cook Oct 21 '11 at 1:39
  • $\begingroup$ GAP also does exact calculations, and has a specialised operation DeterminantIntMat for such cases. For example, entering n:=100; m:=RandomMat(n,n);; DeterminantIntMat(m); time; (where time returns the CPU time the last command took in milliseconds), on a 2.6 GHz Intel dual-core CPU I am getting 100-140 milliseconds, and about 1.5 seconds for 200x200 matrices. $\endgroup$ – Alexander Konovalov Apr 29 '13 at 21:17

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