Re: 2x2 determinant bug in math 9.0.0.0
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- Subject: [mg130831] Re: 2x2 determinant bug in math 9.0.0.0
- From: Bob Hanlon <hanlonr357 at gmail.com>
- Date: Sun, 19 May 2013 05:48:51 -0400 (EDT)
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Also works correctly in Mathematica 9.0.1.0 with Mac OS X 10.8.3 $Version "9.0 for Mac OS X x86 (64-bit) (January 24, 2013)" M = {{-(250 t2p (10 t2p - 8 t1b t2p + t1b^3 (9 + t2p) - 5 t1b^2 (1 + 3 t2p)) + 40 t1 t2p (-50 t2p - 120 t1b t2p + t1b^3 (35 + 3 t2p) - 5 t1b^2 (-5 + 9 t2p)) + t1^3 (250 t2p (9 + t2p) + 40 t1b t2p (35 + 3 t2p) + t1b^3 (425 + 130 t2p + 9 t2p^2) - 5 t1b^2 (225 + 220 t2p + 27 t2p^2)) - 5 t1^2 (250 t2p (1 + 3 t2p) + 40 t1b t2p (-5 + 9 t2p) + t1b^3 (225 + 220 t2p + 27 t2p^2) - 5 t1b^2 (25 + 150 t2p + 81 t2p^2)))/(20 (-5 + t1) (-5 + t1b) (-10 t2p - 10 t1 t2p + t1^2 (5 + t2p)) (-10 t2p - 10 t1b t2p + t1b^2 (5 + t2p))), -(t1^2/(-10 t2p - 10 t1 t2p + t1^2 (5 + t2p))) - t1b^2/(-10 t2p - 10 t1b t2p + t1b^2 (5 + t2p))}, {-(t1^2/(-10 t2p - 10 t1 t2p + t1^2 (5 + t2p))) - t1b^2/(-10 t2p - 10 t1b t2p + t1b^2 (5 + t2p)), 1/(1 - t2p) - 1/t2p + 2/(-t1 + t2p) + 2/(-t1b + t2p) + (10 + 10 t1 - t1^2)/(-10 t2p - 10 t1 t2p + t1^2 (5 + t2p)) + (10 + 10 t1b - t1b^2)/(-10 t2p - 10 t1b t2p + t1b^2 (5 + t2p))}}; Det[M] == M[[1, 1]] M[[2, 2]] - M[[1, 2]] M[[2, 1]] // Simplify True Bob Hanlon On Sat, May 18, 2013 at 2:37 AM, Vivien Lecomte <vivien.lecomte at gmail.com>wrote: > Hi all, > > caution if you compute matrix determinants in Mathematica 9.0.0.0! You'll > find below a 2x2 matrix composed of symbolic rational fractions. Compare > Det[M] and the expected expression M[[1, 1]] M[[2, 2]] - M[[1, 2]] M[[2, > 1]] . > > To your surprise, you'll find different results if you use Mathematica > 9.0.0.0. Affected versions are independent of Linux/Mac/Win OS: > 9.0 for Linux x86 (64-bit) (November 20, 2012a) > 9.0 for Mac OS X x86 (32 bit, 64-bit Kernel) (November 20, 2012) > 9.0 for Microsoft Windows (32-bit) (November 20, 2012) > The determinant is however correctly computed for a generic matrix > M={{a,b},{c,d}} . > > Previous version > 8.0 for Linux x86 (64 - bit) (October 10, 2011) > is not affected. > > The problem is solved with Mathematica 9.0.1.0 > 9.0 for Linux x86 (64-bit) (February 7, 2013) > although i see no reference to related updates in the Mathematica 9.0.1 > changelog. > > Best, > > Vivien > > > PS, here is the matrix (you don't want to know how it was obtained ;) ) > > M = {{-(250 t2p (10 t2p - 8 t1b t2p + t1b^3 (9 + t2p) - > 5 t1b^2 (1 + 3 t2p)) + > 40 t1 t2p (-50 t2p - 120 t1b t2p + t1b^3 (35 + 3 t2p) - > 5 t1b^2 (-5 + 9 t2p)) + > t1^3 (250 t2p (9 + t2p) + 40 t1b t2p (35 + 3 t2p) + > t1b^3 (425 + 130 t2p + 9 t2p^2) - > 5 t1b^2 (225 + 220 t2p + 27 t2p^2)) - > 5 t1^2 (250 t2p (1 + 3 t2p) + 40 t1b t2p (-5 + 9 t2p) + > t1b^3 (225 + 220 t2p + 27 t2p^2) - > 5 t1b^2 (25 + 150 t2p + 81 t2p^2)))/(20 (-5 + t1) (-5 + > t1b) (-10 t2p - 10 t1 t2p + t1^2 (5 + t2p)) (-10 t2p - > 10 t1b t2p + > t1b^2 (5 + t2p))), -(t1^2/(-10 t2p - 10 t1 t2p + > t1^2 (5 + t2p))) - > t1b^2/(-10 t2p - 10 t1b t2p + > t1b^2 (5 + t2p))}, {-(t1^2/(-10 t2p - 10 t1 t2p + > t1^2 (5 + t2p))) - > t1b^2/(-10 t2p - 10 t1b t2p + t1b^2 (5 + t2p)), > 1/(1 - t2p) - 1/t2p + 2/(-t1 + t2p) + > 2/(-t1b + t2p) + (10 + 10 t1 - t1^2)/(-10 t2p - 10 t1 t2p + > t1^2 (5 + t2p)) + (10 + 10 t1b - t1b^2)/(-10 t2p - > 10 t1b t2p + t1b^2 (5 + t2p))}}; > > It is well defined, except for a finite number of values of the > parameters. Giving a numerical value to one of the parameters renders the > evaluation of the determinant correct. > >
- References:
- 2x2 determinant bug in math 9.0.0.0
- From: Vivien Lecomte <vivien.lecomte@gmail.com>
- 2x2 determinant bug in math 9.0.0.0