```Date: May 19, 2013 5:46 AM
Author: Bob Hanlon
Subject: Re: 2x2 determinant bug in math 9.0.0.0

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]] // SimplifyTrueBob HanlonOn Sat, May 18, 2013 at 2:37 AM, Vivien Lecomte <vivien.lecomte@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.>>
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