2x2 determinant bug in math 9.0.0.0

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• Subject: [mg130812] 2x2 determinant bug in math 9.0.0.0
• From: Vivien Lecomte <vivien.lecomte at gmail.com>
• Date: Sat, 18 May 2013 02:37:46 -0400 (EDT)
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```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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