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Topic: 2x2 determinant bug in math 9.0.0.0
Replies: 1   Last Post: May 19, 2013 5:46 AM

 Bob Hanlon Posts: 906 Registered: 10/29/11
Re: 2x2 determinant bug in math 9.0.0.0
Posted: May 19, 2013 5:46 AM

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@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.
>
>