Re: Determinant problem

• To: mathgroup at smc.vnet.net
• Subject: [mg55071] Re: [mg55016] Determinant problem
• From: DrBob <drbob at bigfoot.com>
• Date: Fri, 11 Mar 2005 04:20:50 -0500 (EST)
• References: <200503101024.FAA19238@smc.vnet.net>
• Reply-to: drbob at bigfoot.com
• Sender: owner-wri-mathgroup at wolfram.com

```I think this should give the determinant:

{m,v,c}=LUDecomposition[s1];
Simplify@Tr[m,Times]

(-(1 + t1))*(1 + t10)*(1 + t11)*
(1 + t12)*(1 + t13)*(1 + t14)*
(1 + t15)*(1 + t16)*(1 + t17)*
(1 + t18)*(1 + t19)*(1 + t2)*
(1 + t20)*(1 + t21)*(1 + t22)*
(-1 - t23)*(1 + t3)*(1 + t4)*
(1 + t5)*(1 + t6)*(1 + t7)*
(1 + t8)*(1 + t9)

Be careful, however; if it's really that easy, I'm surprised Det didn't try it.

Bobby

On Thu, 10 Mar 2005 05:24:16 -0500 (EST), Nodar Shubitidze <shubi at nusun.jinr.ru> wrote:

> Hi All !
>
> I have a problem with calculation of determinant of 24*24
> matrix:
> s1={{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1},
> {1,1,1,1,1,1,1,1,1,1,1,1,-t1,-t1,-t1,-t1,-t1,-t1,-t1,-t1,-t1,-t1,-t1,-t1},
> {1,1,1,1,1,1,-t2,-t2,-t2,-t2,-t2,-t2,0,0,0,0,0,0,0,0,0,0,0,0},
> {0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,-t3,-t3,-t3,-t3,-t3,-t3},
> {1,1,1,-t4,-t4,-t4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
> {0,0,0,0,0,0,1,1,1,-t5,-t5,-t5,0,0,0,0,0,0,0,0,0,0,0,0},
> {0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,-t6,-t6,-t6,0,0,0,0,0,0},
> {0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,1,1,1,-t7,-t7,-t7},
> {1,1,-t8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
> {0,0,0,1,1,-t9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
> {0,0,0,0,0,0,1,1,-t10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
> {0,0,0,0,0,0,0,0,0,1,1,-t11,0,0,0,0,0,0,0,0,0,0,0,0},
> {0,0,0,0,0,0,0,0,0,0,0,0,1,1,-t12,0,0,0,0,0,0,0,0,0},
> {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-t13,0,0,0,0,0,0},
> {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-t14,0,0,0},
> {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-t15},
> {1,-t16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
> {0,0,0,1,-t17,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
> {0,0,0,0,0,0,1,-t18,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
> {0,0,0,0,0,0,0,0,0,1,-t19,0,0,0,0,0,0,0,0,0,0,0,0,0},
> {0,0,0,0,0,0,0,0,0,0,0,0,1,-t20,0,0,0,0,0,0,0,0,0,0},
> {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-t21,0,0,0,0,0,0,0},
> {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-t22,0,0,0,0},
> {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-t23,0}};
> s2=Det[s1];
> Mathematica 5.0 on my computer (AMD Atlon XP, 1.4GHz)
> cannot calculate it after 12 hours.
> It is strange, therefore I calculate more complicated (with
> less number of zeros) 68*68 matrix during the seconds.
> Best regards
>                                        Nodar Shubitidze
>
>
>
>

--
DrBob at bigfoot.com

```

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