Re: Determinant problem

• To: mathgroup at smc.vnet.net
• Subject: [mg55073] Re: [mg55016] Determinant problem
• From: DrBob <drbob at bigfoot.com>
• Date: Fri, 11 Mar 2005 04:20:58 -0500 (EST)
• References: <200503101024.FAA19238@smc.vnet.net> <opsnfwkdweiz9bcq@monster.ma.dl.cox.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Actually, it should be

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

The simpler version gets the sign wrong, half the time.

Bobby

On Thu, 10 Mar 2005 14:58:51 -0600, DrBob <drbob at bigfoot.com> wrote:

> 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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