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>*Reply-to*: drbob at bigfoot.com*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. >> Please help establish the reason. >> Best regards >> Nodar Shubitidze >> >> >> >> > > > -- DrBob at bigfoot.com

**References**:**Determinant problem***From:*shubi@nusun.jinr.ru (Nodar Shubitidze)