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. > Please help establish the reason. > Best regards > Nodar Shubitidze > > > > -- DrBob at bigfoot.com

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