Re: Is this the best way to Solve the Katsura 6 problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg73982] Re: Is this the best way to Solve the Katsura 6 problem*From*: "Raj" <rajanikanth at gmail.com>*Date*: Sat, 3 Mar 2007 23:58:11 -0500 (EST)*References*: <200703021140.GAA03968@smc.vnet.net><esb59q$45e$1@smc.vnet.net>

Thanks for correcting my mistake Daniel. Regards, Raj On Mar 2, 11:40 pm, Daniel Lichtblau <d... at wolfram.com> wrote: > Raj wrote: > > hi! > > > Could somebody tell me if this is the best way to solve theKatsura6 > > problem: > > > NSolve[{x1 + 2x2 + 2x3 + 2x4 + 2x5 + 2x6 + 2x7 - 1 , > > 2x4 x3 + 2x5 x2 + 2x6 x1 + 2x7 x2 - x6 , > > x3^2 + 2x4 x2 + 2x5 x1 + 2x6 x2 + 2x7 x3 - x5 , > > 2x3 x2 + 2x4 x1 + 2x5 x2 + 2x6 x3 + 2x7 x4 - x4 , > > x2^2 + 2x3 x1 + 2 x4 x2 + 2 x5 x3 + 2 x6 x4 + 2 x7 x5 - x3 , > > 2 x2 x1 + 2 x3 x2 + 2 x4 x3 + 2 x5 x4 + 2 x6 x5 + 2 x7 x6 - x2 , > > x1^2 + 2 x^2 + 2 x3^2 + 2 x4^2 + 2 x5^2 + 2 x6^2 + 2 x7^2 - x1 }, > > {x1,x2,x3, > > x4,x5,x6,x7}] > > > Thanks, > > > Raj > > For Mathematica I think it is about as good as one can do. Or rather it > would be, if your input did not have a typo. In the last polynomial you > have 2*x^2 instead of 2*x2^2. Below is the corrected version. > > polys = {-1 + x1 + 2*x2 + 2*x3 + 2*x4 + 2*x5 + 2*x6 + 2*x7, > 2*x3*x4 + 2*x2*x5 - x6 + 2*x1*x6 + 2*x2*x7, > x3^2 + 2*x2*x4 - x5 + 2*x1*x5 + 2*x2*x6 + 2*x3*x7, > 2*x2*x3 - x4 + 2*x1*x4 + 2*x2*x5 + 2*x3*x6 + 2*x4*x7, > x2^2 - x3 + 2*x1*x3 + 2*x2*x4 + 2*x3*x5 + 2*x4*x6 + 2*x5*x7, > -x2 + 2*x1*x2 + 2*x2*x3 + 2*x3*x4 + 2*x4*x5 + 2*x5*x6 + 2*x6*x7, > 2*x2^2 - x1 + x1^2 + 2*x3^2 + 2*x4^2 + 2*x5^2 + 2*x6^2 + 2*x7^2}; > vars = {x1, x2, x3, x4, x5, x6, x7}; > > In[16]:= Timing[soln = NSolve[polys, vars];] > Out[16]= {3.35, Null} > > In[17]:= InputForm[Max[Abs[polys /. soln]]] > Out[17]//InputForm= 6.652497580583727*^-10 > > Residuals are less than 10^(-9), which seems fairly good. > > Daniel Lichtblau > Wolfram Research

**References**:**Is this the best way to Solve the Katsura 6 problem***From:*"Raj" <rajanikanth@gmail.com>