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Re: Mathematica 7 is now available

  • To: mathgroup at smc.vnet.net
  • Subject: [mg93711] Re: Mathematica 7 is now available
  • From: Szabolcs <szhorvat at gmail.com>
  • Date: Sat, 22 Nov 2008 06:14:36 -0500 (EST)
  • References: <gg0qf8$c6$1@smc.vnet.net> <gg3c6m$k2t$1@smc.vnet.net>

On Nov 21, 11:32 am, Michael Weyrauch <michael.weyra... at gmx.de> wrote:
> The Tally[] problem is solved. This I checked with a prerelease version
> of Mathematica 7 I got at this year's Mathematica users conference.
>

What about the other bug (the eigenvalue problem), linked from the
same thread I mentioned?

I copied the (wrong) results from Mathematica 6 here:


In[1]:= mat = {{-6, 0, -Sqrt[3], 0, 0, Sqrt[3], 0, 0, 0, 0, 0, 0, 0,
    0}, {0, -6, 0, -Sqrt[3], 0, 0, Sqrt[3], 0, 0, 0, 0, 0, 0,
    0}, {-Sqrt[3], 0, -4, 2 (-1/(4 Sqrt[3]) + (3 Sqrt[3])/4),
    2 Sqrt[2/3], 0, 0, Sqrt[3], 0, 0, 0, 0, 0, 0}, {0, -Sqrt[3],
    2 (-1/(4 Sqrt[3]) + (3 Sqrt[3])/4), -4/3, -(2 Sqrt[2])/3, 0, 0, 0,
     Sqrt[3], 0, 0, 0, 0, 0}, {0, 0, 2 Sqrt[2/3], -(2 Sqrt[2])/3, 7/3,
     0, 0, 0, 0, Sqrt[3], 0, 0, 0, 0}, {Sqrt[3], 0, 0, 0, 0, -4, 0,
    2 (-1/(4 Sqrt[3]) + Sqrt[3]/4), 0, 0, 2 Sqrt[2/3], 0, 0, 0}, {0,
    Sqrt[3], 0, 0, 0, 0, -4, 0, 2 (-1/(4 Sqrt[3]) + Sqrt[3]/4), 0, 0,
    2 Sqrt[2/3], 0, 0}, {0, 0, Sqrt[3], 0, 0,
    2 (-1/(4 Sqrt[3]) + Sqrt[3]/4), 0, -14/3,
    2 (-1/(4 Sqrt[3]) + (3 Sqrt[3])/4), 2 Sqrt[2/3], (2 Sqrt[2])/3, 0,
     0, 0}, {0, 0, 0, Sqrt[3], 0, 0, 2 (-1/(4 Sqrt[3]) + Sqrt[3]/4),
    2 (-1/(4 Sqrt[3]) + (3 Sqrt[3])/4), -2, -(2 Sqrt[2])/3,
    0, (2 Sqrt[2])/3, 0, 0}, {0, 0, 0, 0, Sqrt[3], 0, 0,
    2 Sqrt[2/3], -(2 Sqrt[2])/3, -7/3, 0, 0,
    2 (1/(3 Sqrt[2]) + (2 Sqrt[2])/3), Sqrt[10/3]}, {0, 0, 0, 0, 0,
    2 Sqrt[2/3], 0, (2 Sqrt[2])/3, 0, 0, -16/3,
    2 (-1/(4 Sqrt[3]) + (3 Sqrt[3])/4), 2 Sqrt[2/3], 0}, {0, 0, 0, 0,
    0, 0, 2 Sqrt[2/3], 0, (2 Sqrt[2])/3, 0,
    2 (-1/(4 Sqrt[3]) + (3 Sqrt[3])/4), -8/3, -(2 Sqrt[2])/3, 0}, {0,
    0, 0, 0, 0, 0, 0, 0, 0, 2 (1/(3 Sqrt[2]) + (2 Sqrt[2])/3),
    2 Sqrt[2/3], -(2 Sqrt[2])/3, 1/2,
    2 (-Sqrt[5/3]/16 - Sqrt[15]/16)}, {0, 0, 0, 0, 0, 0, 0, 0, 0,
    Sqrt[10/3], 0, 0, 2 (-Sqrt[5/3]/16 - Sqrt[15]/16), 7/2}};

In[2]:= mat === Conjugate@Transpose[mat]
Out[2]= True

(mat is Hermitian so we expect real eigenvalues.)

In[3]:= N@Eigenvalues[mat]

Out[3]= {-9.41358 + 0.88758 I, -9.41358 - 0.88758 I, -7.37965 +
  2.32729 I, -7.37965 - 2.32729 I, -4.46655 + 2.59738 I, -4.46655 -
  2.59738 I, 4.36971, 3.21081, -2.32456 + 2.10914 I, -2.32456 -
  2.10914 I, 2.04366+ 0.552265 I,
 2.04366- 0.552265 I, -0.249588 + 1.29034 I, -0.249588 - 1.29034 I}

In[4]:= Eigenvalues[N[mat]]

Out[4]= {-9.09122, -7.41855, -7.41855, -7.2915, 4.33734, -4., -4., \
3.2915, -3.24612, -2.38787, -2.38787, 1.80642, 1.80642,
 9.21707*10^-16}


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