| ■No23266に返信(数研さんの記事) > ありがとうございました! との こと。 参考まで; In[1]:= f1 = (2*(y + z))/x - (2*(z + x))/y; f2 = (2*(z + x))/y - (2*(x + y))/z; f = (2*(y + z))/x - k;
In[4]:= GB = GroebnerBasis[{f1, f2, f}, {x, y, z, k}]
Out[4]= {-8 - 2*k + k^2, -2*y - k*y + 2*z + k*z, 2/y + k/y - 2/z - k/z, 2*x + 2*y - k*z, -(2/x) - k/x + 2/z + k/z, -k + (2*y)/x + (2*z)/x, 2/(x*y) - 2/z^2 - k/z^2 + 2/(x*z) + 2/(y*z)}
In[5]:= Solve[% == {0, 0, 0, 0, 0, 0, 0}, {x, y, z, k}]
Out[5]= {{k -> -2, y -> -2*z, x -> z}, {k -> -2, y -> z, x -> -2*z}, {k -> -2, y -> z, x -> -2*z}, {k -> -2, y -> z, x -> -2*z}, {k -> 4, y -> z, x -> z}, {k -> -2, y -> -x - z}} <-------コタエ k=-2,4 In[6]:=2*(y + z)/x /. {y -> -2*z, x -> z}
Out[6]=-2
In[7]:=2*(y + z)/x /. {y -> z, x -> z}
Out[7]=4 -------------------------------------------- In[8]:= A = {{0, 2, 2}, {2, 0, 2}, {2, 2, 0}}
Out[8]= {{0, 2, 2}, {2, 0, 2}, {2, 2, 0}}
In[9]:= Eigenvalues[A]
Out[9]= {-2, -2, 4}
In[10]:= Det[A - λ*IdentityMatrix[3]]
Out[10]= 16 + 12*λ - λ^3
In[11]:= Solve[% == 0, λ]
Out[11]= {{λ -> -2}, {λ -> -2}, {λ -> 4}} <-------コタエ In[12]:= Eigenvectors[A]
Out[12]= {{-1, 0, 1}, {-1, 1, 0}, {1, 1, 1}}
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