 | ■No23028に返信(会長さんの記事)
>
> 対称式の問題だと思うのですが、
>
解決しました との ことですが 参考まで；
In[1]:=
a = 3; b = 9; c = -1;
f1 = x + y + z - a;
f2 = x^2 + y^2 + z^2 - b;
f3 = x*y*z - c;
f = x*(y^3 + z^3) + y*(z^3 + x^3) +
z*(x^3 + y^3) - L;
GB = GroebnerBasis[{f1, f2, f3, f},
{L, x, y, z}]
Out[6]=
{1 - 3*z^2 + z^3, -3*y + y^2 - 3*z + y*z +
z^2, -3 + x + y + z, 3 - L}
In[7]:=
Solve[GB[[4]] == 0, L]
Out[7]=
{{L -> 3}}<----コタエ
In[8]:=
a = 3; b = 9; c = -1; k = 3;
f1 = x + y + z - a;
f2 = x^2 + y^2 + z^2 - b;
f3 = x*y*z - c;
f = x^k + y^k + z^k - L;
GB = GroebnerBasis[{f1, f2, f3, f},
{L, x, y, z}]
Out[13]=
{1 - 3*z^2 + z^3, -3*y + y^2 - 3*z + y*z +
z^2, -3 + x + y + z, 24 - L}
In[14]:=
Solve[GB[[4]] == 0, L]
Out[14]=
{{L -> 24}}<----コタエ
In[15]:=
a = 3; b = 9; c = -1; k = 4;
f1 = x + y + z - a;
f2 = x^2 + y^2 + z^2 - b;
f3 = x*y*z - c;
f = x^k + y^k + z^k - L;
GB = GroebnerBasis[{f1, f2, f3, f},
{L, x, y, z}]
Out[20]=
{1 - 3*z^2 + z^3, -3*y + y^2 - 3*z + y*z +
z^2, -3 + x + y + z, 69 - L}
In[21]:=
Solve[GB[[4]] == 0, L]
Out[21]=
{{L -> 69}}<----コタエ
-----------------------------
In[22]:=
a = 3; b = 9; c = -1; k = 19; <--ついでに
f1 = x + y + z - a;
f2 = x^2 + y^2 + z^2 - b;
f3 = x*y*z - c;
f = x^k + y^k + z^k - L;
GB = GroebnerBasis[{f1, f2, f3, f},
{L, x, y, z}]
Out[27]=
{1 - 3*z^2 + z^3, -3*y + y^2 - 3*z + y*z +
z^2, -3 + x + y + z, 532961346 - L}
In[28]:=
Solve[GB[[4]] == 0, L]
Out[28]=
{{L -> 532961346}}<----コタエ
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