 | ■No23209に返信(Ｎさんの記事)
> f(x)=ax^2+bx+c、g(x)=dx^2+ex+fとおいて考えるのが１つの方法ですに倣い；
In[1]:=
Expand[a*x^2 + b*x + c - (d*x^2 + e*x + f)]
Out[1]=
c - f + b*x - e*x + a*x^2 - d*x^2
In[2]:=
Coefficient[%, x^2]
Out[2]=
a - d
etc
In[3]:=
Expand[(a*x^2 + b*x + c)*(d*x^2 + e*x + f)]
Out[3]=
c*f + c*e*x + b*f*x + c*d*x^2 + b*e*x^2 +
a*f*x^2 + b*d*x^3 + a*e*x^3 + a*d*x^4
In[4]:=
Table[Coefficient[%, x^k], {k, 1, 4}]
Out[4]=
{c*e + b*f, c*d + b*e + a*f, b*d + a*e, a*d}
In[5]:=
GroebnerBasis[{a - d - 2, b - e - -2,
c - f - 2, c*f - 3, c*e + b*f - 2,
c*d + b*e + a*f - 5, b*d + a*e - 2,
a*d - 3}, {a, b, c, d, e, f}]
Out[5]=
{-3 + 2*f + f^2, 1 - e, -d + f, -2 + c - f,
-1 - b, 2 - a + f}
In[6]:=
Solve[% == {0, 0, 0, 0, 0, 0},
{a, b, c, d, e, f}]
Out[6]=
{{a -> -1, b -> -1, c -> -1, d -> -3,
e -> 1, f -> -3}, {a -> 3, b -> -1,
c -> 3, d -> 1, e -> 1, f -> 1}}
In[7]:=
(a*x^2 + b*x + c)*(d*x^2 + e*x + f) /.
{a -> -1, b -> -1, c -> -1, d -> -3,
e -> 1, f -> -3}
Out[7]=
(-3 + x - 3*x^2)*(-1 - x - x^2)
In[8]:=
(a*x^2 + b*x + c)*(d*x^2 + e*x + f) /.
{a -> 3, b -> -1, c -> 3, d -> 1, e -> 1,
f -> 1}
Out[8]=
(1 + x + x^2)*(3 - x + 3*x^2)
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