 | 正規化し.....;
In[1]:=
th = Pi/3;
L = {{Cos[th], -Sin[th]}, {Sin[th],
Cos[th]}};
Eliminate[{(a*1*{1, Sqrt[2]})/Sqrt[3] ==
{q, q^2} - {p, p^2},
(a*1*L . {1, Sqrt[2]})/Sqrt[3] ==
{r, r^2} - {p, p^2}}, a]
Out[3]=
5*q == 7*p + 2*Sqrt[6]*p - 2*r -
2*Sqrt[6]*r &&
(-15*Sqrt[2] + 18*Sqrt[3] + 30*p)*r ==
p*(-15*Sqrt[2] + 18*Sqrt[3] + 30*p) &&
(12*Sqrt[2] + 9*Sqrt[3])*r + 15*r^2 ==
p*(12*Sqrt[2] + 9*Sqrt[3] + 15*p)
In[4]:=
sol = Solve[%, {p, q, r}]
sol[[4]]
Out[4]=
{{q -> r, p -> r},
{q -> 1/10*(5*Sqrt[2] - 6*Sqrt[3]),
r -> 1/10*(5*Sqrt[2] - 6*Sqrt[3]),
p -> 1/10*(5*Sqrt[2] - 6*Sqrt[3])},
{q -> 1/10*(-4*Sqrt[2] - 3*Sqrt[3]),
p -> 1/10*(-4*Sqrt[2] - 3*Sqrt[3]),
r -> 1/10*(-4*Sqrt[2] - 3*Sqrt[3])},
{q -> 1/10*(5*Sqrt[2] + 6*Sqrt[3]),
r -> -(13/(5*Sqrt[2])),
p -> 1/10*(5*Sqrt[2] - 6*Sqrt[3])}}
Out[5]=
{q -> 1/10*(5*Sqrt[2] + 6*Sqrt[3]),
r -> -(13/(5*Sqrt[2])),
p -> 1/10*(5*Sqrt[2] - 6*Sqrt[3])}
In[6]:=
Simplify[Sqrt[({q, q^2} - {p, p^2}) .
({q, q^2} - {p, p^2}) /.
{q -> (1*(5*Sqrt[2] + 6*Sqrt[3]))/10,
r -> -(13/(5*Sqrt[2])),
p -> (1*(5*Sqrt[2] - 6*Sqrt[3]))/10}]]
Out[6]=
18/5
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