#範例2-17：用4次多項式近似sin積分
#已經知道5個點舒服
#x1=0, x2=0.25, x3=0.5, x4=0.75, x5=1
#y1=0, y2=𝟎.𝟎𝟗𝟖𝟎𝟏𝟕, y3=𝟎.𝟑𝟖𝟐𝟔𝟖𝟑, y4=𝟎.𝟕𝟕𝟑𝟎𝟏,y5=1
#求4次多項式 = a0 + a1×x + a2*x^2 + a3*x^3 + a4*x^4
#解出多項式的係數（a0, a1, a2, a3, a4)
from sympy import *
x0,x1,x2,x3,x4 = symbols('x0 x1 x2 x3 x4')
#注意：M矩陣的最右邊=y=轉換後座標
A = Matrix([
    [1,0,0,0,0,0],
    [1,0.25,0.25**2,0.25**3,0.25**4,0.098017],
    [1,0.5,0.5**2,0.5**3,0.5**4,0.382683],
    [1,0.75,0.75**2,0.75**3,0.75**4,0.77301],
    [1,1,1,1,1,1]
    ])
ans = solve_linear_system(A, x0,x1,x2,x3,x4)
print('X=', ans)