Can sombody simplify this equation for me?

问题:

I know I can use Mathematica, but sadly I dont have one. I just want to find the A,B,C,D form matrix

| X1^3 x1^2 X1 1 |   |A|   |y0|
| X2^3 x2^2 X2 1 |   |B|   |y1|
| X3^3 x3^2 X3 1 | X |C| = |y2|
| X4^3 x4^2 X4 1 |   |D|   |y3|

I just want to find the simplified equations for A, B, C and D.

Actually I am trying to do a program in arduino that requires curve fitting using 4 points, so that I can predict the future points. I have seen this post , but parabola isn't accurate enough for my need.

I have already tried http://www.wolframalpha.com/.

linearSolve [{{(x1)^3, (x1)^2, x1, 1},
              {(x2)^3, (x2)^2, x2, 1},
              {(x3)^3, (x3)^2, x3, 1},
              {(x4)^3, (x4)^2, x4, 1}}, {{y1},{y2},{y3},{y4}}]

It returns a long result, which can be simplified. But, I cannot enter the full result in the search bar for simplifying (It gives me the error :Input Too Long!).

Any Ideas? Well I guess it would be possible in desktop versions.

Even after that, if the result is quite long, please substitute x1 = 0 and let me know the simplified result.

回答1:

// Input data: arrays x[] and y[]
// x[1],x[2],x[3],x[4] - X values
// y[1],y[2],y[3],y[4] - Y values

// Calculations
A = 0
B = 0
C = 0
D = 0
S1 = x[1] + x[2] + x[3] + x[4]
S2 = x[1]*x[2] + x[1]*x[3] + x[1]*x[4] + x[2]*x[3] + x[2]*x[4] + x[3]*x[4]
S3 = x[1]*x[2]*x[3] + x[1]*x[2]*x[4] + x[1]*x[3]*x[4] + x[2]*x[3]*x[4]
for i = 1 to 4 loop
   C0 = y[i]/(((4*x[i]-3*S1)*x[i]+2*S2)*x[i]-S3)
   C1 = C0*(S1 - x[i])
   C2 = S2*C0 - C1*x[i]
   C3 = S3*C0 - C2*x[i]
   A = A + C0
   B = B - C1
   C = C + C2
   D = D - C3
end-loop

// Result: A, B, C, D

回答2:

If you don't have Mathematica you can use wolframalpha

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