Cheta with base-change: preliminary results

[jaydfox]

Actually, since I'm trying to find the Taylor series, I don't worry about the factorials. So I work directly with the matrix above, where the first row is [1 -2 4 -8 16].

Inverting this and multiplying by 4!, or (n-1)! in general, I get back a matrix of integer coefficients. For this 5x5 matrix, I get:

Code:

[  0   0  24   0   0]
[  2 -16   0  16  -2]
[ -1  16 -30  16  -1]
[ -2   4   0  -4   2]
[  1  -4   6  -4   1]

Yes, exactly that's wat XI is for.
Using

Code:

´
  dim=5
  ScI = XI *FacI*PI *(dim-1)!

I get ScI (= Sc^-1 without general matrix-inversion!)

Code:

´
   0    0   24   0   0
   2  -16    0  16  -2
  -1   16  -30  16  -1
  -2    4    0  -4   2
   1   -4    6  -4   1

Yes, this is it! This is much faster than what I was using before!