### 2.48.5 LU decomposition (for TI compatibility) : `LU`

`LU` takes as argument a numeric square matrix A of size n and three variable names, `var1`, `var2` and `var3`.
`LU(A,var1,var2,var3)` returns P, a permutation matrix, and stores :

- a lower triangular matrix L, with 1 on the diagonal, in `var1`,
- an upper triangular matrix U in `var2`,
- the permutation matrix P, result of the command `LU`, in `var3`.

These matrix are such that

the equation A*x=B is equivalent to L*U*x=P*B.

Input :

`LU([[3,5],[4,5]],L,U,P)`

Output :

`[[0,1],[1,0]]`

Input :

`L`

Output :

`[[1,0],[0.75,1]]`

Input :

`U`

Output :

`[[4,5],[0,1.25]]`

Input :

`P`

Output :

`[[0,1],[1,0]]`