In Xcas mode, Rref is simply the inert form of rref; namely, it returns rref without evaluating it. (See Section 5.56.3.) In Maple mode, the Rref command can additionally be used in conjunction with mod to find the reduced row echelon form of a matrix whose elements are in ℤ/pℤ.
Solve in ℤ/13ℤ:
⎧ ⎨ ⎩ |
|
Input (in Xcas mode):
Output:
rref | ⎛ ⎜ ⎜ ⎜ ⎝ | ⎡ ⎢ ⎢ ⎢ ⎣ |
| ⎤ ⎥ ⎥ ⎥ ⎦ | ⎞ ⎟ ⎟ ⎟ ⎠ |
To actually get the reduced echelon form, you can enter:
Input:
Output:
⎡ ⎢ ⎣ |
| ⎤ ⎥ ⎦ |
and conclude that x=3%13 and y=3%13.
Input (in Maple mode):
Output:
⎡ ⎢ ⎣ |
| ⎤ ⎥ ⎦ |
and again conclude that x=3%13 and y=3%13.