ApCoCoA-1:LinAlg.EF

LinAlg.EF

Computes a row echelon form of a matrix with record keeping.

Syntax

```LinAlg.EF(M:LIST, L1:LIST, L2:LIST):MAT
```

Description

Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.

This function allows you to compute a row echelon form of a matrix M defined over the field F_2.

• @param M: A List of Lists whose row echelon form to compute.

• @param L1: List of integers. For example, the integers could represent the order of lists in the list M.

• @param L2: List of integers. For example, the integers could be 0-1 to represent the lists already reduced(0) and to be reduced(1).

• @return A row echelon form of M together with lists L1 and L2.

Example

```Use ZZ/(2)[x,y];
M := [
[1, 1, 0, 1, 0],
[0, 1, 1, 0, 1],
[1, 0, 1, 0, 0],
[1, 1, 1, 0, 1]
];
-- order of lists in M
L1:=[1, 2, 3, 4];

-- 0 for lists which are already in echelon form and 1 for those to be reduced.
L2:=[0, 0, 1, 1];

LinAlg.EF(M, L1, L2);

-- CoCoAServer: computing Cpu Time = 0
-------------------------------
[ [[1, 1, 0, 1, 0], [0, 1, 1, 0, 1], [0, 0, 1, 1, 1], [0, 0, 0, 1, 1]], [1, 2, 4, 3], [0, 0, 1, 1]]

-- The last two lists represent the new order of lists in M.
```

Example

```Use ZZ/(2)[x,y];
M := [
[0, 1, 0, 1, 0],
[0, 1, 0, 0, 1],
[1, 0, 1, 1, 0],
[1, 1, 0, 0, 1]
];
-- order of lists in M
L1:=[1, 2, 3, 4];

-- 0 for lists which are already in echelon form and 1 for those to be reduced.
L2:=[0, 0, 1, 1];

LinAlg.EF(M, L1, L2);

-- CoCoAServer: computing Cpu Time = 0.015
-------------------------------
[[[1, 0, 1, 1, 0], [0, 1, 0, 1, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 1]], [3, 1, 4, 2], [1, 0, 1, 0]]
-------------------------------

-- The last two lists represent the new order of lists in M.

```