# Difference between revisions of "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):LIST
```

### 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. It alows to keep record of the order of rows inside the matrix using the parameter L1. If the matrix contains some rows which are already in echlon form then the parameter L2 represent them with 0 and all others with 1.

• @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.

```