# ApCoCoA-1:CharP.LAAlgorithm

## CharP.LAAlgorithm

Computes the unique F_2-rational zero of a given polynomial system over F_2.

### Syntax

```CharP.LAAlgorithm(F: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 computes the unique zero in F_2^n of a polynomial system over F_2 . It uses LA-Algorithm to find the unique zero. The LA-Algorithm generates a sequence of linear systems to solve the given system. The LA-Algorithm can find the unique zero only. If the given polynomial system has more than one zero's in F_2^n then this function does not find any zero. In this case the trivial solution is given. To solve linear systems naive Gaußian elimination is used.

• @param F: List of polynomials of given system.

• @return The unique solution of the given system in F_2^n.

#### Example

```Use Z/(2)[x[1..4]];
F:=[
xx + xx + xx + xx + x + x + 1,
xx + xx + xx + xx + x + x + 1,
xx + xx + xx + xx + x + x + 1,
xx + xx + xx + xx + 1
];

-- Then we compute the solution with
CharP.LAAlgorithm(F);

[0, 1, 0, 1]

```

#### Example

```Use Z/(2)[x[1..4]];
F:=[
xx + xx + xx + xx + x + x + x + x,
xx + xx + xx + x + x + x,
xx + xx + xx + xx + x + x,
xx + xx + xx + xx + x + x
];

-- Solution is not unique i.e. [0, 1, 1, 1], [0, 0, 0, 0], and [1, 1, 1, 1] are solutions

-- Then we compute the solution with
CharP.LAAlgorithm(F);

[0, 0, 0, 0]

```