# ApCoCoA-1:Slinalg.SEF

## Slinalg.SEF

Calculates the Echelon form of a sparse matrix over F2.

### Syntax

```Slinalg.SEF(NRow,NCol, Mat: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.

• @param NRow: Number of rows of matrix.

• @param NCol: Number of Columns of matrix.

• @return A list of lists containing the Echelon form of matrix.

#### Example

```-- We want to solve the system x^2+y^2-5=0,xy-2=0, using multi-homogenization, for adaptive precision.

Use S ::= QQ[x,y];             --  Define appropriate ring
M := [x^2+y^2-5,xy-2];
ConfigSet := [<quotes>MPTYPE: 2</quotes>];

-- Then we compute the solution with
Bertini.BCMSolve(M,ConfigSet);

-- And we achieve a list of lists containing finite solutions:
----------------------------------------
[[Vector(1000000000000017/1000000000000000, 145132717332349/15625000000000000000000000000),
Vector(49999999999999/25000000000000, -3537662353156057/100000000000000000000000000000)],
[Vector(-62500000000003/62500000000000, 4415730565392687/100000000000000000000000000000),
Vector(-499999999999983/250000000000000, -66866973306543/400000000000000000000000000)],
[Vector(999999999999983/500000000000000, -1787591178181031/50000000000000000000000000000),
Vector(1000000000000013/1000000000000000, 281412486737749/25000000000000000000000000000)],
[Vector(-499999999999999/250000000000000, -3956938527452181/1000000000000000000000000000000),
Vector(-9999999999999989/10000000000000000, -596634837824491/1250000000000000000000000000000)]]

--For other Bertini output files please refer to Bertini directory (.../ApCoCoA-1.2/Bertini/).
```