# Difference between revisions of "ApCoCoA-1:IML.Solve"

## Solve

solve linear equation system

### Syntax

```IML.Solve(M:MAT, B:MAT):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. Please also not that you need an ApCoCoAServer with enabled IML support.

Let M and B be matrices defined over the ring of integers, a finite field or the field of rationals. This function tries to solve the linear equation system M*X = B by using the ApCoCoAServer supported by the IML library.

The return value will be a solution vector of the linear equation system or an empty matrix if no solution has been found.

#### Example

```Use Z/(19)[x];
M := BringIn(Mat([[1,3,4], [0,2,1]]));
B := BringIn(Mat([[1], [2]]));
IML.Solve(M, B);
-------------------------------
Mat([
[-2 % 19],
[1 % 19],
[0 % 19]
])
-------------------------------

Use Q[x];
M := Mat([ [1,3,4], [0,2,1], [1,3,4] ]);
B := Mat([ [1], [2], [0] ]);
IML.Solve(M, B);
-------------------------------
Mat([
[ ]
])
-------------------------------
```