# ApCoCoA-1:Latte.Count

## Latte.Count

```Counts the lattice points of a polyhedral given by a number of linear constraints
```

### Syntax

```Latte.Count(Equations: LIST, LesserEq: LIST, GreaterEq: LIST):INT
```

### Syntax

```Latte.Count(Equations: LIST, LesserEq: LIST, GreaterEq: LIST, Dil: INT):INT
```

### 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.

• Equations: A list of linear polynomials, which are equivalent to the equality-part of the polyhedral constraints

• LesserEq: A list of linear polynomials, which are equivalent to the lower or equal-part of the polyhedral constraints

• LesserEq: A list of linear polynomials, which are equivalent to the greater or equal-part of the polyhedral constraints

• Dil: Integer > 0, factor for dilation of the polyhedral P, to count the lattice points of the polyhedral n*P

#### Example

```To count the lattice points in the polyhedral P = {x &gt;= 0, y &gt;= 0, x &lt;= 1, x + y &lt;= 1}:
Use S ::= QQ[x,y];
Equations := [];
LesserEq := [x-1, x+y-1];
GreaterEq := [x,y];
Latte.Count(Equations, LesserEq, GreaterEq);
```