# ApCoCoA:Latte.Count

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## 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
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.

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

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

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

• @return The number of lattice points in the given polyhedral P

The following parameter is optional:

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

IMPORTANT: If the given polyhedral is unbound, the output of LattE is zero, as for an empty polyhedral.

#### Example

```Use S ::= QQ[x,y];
Equations := [];
LesserEq := [1/2*x-1, x+1/3y-1];
GreaterEq := [x,y];
Latte.Count(Equations, LesserEq, GreaterEq);

5
-------------------------------
```