# ApCoCoA-1:Latte.Count

From ApCoCoAWiki

## 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 >= 0, y >= 0, x <= 1, x + y <= 1}: Use S ::= QQ[x,y]; Equations := []; LesserEq := [x-1, x+y-1]; GreaterEq := [x,y]; Latte.Count(Equations, LesserEq, GreaterEq);