# 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
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

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

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