# 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

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

-- 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);

3

</example>