# ApCoCoA-1:Latte.Ehrhart

## Latte.Ehrhart

Computes the ehrhart series as a rational function for a polyhedral P given by a number of linear constraints.

### Syntax

Latte.Ehrhart(Equations: LIST, LesserEq: LIST, GreaterEq: LIST):RATFUN Latte.Ehrhart(Equations: LIST, LesserEq: LIST, GreaterEq: LIST, Degree: INT):RATFUN

### 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 Ehrhart-series (or the Taylor series expansion to degree n of the Ehrhart series) of the polyhedral P

The following parameter is optional:

@param

*Degree*: Integer n > 0, when using this parameter, the function computes the Taylor series expansion of the Ehrhart series to degree n

#### Example

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