ApCoCoA-1:Latte.Ehrhart

This article is about a function from ApCoCoA-1.

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)
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