Difference between revisions of "ApCoCoA-1:Latte.Ehrhart"

From ApCoCoAWiki
(Updated example. (Skaspar))
m (insert version info)
 
(2 intermediate revisions by 2 users not shown)
Line 1: Line 1:
 +
{{Version|1}}
 
<command>
 
<command>
 
<title>Latte.Ehrhart</title>
 
<title>Latte.Ehrhart</title>
Line 14: Line 15:
 
<item>@param <em>LesserEq</em>: A list of linear polynomials, which are equivalent to the lower or equal-part of the polyhedral constraints</item>
 
<item>@param <em>LesserEq</em>: A list of linear polynomials, which are equivalent to the lower or equal-part of the polyhedral constraints</item>
 
<item>@param <em>GreaterEq</em>: A list of linear polynomials, which are equivalent to the greater or equal-part of the polyhedral constraints</item>
 
<item>@param <em>GreaterEq</em>: A list of linear polynomials, which are equivalent to the greater or equal-part of the polyhedral constraints</item>
 +
<item>@return The Ehrhart-series (or the Taylor series expansion to degree n of the Ehrhart series) of the polyhedral P</item>
 +
</itemize>
 +
The following parameter is optional:
 +
<itemize>
 
<item>@param <em>Degree</em>: Integer n > 0, when using this parameter, the function computes the Taylor series expansion of the Ehrhart series to degree n</item>
 
<item>@param <em>Degree</em>: Integer n > 0, when using this parameter, the function computes the Taylor series expansion of the Ehrhart series to degree n</item>
<item>@return The Ehrhart-series (or the Taylor series expansion to degree n of the Ehrhart series) of the polyhedral P</item>
 
 
</itemize>
 
</itemize>
  
Line 37: Line 41:
 
<key>Ehrhart-series</key>
 
<key>Ehrhart-series</key>
 
<key>Latte.Ehrhart</key>
 
<key>Latte.Ehrhart</key>
<wiki-category>Package_latte</wiki-category>
+
<wiki-category>ApCoCoA-1:Package_latte</wiki-category>
 
</command>
 
</command>

Latest revision as of 10:10, 7 October 2020

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)
-------------------------------