Difference between revisions of "ApCoCoA-1:Latte.Ehrhart"
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<command> | <command> | ||
<title>Latte.Ehrhart</title> | <title>Latte.Ehrhart</title> | ||
| − | <short_description> Computes the ehrhart series as a rational | + | <short_description>Computes the ehrhart series as a rational function for a polyhedral P given by a number of linear constraints.</short_description> |
<syntax> | <syntax> | ||
Latte.Ehrhart(Equations: LIST, LesserEq: LIST, GreaterEq: LIST):RATFUN | Latte.Ehrhart(Equations: LIST, LesserEq: LIST, GreaterEq: LIST):RATFUN | ||
| − | |||
| − | |||
| − | |||
Latte.Ehrhart(Equations: LIST, LesserEq: LIST, GreaterEq: LIST, Degree: INT):RATFUN | Latte.Ehrhart(Equations: LIST, LesserEq: LIST, GreaterEq: LIST, Degree: INT):RATFUN | ||
</syntax> | </syntax> | ||
<description> | <description> | ||
| − | + | <em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | |
<itemize> | <itemize> | ||
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<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> | ||
| − | |||
</itemize> | </itemize> | ||
<example> | <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) | ||
| + | ------------------------------- | ||
</example> | </example> | ||
</description> | </description> | ||
<types> | <types> | ||
| − | <type> | + | <type>apcocoaserver</type> |
</types> | </types> | ||
| − | <key> | + | <key>Latte</key> |
<key>Ehrhart</key> | <key>Ehrhart</key> | ||
<key>Ehrhart-series</key> | <key>Ehrhart-series</key> | ||
<key>Latte.Ehrhart</key> | <key>Latte.Ehrhart</key> | ||
| − | + | <wiki-category>ApCoCoA-1:Package_latte</wiki-category> | |
| − | <wiki-category>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) -------------------------------
