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

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{{Version|1}}
 
<command>
 
<command>
 
<title>Latte.Count</title>
 
<title>Latte.Count</title>
<short_description> Counts the lattice points of a polyhedral given by a number of linear constraints</short_description>
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<short_description>Counts the lattice points of a polyhedral given by a number of linear constraints.</short_description>
 
<syntax>
 
<syntax>
 
Latte.Count(Equations: LIST, LesserEq: LIST, GreaterEq: LIST):INT
 
Latte.Count(Equations: LIST, LesserEq: LIST, GreaterEq: LIST):INT
</syntax>
 
 
<syntax>
 
 
Latte.Count(Equations: LIST, LesserEq: LIST, GreaterEq: LIST, Dil: INT):INT
 
Latte.Count(Equations: LIST, LesserEq: LIST, GreaterEq: LIST, Dil: INT):INT
 
</syntax>
 
</syntax>
  
 
<description>
 
<description>
{{ApCoCoAServer}}
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<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>
<item><em>Equations</em>: A list of linear polynomials, which are equivalent to the equality-part of the polyhedral constraints</item>
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<item>@param <em>Equations</em>: A list of linear polynomials, which are equivalent to the equality-part of the polyhedral constraints</item>
<item><em>LesserEq</em>: A list of linear polynomials, which are equivalent to the lower or equal-part of the polyhedral constraints</item>
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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><em>LesserEq</em>: A list of linear polynomials, which are equivalent to the greater or equal-part of the polyhedral constraints</item>
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<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><em>Dil</em>: Integer > 0, factor for dilation of the polyhedral P, to count the lattice points of the polyhedral n*P</item>
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<item>@return The number of lattice points in the given polyhedral P </item>
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</itemize>
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The following parameter is optional:
 +
<itemize>
 +
<item>@param <em>Dil</em>: Integer > 0, factor for dilation of the polyhedral P, to count the lattice points of the polyhedral n*P</item>
 
</itemize>
 
</itemize>
 +
 +
<em>IMPORTANT:</em> If the given polyhedral is unbound, the output of LattE is zero, as for an empty polyhedral.
  
 
<example>
 
<example>
To count the lattice points in the polyhedral P = {x &gt;= 0, y &gt;= 0, x &lt;= 1, x + y &lt;= 1}:
 
 
Use S ::= QQ[x,y];
 
Use S ::= QQ[x,y];
 
Equations := [];
 
Equations := [];
LesserEq := [x-1, x+y-1];
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LesserEq := [1/2*x-1, x+1/3y-1];
 
GreaterEq := [x,y];
 
GreaterEq := [x,y];
 
Latte.Count(Equations, LesserEq, GreaterEq);
 
Latte.Count(Equations, LesserEq, GreaterEq);
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 +
5
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-------------------------------
 
</example>
 
</example>
  
 
</description>
 
</description>
 
<types>
 
<types>
   <type>cocoaserver</type>
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   <type>apcocoaserver</type>
 
</types>
 
</types>
<key>LattE</key>
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<key>Latte</key>
 
<key>Count</key>
 
<key>Count</key>
 
<key>Latte.Count</key>
 
<key>Latte.Count</key>
 
<key>latte.Count</key>
 
<key>latte.Count</key>
<wiki-category>Package_latte</wiki-category>
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<wiki-category>ApCoCoA-1:Package_latte</wiki-category>
 
</command>
 
</command>

Latest revision as of 10:09, 7 October 2020

This article is about a function from ApCoCoA-1.

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

  • @return The number of lattice points in the given polyhedral P

The following parameter is optional:

  • @param Dil: Integer > 0, factor for dilation of the polyhedral P, to count the lattice points of the polyhedral n*P

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

Example

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

5
-------------------------------