Difference between revisions of "ApCoCoA-1:Latte.Count"
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<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> | + | <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 | ||
| − | |||
| − | |||
| − | |||
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> | ||
| − | + | <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> | ||
| Line 17: | 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 number of lattice points in the given polyhedral P </item> | ||
| + | </itemize> | ||
| + | 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> | <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> | ||
| − | |||
Use S ::= QQ[x,y]; | Use S ::= QQ[x,y]; | ||
Equations := []; | Equations := []; | ||
| − | LesserEq := [x-1, x+ | + | 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); | ||
| + | |||
| + | 5 | ||
| + | ------------------------------- | ||
</example> | </example> | ||
</description> | </description> | ||
<types> | <types> | ||
| − | <type> | + | <type>apcocoaserver</type> |
</types> | </types> | ||
| − | <key> | + | <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> | + | <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 -------------------------------
