ApCoCoA:Latte.Count

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<command> <title>Latte.Count</title> <short_description>Counts the lattice points of a polyhedral given by a number of linear constraints.</short_description> <syntax> Latte.Count(Equations: LIST, LesserEq: LIST, GreaterEq: LIST):INT Latte.Count(Equations: LIST, LesserEq: LIST, GreaterEq: LIST, Dil: INT):INT </syntax>

<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.

<itemize> <item>@param Equations: A list of linear polynomials, which are equivalent to the equality-part of the polyhedral constraints</item> <item>@param LesserEq: A list of linear polynomials, which are equivalent to the lower or equal-part of the polyhedral constraints</item> <item>@param GreaterEq: 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 Dil: Integer > 0, factor for dilation of the polyhedral P, to count the lattice points of the polyhedral n*P</item> </itemize>

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);

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</example>

</description> <types>

 <type>apcocoaserver</type>

</types> <key>Latte</key> <key>Count</key> <key>Latte.Count</key> <key>latte.Count</key> <wiki-category>Package_latte</wiki-category> </command>