Difference between revisions of "ApCoCoA-1:GLPK.L01PSolve"

From ApCoCoAWiki
(New page: <command> <title>GLPK.MIPSolve</title> <short_description>Solving linear programmes.</short_description> <syntax> GLPK.MIPSolve(Objective_f:POLY, EQ_Poly:LIST, LE_Poly:LIST, GE_Poly:LIST, ...)
 
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<command>
 
<command>
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<title>GLPK.MIPSolve</title>
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<title>GLPK.L01PSolve</title>
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<short_description>Solving linear programmes.</short_description>
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<short_description>Solve a system of polynomial equations over <tt>F_2</tt> for one solution in <tt>F_2^n</tt>.</short_description>
 
<syntax>
 
<syntax>
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GLPK.MIPSolve(Objective_f:POLY, EQ_Poly:LIST, LE_Poly:LIST, GE_Poly:LIST, Bounds:LIST, IntNum:LIST, Binaries:LIST, MinMax:STRING)
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GLPK.L01PSolve(F:LIST, CuttingNumber:INT, QStrategy:INT, CStrategy:INT, MinMax:STRING)
 
</syntax>
 
</syntax>
 
<description>
 
<description>
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<itemize>
 
<itemize>
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<item>@param <em>Objective_f</em>: A linear polynomial which is equivalent to the linear objective function.</item>
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<item>@param <em>F</em>: A List containing the polynomials of the given system.</item>  
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<item>@param <em>EQ_Poly</em>: List of linear polynomials, which are equivalent to the equality-part in the list of conditions.</item>
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<item>@param <em>CuttingNumber</em>: Maximal support-length of the linear polynomials for conversion to CNF. The possible value could be from 3 to 6. </item>
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<item>@param <em>LE_Poly</em>: List of linear polynomials, which are equivalent to the lower or equal-part in the list of conditions.</item>
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<item>@param <em>QStrategy</em>: Strategy for quadratic substitution. 0 - Standard; 1 - Linear Partner; and 2 - Double Linear Partner;</item>
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<item>@param <em>GE_Poly</em>: List of linear polynomials, which are equivalent to the greater or equal-part in the list of conditions.</item>
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<item>@param <em>CStrategy</em>: Strategy for cubic substitution. 0 - Standard; and 1 - Quadratic Partner;</item>
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<item>@param <em>Bounds</em>: List of lists with two elements. Each List contains the lower and upper bounds for each variable. You can choose between INT or RAT for the type of each bound, if you type in a (empty) string, then it means minus infinity (first place) or plus infinity (second place).</item>
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<item>@param <em>MinMax</em>: Optimization direction i.e. minimization (<quotes>Min</quotes>) or maximization (<quotes>Max</quotes>).</item>
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<item>@param <em>IntNum</em>: List of variables, which should be integer. <em>Note</em>: For each variable in this list, the borders get rounded (lower bound: up and upper bound: down). In the case that the lower rounded bound becomes greater then the upper rounded bound, glpk returns: Solution Status: INTEGER UNDEFINED - Value of objective function: 0.</item>
 
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<item>@param <em>Binaries</em>: List of variables, which should be binaries (0 or 1).</item>
 
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<item>@param <em>MinMax</em>: Minimization (<quotes>Min</quotes>) or maximization (<quotes>Max</quotes>), that's the question.</item>
 
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<item>@return List of linear polynomials, the zeros of the polynomials are the points where the optimal value of the objective function is achieved</item>
 
 
</itemize>
 
</itemize>
  

Revision as of 14:28, 7 December 2010

GLPK.L01PSolve

Solve a system of polynomial equations over F_2 for one solution in F_2^n.

Syntax

GLPK.L01PSolve(F:LIST, CuttingNumber:INT, QStrategy:INT, CStrategy:INT, MinMax:STRING)

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 F: A List containing the polynomials of the given system.

  • @param CuttingNumber: Maximal support-length of the linear polynomials for conversion to CNF. The possible value could be from 3 to 6.

  • @param QStrategy: Strategy for quadratic substitution. 0 - Standard; 1 - Linear Partner; and 2 - Double Linear Partner;

  • @param CStrategy: Strategy for cubic substitution. 0 - Standard; and 1 - Quadratic Partner;

  • @param MinMax: Optimization direction i.e. minimization ("Min") or maximization ("Max").

Example

-- We want to maximize the Function y = - 1/2x, 
-- with the two conditions y ≤ 6 - 3/4x and y ≥ 1 - x and the bounds 0 ≤ x ≤ 6 and 1/3 ≤ y ≤ 4.

-- We prename the input of GLPK.MIPSolve-function.
Use S::=QQ[x,y];
OF := 1/2x + y;
LE := [3/4x + y - 6];
GE := [x + y - 1];
Bounds:=[[0,6], [1/3,4]];
IntNum:=[x,y];

-- Then we compute the solution with
GLPK.MIPSolve(OF, [], LE, GE, Bounds, IntNum, [], <quotes>Max</quotes>);


-- And we achieve:
Solution Status: INTEGER OPTIMAL
Value of objective function: 5
[x - 2, y - 4]





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