Difference between revisions of "ApCoCoA-1:GLPK.IPCSolve"
| Line 3: | Line 3: | ||
<short_description>Solves a system of polynomial equations over <tt>F_2</tt> for one solution in <tt>F_2^n</tt>.</short_description> | <short_description>Solves a system of polynomial equations over <tt>F_2</tt> for one solution in <tt>F_2^n</tt>.</short_description> | ||
<syntax> | <syntax> | ||
| − | GLPK.IPCSolve(F:LIST, QStrategy:INT, CStrategy:INT, MinMax:STRING) | + | GLPK.IPCSolve(F:LIST, QStrategy:INT, CStrategy:INT, MinMax:STRING):LIST |
</syntax> | </syntax> | ||
<description> | <description> | ||
| Line 16: | Line 16: | ||
<item>@param <em>CStrategy</em>: Strategy for cubic substitution. 0 - Standard; and 1 - Quadratic Partner;</item> | <item>@param <em>CStrategy</em>: Strategy for cubic substitution. 0 - Standard; and 1 - Quadratic Partner;</item> | ||
<item>@param <em>MinMax</em>: Optimization direction i.e. minimization (<quotes>Min</quotes>) or maximization (<quotes>Max</quotes>).</item> | <item>@param <em>MinMax</em>: Optimization direction i.e. minimization (<quotes>Min</quotes>) or maximization (<quotes>Max</quotes>).</item> | ||
| + | <item>@return A list containing a zero of the system F.</item> | ||
</itemize> | </itemize> | ||
Revision as of 12:14, 23 August 2011
GLPK.IPCSolve
Solves a system of polynomial equations over F_2 for one solution in F_2^n.
Syntax
GLPK.IPCSolve(F:LIST, QStrategy:INT, CStrategy:INT, MinMax:STRING):LIST
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.
This function finds one solution in F_2^n of a system of polynomial equations over the field F_2. It uses Integer Polynomial Conversion (IPC) along with some strategies from propositional logic to model a mixed integer linear programming problem. Then the modelled mixed integer linear programming problem is solved using glpk.
@param F: A List containing the polynomials of the given system.
@param QStrategy: Strategy for quadratic substitution. 0 - Standard; 1 - Linear Partner; 2 - Double Linear Partner; 3 - Quadratic Partner;
@param CStrategy: Strategy for cubic substitution. 0 - Standard; and 1 - Quadratic Partner;
@param MinMax: Optimization direction i.e. minimization ("Min") or maximization ("Max").
@return A list containing a zero of the system F.
Example
Use Z/(2)[x[1..4]];
F:=[
x[1]x[2] + x[2]x[3] + x[2]x[4] + x[3]x[4] + x[1] + x[3] + 1,
x[1]x[2] + x[1]x[3] + x[1]x[4] + x[3]x[4] + x[2] + x[3] + 1,
x[1]x[2] + x[1]x[3] + x[2]x[3] + x[3]x[4] + x[1] + x[4] + 1,
x[1]x[3] + x[2]x[3] + x[1]x[4] + x[2]x[4] + 1
];
QStrategy:=0;
CStrategy:=0;
MinMax:=<quotes>Max</quotes>;
-- Then we compute the solution with
GLPK.IPCSolve(F, QStrategy, CStrategy, MinMax);
-- The result will be the following:
Modelling the system as a mixed integer programming problem.
QStrategy: Standard, CStrategy: Standard.
Model is ready to solve with GLPK...
Solution Status: INTEGER OPTIMAL
Value of objective function: 2
[0, 1, 0, 1]
-------------------------------
Example
Use S::=Z/(2)[x[1..5]]; F:=[ x[1]x[5] + x[3]x[5] + x[4]x[5] + x[1] + x[4], x[1]x[2] + x[1]x[4] + x[3]x[4] + x[1]x[5] + x[2]x[5] + x[3]x[5] + x[1] + x[4] + x[5] + 1, x[1]x[2] + x[4]x[5] + x[1] + x[2] + x[4], x[1]x[4] + x[3]x[4] + x[2]x[5] + x[1] + x[2] + x[4] + x[5] + 1, x[1]x[4] + x[2]x[4] + x[3]x[4] + x[2]x[5] + x[4]x[5] + x[1] + x[2] + x[4] + x[5] ]; QStrategy:=1; CStrategy:=0; MinMax:=<quotes>Max</quotes>; -- Then we compute the solution with GLPK.IPCSolve(F, QStrategy, CStrategy, MinMax); -- The result will be the following: Modelling the system as a mixed integer programming problem. QStrategy: LinearPartner, CStrategy: Standard. Model is ready to solve with GLPK... Solution Status: INTEGER OPTIMAL Value of objective function: 4 [1, 1, 1, 1, 0] -------------------------------
Example
Use ZZ/(2)[x[1..3]];
F := [ x[1]x[2]x[3] + x[1]x[2] + x[2]x[3] + x[1] + x[3] +1,
x[1]x[2]x[3] + x[1]x[2] + x[2]x[3] + x[1] + x[2],
x[1]x[2] + x[2]x[3] + x[2]
];
QStrategy:=0;
CStrategy:=1;
MinMax:=<quotes>Max</quotes>;
-- Then we compute the solution with
GLPK.IPCSolve(F, QStrategy, CStrategy, MinMax);
-- The result will be the following:
Modelling the system as a mixed integer programming problem.
QStrategy: Standard, CStrategy: CubicParnterDegree2.
Model is ready to solve with GLPK...
Solution Status: INTEGER OPTIMAL
Value of objective function: 1
[0, 0, 1]
-------------------------------
