Difference between revisions of "ApCoCoA-1:CharP.MBBasisF2"
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(New page: <command> <title>CharP.MBBasis</title> <short_description>Computing a Border Basis of a given ideal over <tt>F_2</tt>. </short_description> <syntax> CharP.MBBasisF2(F:LIST):LIST </...) |
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<syntax> | <syntax> | ||
CharP.MBBasisF2(F:LIST):LIST | CharP.MBBasisF2(F:LIST):LIST | ||
| + | CharP.MBBasisF2(F:LIST, NSol: INT):LIST | ||
</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. | <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. | ||
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<par/> | <par/> | ||
| − | Let <tt>f_1</tt>, ... , <tt>f_m</tt> is a set of polynomials which generate a zero-dimensional ideal. This function computes a Border Basis of the zero-dimensional radical ideal generated by <tt>f_1</tt>, ... , <tt>f_m</tt> and the field polynomials. | + | Let <tt>f_1</tt>, ... , <tt>f_m</tt> is a set of polynomials which generate a zero-dimensional ideal. This function computes a Border Basis of the zero-dimensional radical ideal generated by <tt>f_1</tt>, ... , <tt>f_m</tt> and the field polynomials. Furthermore, it uses mutant strategy to compute a U-stable span. |
| + | If you want to use the second version with the parameter NSol, you need to provide the exact number of <tt>F_2</tt> rational solutions. The first version is safe to use if you do not know the exact number of <tt>F_2</tt> rational solutions. | ||
<itemize> | <itemize> | ||
<item>@param <em>F:</em> List of polynomials.</item> | <item>@param <em>F:</em> List of polynomials.</item> | ||
| + | <item>@param <em>NSol:</em> Number of <tt>F_2</tt> rational solutions. </item> | ||
<item>@return A Border Basis of zero-dimensional radical ideal generated by the polynomials in F and the field polynomials. </item> | <item>@return A Border Basis of zero-dimensional radical ideal generated by the polynomials in F and the field polynomials. </item> | ||
</itemize> | </itemize> | ||
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-- Then we compute the solution with | -- Then we compute the solution with | ||
| − | CharP. | + | CharP.MBBasisF2(F); |
-- And we achieve the following information on the screen together with the solution at the end. | -- And we achieve the following information on the screen together with the solution at the end. | ||
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</example> | </example> | ||
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-- Then we compute the solution with | -- Then we compute the solution with | ||
| − | CharP. | + | CharP.MBBasisF2(F,NSol); |
-- And we achieve the following information on the screen. | -- And we achieve the following information on the screen. | ||
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</example> | </example> | ||
Revision as of 13:18, 28 April 2011
CharP.MBBasis
Computing a Border Basis of a given ideal over F_2.
Syntax
CharP.MBBasisF2(F:LIST):LIST CharP.MBBasisF2(F:LIST, NSol: INT):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.
Let f_1, ... , f_m is a set of polynomials which generate a zero-dimensional ideal. This function computes a Border Basis of the zero-dimensional radical ideal generated by f_1, ... , f_m and the field polynomials. Furthermore, it uses mutant strategy to compute a U-stable span.
If you want to use the second version with the parameter NSol, you need to provide the exact number of F_2 rational solutions. The first version is safe to use if you do not know the exact number of F_2 rational solutions.
@param F: List of polynomials.
@param NSol: Number of F_2 rational solutions.
@return A Border Basis of zero-dimensional radical ideal generated by the polynomials in F and the field polynomials.
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
];
-- Then we compute the solution with
CharP.MBBasisF2(F);
-- And we achieve the following information on the screen together with the solution at the end.
----------------------------------------
Example
Use Z/(2)[x[1..4]];
F:=[
x[2]x[3] + x[1]x[4] + x[2]x[4] + x[3]x[4] + x[1] + x[2] + x[3] + x[4],
x[2]x[3] + x[2]x[4] + x[3]x[4] + x[2] + x[3] + x[4],
x[1]x[2] + x[2]x[3] + x[2]x[4] + x[3]x[4] + x[1] + x[2],
x[1]x[2] + x[2]x[3] + x[2]x[4] + x[3]x[4] + x[1] + x[2]
];
-- Solution is not unique i.e. [0, 1, 1, 1], [0, 0, 0, 0], and [1, 1, 1, 1] are solutions
-- Then we compute the solution with
CharP.MBBasisF2(F,NSol);
-- And we achieve the following information on the screen.
----------------------------------------
See also
Introduction to Groebner Basis in CoCoA
