Difference between revisions of "ApCoCoA-1:CharP.BBasisMutantStrategyF2"
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<command> | <command> | ||
| − | <title> | + | <title>CharP.BBasisMutantStrategyF2</title> |
<short_description>Computes a Border Basis of a given ideal over <tt>F_2</tt>. </short_description> | <short_description>Computes a Border Basis of a given ideal over <tt>F_2</tt>. </short_description> | ||
<syntax> | <syntax> | ||
| − | + | CharP.BBasisMutantStrategyF2(I:IDEAL):LIST of POLY | |
</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. | ||
<par/> | <par/> | ||
| − | Let <em>I</em> be a zero-dimensional ideal over a polynomial ring with coefficient ring | + | Let <em>I</em> be a zero-dimensional ideal over a polynomial ring with coefficient ring F_2. This function computes a border basis of the zero-dimensional radical ideal generated by <em>I</em> and the field polynomials. Furthermore, it uses the Mutant Strategy for stable span computations. |
| + | <par/> | ||
| + | Please note that this function is a completely ApCoCoALib driven version of the function <ref>ApCoCoA-1:CharP.MBBasisF2|CharP.MBBasisF2</ref>. | ||
<itemize> | <itemize> | ||
<item>@param <em>I</em> A zero-dimensional ideal.</item> | <item>@param <em>I</em> A zero-dimensional ideal.</item> | ||
| Line 23: | Line 26: | ||
]; | ]; | ||
| − | -- Then we compute a | + | -- Then we compute a border basis with |
| − | + | CharP.BBasisMutantStrategyF2(Ideal(F)); | |
| + | -- Result is | ||
[x[4] + 1, x[3], x[2] + 1, x[1]] | [x[4] + 1, x[3], x[2] + 1, x[1]] | ||
| − | |||
</example> | </example> | ||
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</description> | </description> | ||
<seealso> | <seealso> | ||
| − | <see>CharP.MXLSolve</see> | + | <see>ApCoCoA-1:CharP.MXLSolve|CharP.MXLSolve</see> |
| − | <see>Introduction to CoCoAServer</see> | + | <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see> |
| − | <see>Introduction to Groebner Basis in CoCoA</see> | + | <see>ApCoCoA-1:Introduction to Groebner Basis in CoCoA|Introduction to Groebner Basis in CoCoA</see> |
| − | <see>CharP.IMNLASolve</see> | + | <see>ApCoCoA-1:CharP.IMNLASolve|CharP.IMNLASolve</see> |
| − | <see>CharP.IMBBasisF2</see> | + | <see>ApCoCoA-1:CharP.IMBBasisF2|CharP.IMBBasisF2</see> |
| + | <see>ApCoCoA-1:CharP.MBBasisF2|CharP.MBBasisF2</see> | ||
</seealso> | </seealso> | ||
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<key>bbasismutantstrategyf2</key> | <key>bbasismutantstrategyf2</key> | ||
<key>finite field</key> | <key>finite field</key> | ||
| − | <wiki-category>Package_charP</wiki-category> | + | <wiki-category>ApCoCoA-1:Package_charP</wiki-category> |
</command> | </command> | ||
Latest revision as of 09:53, 7 October 2020
| This article is about a function from ApCoCoA-1. |
CharP.BBasisMutantStrategyF2
Computes a Border Basis of a given ideal over F_2.
Syntax
CharP.BBasisMutantStrategyF2(I:IDEAL):LIST of POLY
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 I be a zero-dimensional ideal over a polynomial ring with coefficient ring F_2. This function computes a border basis of the zero-dimensional radical ideal generated by I and the field polynomials. Furthermore, it uses the Mutant Strategy for stable span computations.
Please note that this function is a completely ApCoCoALib driven version of the function CharP.MBBasisF2.
@param I A zero-dimensional ideal.
@return A border basis of the zero-dimensional radical ideal generated by the Ideal I 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 a border basis with
CharP.BBasisMutantStrategyF2(Ideal(F));
-- Result is
[x[4] + 1, x[3], x[2] + 1, x[1]]
See also
Introduction to Groebner Basis in CoCoA
