ApCoCoA-1:CharP.BBasisMutantStrategyF2: Difference between revisions
Initial version. |
Minor update. |
||
| Line 1: | Line 1: | ||
<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>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 25: | ||
]; | ]; | ||
-- 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> | ||
| Line 37: | Line 39: | ||
<see>Introduction to Groebner Basis in CoCoA</see> | <see>Introduction to Groebner Basis in CoCoA</see> | ||
<see>CharP.IMNLASolve</see> | <see>CharP.IMNLASolve</see> | ||
<see>CharP.IMBBasisF2</see> | <see>CharP.IMBBasisF2</see> | ||
<see>CharP.MBBasisF2</see> | |||
</seealso> | </seealso> | ||
Revision as of 17:31, 11 November 2011
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
