Difference between revisions of "ApCoCoA-1:CharP.BBasisMutantStrategyF2"
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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. | 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/> | <par/> | ||
| − | Please note that this function is a completely ApCoCoALib driven version of the function <ref>CharP.MBBasisF2</ref>. | + | 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 35: | Line 35: | ||
</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>CharP.MBBasisF2</see> | + | <see>ApCoCoA-1:CharP.MBBasisF2|CharP.MBBasisF2</see> |
</seealso> | </seealso> | ||
Revision as of 08:06, 7 October 2020
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
