Difference between revisions of "ApCoCoA-1:CharP.GBasisF4"
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<command> | <command> | ||
<title>CharP.GBasisF4</title> | <title>CharP.GBasisF4</title> | ||
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<seealso> | <seealso> | ||
| − | <see>GBasis</see> | + | <see>ApCoCoA-1:GBasis|GBasis</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.GBasisF2</see> | + | <see>ApCoCoA-1:CharP.GBasisF2|CharP.GBasisF2</see> |
| − | <see>CharP.GBasisF8</see> | + | <see>ApCoCoA-1:CharP.GBasisF8|CharP.GBasisF8</see> |
| − | <see>CharP.GBasisF16</see> | + | <see>ApCoCoA-1:CharP.GBasisF16|CharP.GBasisF16</see> |
| − | <see>CharP.GBasisF32</see> | + | <see>ApCoCoA-1:CharP.GBasisF32|CharP.GBasisF32</see> |
| − | <see>CharP.GBasisF64</see> | + | <see>ApCoCoA-1:CharP.GBasisF64|CharP.GBasisF64</see> |
| − | <see>CharP.GBasisF128</see> | + | <see>ApCoCoA-1:CharP.GBasisF128|CharP.GBasisF128</see> |
| − | <see>CharP.GBasisF256</see> | + | <see>ApCoCoA-1:CharP.GBasisF256|CharP.GBasisF256</see> |
| − | <see>CharP.GBasisF512</see> | + | <see>ApCoCoA-1:CharP.GBasisF512|CharP.GBasisF512</see> |
| − | <see>CharP.GBasisF1024</see> | + | <see>ApCoCoA-1:CharP.GBasisF1024|CharP.GBasisF1024</see> |
| − | <see>CharP.GBasisF2048</see> | + | <see>ApCoCoA-1:CharP.GBasisF2048|CharP.GBasisF2048</see> |
| − | <see>CharP.GBasisModSquares</see> | + | <see>ApCoCoA-1:CharP.GBasisModSquares|CharP.GBasisModSquares</see> |
| − | <see>Representation of finite fields</see> | + | <see>ApCoCoA-1:Representation of finite fields|Representation of finite fields</see> |
</seealso> | </seealso> | ||
Latest revision as of 09:55, 7 October 2020
| This article is about a function from ApCoCoA-1. |
CharP.GBasisF4
Computing a Groebner Basis of a given ideal in F_4.
Syntax
CharP.GBasisF4(Ideal:IDEAL):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 command computes a Groebner basis in the field F_4 = (Z/(2))[x]/(x^2 + x +1).
@param Ideal An Ideal in a Ring over Z, where the elements 0,...,3 represent the elements of the field F_4. For short, the binary representation of the number represents the coefficient vector if the polynomial in the field, e.g. 11 = 8 + 2 + 1 = 2^3 + 2^1 + 2^0. So the number 11 corresponds to the polynomial x^3 + x + 1.
@return A Groebner Basis of the given ideal.
Example
Use R::=QQ[x,y,z]; I:=Ideal(x-y^2,x^2+xy,y^3); GBasis(I); [x^2 + xy, -y^2 + x, -xy] ------------------------------- Use Z::=ZZ[x,y,z]; -- WARNING: Coeffs are not in a field -- GBasis-related computations could fail to terminate or be wrong ------------------------------- I:=Ideal(x-y^2,x^2+xy,y^3); CharP.GBasisF4(I); -- WARNING: Coeffs are not in a field -- GBasis-related computations could fail to terminate or be wrong -- CoCoAServer: computing Cpu Time = 0 ------------------------------- [y^2 + 2x, x^2, xy] -------------------------------
See also
Introduction to Groebner Basis in CoCoA
Representation of finite fields
