ApCoCoA:CharP.GBasisF1024

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<command>

   <title>CharP.GBasisF1024</title>
   <short_description>Computing a Groebner basis of a given ideal in F_1024.</short_description>

<syntax> CharP.GBasisF1024(Ideal:IDEAL):LIST </syntax>

   <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. <par/> This command computes a Groebner basis in the field F_1024 = (Z/(2))[x]/(x^10 + x^3 + x^2 + x + 1).

<itemize> <item>@param Ideal An Ideal in a Ring over Z, where the elements 0,...,1023 represent the elements of the finite field. For short, the binary representation of the number represents the coefficient vector of 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.</item>

<item>@return A Groebner Basis of the given ideal.</item> </itemize>

<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]; I:=Ideal(x-y^2,x^2+xy,y^3); -- WARNING: Coeffs are not in a field -- GBasis-related computations could fail to terminate or be wrong CharP.GBasisF1024(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 + 218x, x^2, xy]


</example>

   </description>
   <seealso>
     <see>GBasis</see>
    <see>Introduction to Groebner Basis in CoCoA</see>
   <see>Introduction to CoCoAServer</see>
   <see>CharP.GBasisF2</see> 
   <see>CharP.GBasisF4</see>
    <see>CharP.GBasisF8</see>
    <see>CharP.GBasisF16</see>
    <see>CharP.GBasisF32</see>
    <see>CharP.GBasisF64</see>
    <see>CharP.GBasisF128</see>
    <see>CharP.GBasisF256</see>
    <see>CharP.GBasisF512</see>
    <see>CharP.GBasisF2048</see>
    <see>CharP.GBasisModSquares</see>
    <see>Representation of finite fields</see>
  </seealso>

<types>

<type>groebner</type>
<type>ideal</type>
<type>apcocoaserver</type>

</types>

   <key>charP.GBasisF1024</key>
   <key>GBasisF1024</key>
   <key>finite field</key>
   <wiki-category>Package_charP</wiki-category>
 </command>