ApCoCoA:CharP.GBasisF16

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 <command>
   <title>CharP.GBasisF16</title>
   <short_description>Computing a Groebner Basis of a given ideal in F_16.</short_description>

<syntax> CharP.GBasisF16(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_16 = (Z/(2))[x]/(x^4 + x^3 +1).

<itemize> <item>@param Ideal An Ideal in a Ring over Z, where the elements 0,...,15 represent the elements of the field F_16. 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 The 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]; -- 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.GBasisF16(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 + 8x, x^2, xy]


</example>

   </description>
   <seealso>
     <see>GBasis</see>
    <see>Introduction to CoCoAServer</see>
    <see>Introduction to Groebner Basis in CoCoA</see>
    <see>CharP.GBasisF2</see>
    <see>CharP.GBasisF4</see>
    <see>CharP.GBasisF8</see>
    <see>CharP.GBasisF32</see>
    <see>CharP.GBasisF64</see>
    <see>CharP.GBasisF128</see>
    <see>CharP.GBasisF256</see>
    <see>CharP.GBasisF512</see>
    <see>CharP.GBasisF1024</see>
    <see>CharP.GBasisF2048</see>
    <see>CharP.GBasisModSquares</see>
    <see>Representation of finite fields</see> 
  </seealso>
   <types>
     <type>apcocoaserver</type>
     <type>ideal</type>
     <type>groebner</type>
   </types>
   <key>charP.GBasisF16</key>
   <key>GBasisF16</key>
   <key>finite field</key>
   <wiki-category>Package_charP</wiki-category>
 </command>