ApCoCoA:CharP.GBasisF2

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<command>
   <title>CharP.GBasisF2</title>
   <short_description>Computing a Groebner Basis of a given ideal in F_2.</short_description>

<syntax> CharP.GBasisF2(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_2 = Z/(2).

<itemize> <item>@param Ideal An Ideal in a Ring over Z, where the elements 0,1 represent the elements of the field.</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.GBasisF2(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 + x, x^2, xy]


</example>

   </description>
   <seealso>
     <see>GBasis</see>
    <see>Introduction to CoCoAServer</see>
    <see>Introduction to Groebner Basis in CoCoA</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.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.GBasisF2</key>
   <key>GBasisF2</key>
   <key>finite field</key>
   <wiki-category>Package_charP</wiki-category>
 </command>