ApCoCoA:CharP.GBasisF256

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Revision as of 21:02, 30 March 2008 by Dheldt (talk | contribs) (fixing formula)
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<command>

   <title>Char2.GBasisF256</title>
   <short_description>computing a gbasis of a given ideal in <formula>\mathbb{F}_{256}</formula></short_description>

<syntax> $char2.GBasisF256(Ideal):List </syntax>

   <description>

This command computes a Groebner basis in the field <formula> \mathbb{F}_{256} = (\mathbb{Z}_{\setminus(2)} [x])_{\setminus(x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + 1 )}</formula>. It uses the ApCoCoA Server and the ApCoCoALib's class RingF256.

The command's input is a an Ideal in a Ring over Z, where the elements 0,..., 255 represent the field's elements. Details on this representation can be found here. For short, the binary representation of the number represents the coefficient vector if the polynomial in the field, e.g. <formula> 11 = 8 + 2 + 1 = 2^3 + 2^1 + 2^0</formula> So the number <formula>11</formula> corresponds to the polynomial <formula>x^3 + x + 1</formula>.

   </description>
   <seealso>
     <see>GBasis</see>
   <see>char2.GBasisF2</see> 
   <see>char2.GBasisF4</see>
    <see>char2.GBasisF8</see>
    <see>char2.GBasisF16</see>
    <see>char2.GBasisF32</see>
    <see>char2.GBasisF64</see>
    <see>char2.GBasisF128</see>
    <see>char2.GBasisF512</see>
    <see>char2.GBasisF1024</see>
    <see>char2.GBasisF2048</see>
    <see>char2.GBasisF4096</see>
    <see>char2.GBasisModSquares</see>
 
  </seealso>
   <key>heldt</key>
   <key>char2.GBasisF256</key>
   <wiki-category>Package_char2</wiki-category>
 </command>