Difference between revisions of "ApCoCoA-1:CharP.GBasisF2"

From ApCoCoAWiki
(Added ApCoCoAServer note)
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  <command>
 
  <command>
 
     <title>Char2.GBasisF2</title>
 
     <title>Char2.GBasisF2</title>
     <short_description>computing a gbasis of a given ideal in <formula>\mathbb{F}_{2}</formula></short_description>
+
     <short_description>Computing a Groebner Basis of a given ideal in <formula>\mathbb{F}_{2}</formula>.</short_description>
 
<syntax>
 
<syntax>
$char2.GBasisF2(Ideal):List
+
Char2.GBasisF2(Ideal:IDEAL):LIST
 
</syntax>
 
</syntax>
 
     <description>
 
     <description>
{{ApCoCoAServer}}
+
<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.
 
+
<par/>
This command computes a Groebner basis in the field <formula> \mathbb{F}_{2} = (\mathbb{Z}_{\setminus(2)} </formula>. It uses the ApCoCoA Server and the ApCoCoALib's class [[ApCoCoALib:RingF2|RingF2]].
+
This command computes a Groebner Basis in the field <formula> \mathbb{F}_{2} = (\mathbb{Z}_{\setminus(2)} </formula>.
 
 
The command's input is a an Ideal in a Ring over Z, where the elements 0,..., 1 represent the field's elements. Details on this representation can be found [[ApCoCoA:Representation_of_finite_fields|here]].
 
  
 +
<itemize>
 +
<item>@param <em>Ideal</em> 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>
 
     </description>
 
     </description>
 
     <seealso>
 
     <seealso>
 
       <see>GBasis</see>
 
       <see>GBasis</see>
     <see>char2.GBasisF4</see>
+
     <see>Char2.GBasisF4</see>
     <see>char2.GBasisF8</see>
+
     <see>Char2.GBasisF8</see>
     <see>char2.GBasisF16</see>
+
     <see>Char2.GBasisF16</see>
     <see>char2.GBasisF32</see>
+
     <see>Char2.GBasisF32</see>
     <see>char2.GBasisF64</see>
+
     <see>Char2.GBasisF64</see>
     <see>char2.GBasisF128</see>
+
     <see>Char2.GBasisF128</see>
     <see>char2.GBasisF256</see>
+
     <see>Char2.GBasisF256</see>
     <see>char2.GBasisF512</see>
+
     <see>Char2.GBasisF512</see>
     <see>char2.GBasisF1024</see>
+
     <see>Char2.GBasisF1024</see>
     <see>char2.GBasisF2048</see>
+
     <see>Char2.GBasisF2048</see>
     <see>char2.GBasisF4096</see>
+
     <see>Char2.GBasisF4096</see>
     <see>char2.GBasisModSquares</see>
+
     <see>Char2.GBasisModSquares</see>
 
    
 
    
 
   </seealso>
 
   </seealso>
    <key>heldt</key>
 
 
     <key>char2.GBasisF2</key>
 
     <key>char2.GBasisF2</key>
 +
    <key>GBasisF2</key>
 
     <wiki-category>Package_char2</wiki-category>
 
     <wiki-category>Package_char2</wiki-category>
 
   </command>
 
   </command>

Revision as of 16:42, 22 April 2009

Char2.GBasisF2

Computing a Groebner Basis of a given ideal in <formula>\mathbb{F}_{2}</formula>.

Syntax

Char2.GBasisF2(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 <formula> \mathbb{F}_{2} = (\mathbb{Z}_{\setminus(2)} </formula>.

  • @param Ideal An Ideal in a Ring over Z, where the elements 0,1 represent the elements of the field.

  • @return The Groebner Basis of the given ideal.

See also

GBasis

Char2.GBasisF4

Char2.GBasisF8

Char2.GBasisF16

Char2.GBasisF32

Char2.GBasisF64

Char2.GBasisF128

Char2.GBasisF256

Char2.GBasisF512

Char2.GBasisF1024

Char2.GBasisF2048

Char2.GBasisF4096

Char2.GBasisModSquares