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

From ApCoCoAWiki
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  <command>
 
  <command>
 
     <title>Char2.GBasisF2</title>
 
     <title>Char2.GBasisF2</title>
     <short_description>Computing a Groebner Basis of a given ideal in F_2.</short_description>
+
     <short_description>Computing a Groebner Basis of a given ideal in <tt>F_2</tt>.</short_description>
 
<syntax>
 
<syntax>
 
Char2.GBasisF2(Ideal:IDEAL):LIST
 
Char2.GBasisF2(Ideal:IDEAL):LIST
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<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.
 
<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/>
 
<par/>
This command computes a Groebner Basis in the field F_2 = Z/(2).   
+
This command computes a Groebner Basis in the field <tt>F_2 = Z/(2)</tt>.   
  
 
<itemize>
 
<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>
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<item>@param <em>Ideal</em> An Ideal in a Ring over <tt>Z</tt>, where the elements <tt>0,1</tt> represent the elements of the field.</item>
 
<item>@return The Groebner Basis of the given ideal.</item>
 
<item>@return The Groebner Basis of the given ideal.</item>
 
</itemize>
 
</itemize>
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     <see>Char2.GBasisF1024</see>
 
     <see>Char2.GBasisF1024</see>
 
     <see>Char2.GBasisF2048</see>
 
     <see>Char2.GBasisF2048</see>
    <see>Char2.GBasisF4096</see>
 
 
     <see>Char2.GBasisModSquares</see>
 
     <see>Char2.GBasisModSquares</see>
 
     <see>Representation of finite fields</see>
 
     <see>Representation of finite fields</see>

Revision as of 08:24, 14 July 2009

Char2.GBasisF2

Computing a Groebner Basis of a given ideal in F_2.

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 F_2 = Z/(2).

  • @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.

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);
Char2.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]
-------------------------------


See also

GBasis

Introduction to CoCoAServer

Introduction to Groebner Basis in CoCoA

Char2.GBasisF4

Char2.GBasisF8

Char2.GBasisF16

Char2.GBasisF32

Char2.GBasisF64

Char2.GBasisF128

Char2.GBasisF256

Char2.GBasisF512

Char2.GBasisF1024

Char2.GBasisF2048

Char2.GBasisModSquares

Representation of finite fields