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

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  <command>
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  {{Version|1}}
     <title>Char2.GBasisF2</title>
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<command>
     <short_description>Computing a Groebner Basis of a given ideal in F_2.</short_description>
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     <title>CharP.GBasisF2</title>
 +
     <short_description>Computing a Groebner Basis of a given ideal in <tt>F_2</tt>.</short_description>
 
<syntax>
 
<syntax>
Char2.GBasisF2(Ideal:IDEAL):LIST
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CharP.GBasisF2(Ideal:IDEAL):LIST
 
</syntax>
 
</syntax>
 
     <description>
 
     <description>
 
<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).   
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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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-------------------------------
 
-------------------------------
 
I:=Ideal(x-y^2,x^2+xy,y^3);
 
I:=Ideal(x-y^2,x^2+xy,y^3);
Char2.GBasisF2(I);
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CharP.GBasisF2(I);
 
-- WARNING: Coeffs are not in a field
 
-- WARNING: Coeffs are not in a field
 
-- GBasis-related computations could fail to terminate or be wrong
 
-- GBasis-related computations could fail to terminate or be wrong
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     </description>
 
     </description>
 
     <seealso>
 
     <seealso>
       <see>GBasis</see>
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       <see>ApCoCoA-1:GBasis|GBasis</see>
     <see>Introduction to CoCoAServer</see>
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     <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see>
     <see>Introduction to Groebner Basis in CoCoA</see>
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     <see>ApCoCoA-1:Introduction to Groebner Basis in CoCoA|Introduction to Groebner Basis in CoCoA</see>
     <see>Char2.GBasisF4</see>
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     <see>ApCoCoA-1:CharP.GBasisF4|CharP.GBasisF4</see>
     <see>Char2.GBasisF8</see>
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     <see>ApCoCoA-1:CharP.GBasisF8|CharP.GBasisF8</see>
     <see>Char2.GBasisF16</see>
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     <see>ApCoCoA-1:CharP.GBasisF16|CharP.GBasisF16</see>
     <see>Char2.GBasisF32</see>
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     <see>ApCoCoA-1:CharP.GBasisF32|CharP.GBasisF32</see>
     <see>Char2.GBasisF64</see>
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     <see>ApCoCoA-1:CharP.GBasisF64|CharP.GBasisF64</see>
     <see>Char2.GBasisF128</see>
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     <see>ApCoCoA-1:CharP.GBasisF128|CharP.GBasisF128</see>
     <see>Char2.GBasisF256</see>
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     <see>ApCoCoA-1:CharP.GBasisF256|CharP.GBasisF256</see>
     <see>Char2.GBasisF512</see>
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     <see>ApCoCoA-1:CharP.GBasisF512|CharP.GBasisF512</see>
     <see>Char2.GBasisF1024</see>
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     <see>ApCoCoA-1:CharP.GBasisF1024|CharP.GBasisF1024</see>
     <see>Char2.GBasisF2048</see>
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     <see>ApCoCoA-1:CharP.GBasisF2048|CharP.GBasisF2048</see>
     <see>Char2.GBasisF4096</see>
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     <see>ApCoCoA-1:CharP.GBasisModSquares|CharP.GBasisModSquares</see>
    <see>Char2.GBasisModSquares</see>
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     <see>ApCoCoA-1:Representation of finite fields|Representation of finite fields</see>
     <see>Representation of finite fields</see>
 
 
   </seealso>
 
   </seealso>
  
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     </types>
 
     </types>
  
     <key>char2.GBasisF2</key>
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     <key>charP.GBasisF2</key>
 
     <key>GBasisF2</key>
 
     <key>GBasisF2</key>
 
     <key>finite field</key>
 
     <key>finite field</key>
     <wiki-category>Package_char2</wiki-category>
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     <wiki-category>ApCoCoA-1:Package_charP</wiki-category>
 
   </command>
 
   </command>

Latest revision as of 09:54, 7 October 2020

This article is about a function from ApCoCoA-1.

CharP.GBasisF2

Computing a Groebner Basis of a given ideal in F_2.

Syntax

CharP.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);
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]
-------------------------------


See also

GBasis

Introduction to CoCoAServer

Introduction to Groebner Basis in CoCoA

CharP.GBasisF4

CharP.GBasisF8

CharP.GBasisF16

CharP.GBasisF32

CharP.GBasisF64

CharP.GBasisF128

CharP.GBasisF256

CharP.GBasisF512

CharP.GBasisF1024

CharP.GBasisF2048

CharP.GBasisModSquares

Representation of finite fields