ApCoCoA-1:Weyl.WGB: Difference between revisions

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   <command>
   <command>
     <title>Weyl.WGB</title>
     <title>Weyl.WGB</title>
     <short_description>Computes the Groebner basis of an ideal I in Weyl algebra <math>A_n</math>, using corresponding
     <short_description>Computes the Groebner basis of an ideal I in Weyl algebra <tt>A_n</tt>.</short_description>
implementation in CoCoALib.</short_description>
<syntax>
<syntax>
Weyl.WGB(I):LIST
Weyl.WGB(I: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.


This function computes a Groebner Basis for an Ideal <math>I = (f_1,f_2, ..., f_r)</math> where every generator <math>f_i</math> should be a Weyl polynomial in Normal form.
This function computes a Groebner Basis for an Ideal <tt>I = (f_1,f_2, ..., f_r)</tt> where every generator <tt>f_i</tt> should be a Weyl polynomial in Normal form.
 
<itemize>
<item>@param <em>I</em> An ideal in the Weyl algebra.</item>
<item>@return A Groebner Basis of the given ideal.</item>
</itemize>


<example>
<example>
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     <types>
     <types>
       <type>cocoaserver</type>
       <type>cocoaserver</type>
      <type>ideal</type>
      <type>Groebner, and more</type>
     </types>
     </types>
     <key>weyl.wgb</key>
     <key>weyl.wgb</key>
    <key>wgb</key>
     <wiki-category>Package_weyl</wiki-category>
     <wiki-category>Package_weyl</wiki-category>
   </command>
   </command>

Revision as of 12:23, 23 April 2009

Weyl.WGB

Computes the Groebner basis of an ideal I in Weyl algebra A_n.

Syntax

Weyl.WGB(I: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 function computes a Groebner Basis for an Ideal I = (f_1,f_2, ..., f_r) where every generator f_i should be a Weyl polynomial in Normal form.

  • @param I An ideal in the Weyl algebra.

  • @return A Groebner Basis of the given ideal.

Example

A1::=QQ[x,d];	--Define appropraite ring
Use A1;
I:=Ideal(x,d);  -- Now start ApCoCoA server for executing next command
Weyl.WeylGB(I);
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
[1]
-------------------------------
Note that Groebner basis you obtained is minimal.
A2::=QQ[x[1..2],y[1..2]];
Use A2;
I1:=Ideal(x[1]^7,y[1]^7);
Weyl.WGB(I1);
-- CoCoAServer: computing Cpu Time = 0.094
-------------------------------
[1]
-------------------------------

Example

W3::=ZZ/(7)[x[1..3],d[1..3]];
Use W3;
I2:=Ideal(x[1]^7,d[1]^7);  --is a 2-sided ideal in W3
Weyl.WGB(I2);   --ApCoCOAServer should be running
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
[x[1]^7, d[1]^7]
-------------------------------

I3:=Ideal(x[1]^3d[2],x[2]*d[1]^2);

Weyl.WGB(I3);
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
[x[2]^2d[2], x[2]d[2]^2 + 2d[2], x[1]^3d[1]^2 + x[1]^2x[2]d[1]d[2] + x[1]x[2]d[2], x[1]^3d[2], x[2]d[1]^2]
-------------------------------

See also

Weyl.WNormalForm