Difference between revisions of "ApCoCoA:Weyl.WMul"

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(adding keys and types)
(update wtr. http://www.apcocoa.org/forum/viewtopic.php?f=20&t=886)
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     <short_description>computing a Groebner basis.</short_description>
 
     <short_description>computing a Groebner basis.</short_description>
 
<syntax>
 
<syntax>
Weyl.GBasis(P):LIST
+
Weyl.GBasis(I):LIST
 
</syntax>
 
</syntax>
 
     <description>
 
     <description>
 
{{Beta}}
 
{{Beta}}
  
This method computes an both sided ideal's Groebner basis and returns it as a list of WeylPolynoms. Currently, it is not yet implemented, due to some missing link in the server/client communication.  
+
This function computes a Groebner Basis for an ideal in a Weyl Algebra. It is currently completely independent from the other methods of package Weyl and does NOT use its data types.  
  
 +
The input is an ideal in a ring, having 2n indeterminates. The last n indeterminates are assumed to be the derivatives. All polynomails are assumed to be in their normal form with respect to the indeterminates' commutators, e.g. all <formula>x_i </formula> are in front of all <formula \partial_i </formula>, so the  'normal' CoCoA polynomials can be (and are) used to store the weyl polynomials. The output is again a list of polynomials in a normal ring, containing the Weyl-GBasis polynomials in their normal forms.
 +
 +
This implementation is not the final one, but currently due to requests enabled. In a later stage, the packages  data types should be used.
 
{{Stub}}
 
{{Stub}}
 
   </description>
 
   </description>

Revision as of 13:28, 10 March 2008

 <command>
   <title>Weyl.GBasis</title>
   <short_description>computing a Groebner basis.</short_description>

<syntax> Weyl.GBasis(I):LIST </syntax>

   <description>

Beta Warning: This method, package or class is a beta version. It may not work as intended or its interface may change in the next version! So please be careful when you're intending to use it.

This function computes a Groebner Basis for an ideal in a Weyl Algebra. It is currently completely independent from the other methods of package Weyl and does NOT use its data types.

The input is an ideal in a ring, having 2n indeterminates. The last n indeterminates are assumed to be the derivatives. All polynomails are assumed to be in their normal form with respect to the indeterminates' commutators, e.g. all <formula>x_i </formula> are in front of all <formula \partial_i </formula>, so the 'normal' CoCoA polynomials can be (and are) used to store the weyl polynomials. The output is again a list of polynomials in a normal ring, containing the Weyl-GBasis polynomials in their normal forms.

This implementation is not the final one, but currently due to requests enabled. In a later stage, the packages data types should be used. This article is a stub.

You can make this wiki more useful by adding information.

  </description>
   <seealso>
     <see>Weyl.WeylIdeal</see>
     <see>Weyl.WeylPolynom</see>
     <see>Weyl.NewWeylIdeal</see>
   </seealso>
   <types>
     <type>cocoaserver</type>
   </types>
   <key>heldt</key>
   <key>weyl.gbasis</key>
   <wiki-category>Package_Weyl</wiki-category>
 </command>