# Difference between revisions of "ApCoCoA:Weyl.WMul"

 <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>