# 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.

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</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>