# ApCoCoA-1:Weyl.WMul

## Weyl.GBasis

computing a Groebner basis.

### Syntax

Weyl.GBasis(I):LIST

### 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.

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### See also