# Difference between revisions of "ApCoCoA-1:Weyl.WRGB"

From ApCoCoAWiki

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− | This function converts Groebner basis <tt>GB</tt> computed by ApCoCoAServer into the reduced Groebner Basis. If <tt>GB</tt> is not a Groebner basis then the output will not be the reduced Groebner basis. In fact, this function reduces a list <tt>GB</tt> of Weyl polynomials using <ref>Weyl.WNR</ref> into a new list L such that Ideal(L) = Ideal(GB), every polynomial is reduced with respect to the remaining polynomials in the list L and leading coefficient of each polynomial in L is 1. | + | This function converts a Weyl Groebner basis <tt>GB</tt> computed by ApCoCoAServer into the reduced Weyl Groebner Basis. If <tt>GB</tt> is not a Groebner basis then the output will not be the reduced Groebner basis. In fact, this function reduces a list <tt>GB</tt> of Weyl polynomials using <ref>Weyl.WNR</ref> into a new list <tt>L</tt> such that <tt>Ideal(L) = Ideal(GB)</tt>, every polynomial is reduced with respect to the remaining polynomials in the list <tt>L</tt> and leading coefficient of each polynomial in <tt>L</tt> is 1. |

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## Revision as of 11:10, 25 May 2010

## Weyl.WRGB

Reduced Groebner basis of an ideal `I` in Weyl algebra `A_n`.

### Syntax

Weyl.WRGB(GB:LIST):LIST

### Description

This function converts a Weyl Groebner basis `GB` computed by ApCoCoAServer into the reduced Weyl Groebner Basis. If `GB` is not a Groebner basis then the output will not be the reduced Groebner basis. In fact, this function reduces a list `GB` of Weyl polynomials using Weyl.WNR into a new list `L` such that `Ideal(L) = Ideal(GB)`, every polynomial is reduced with respect to the remaining polynomials in the list `L` and leading coefficient of each polynomial in `L` is 1.

@param

*GB*Groebner Basis of an ideal in the Weyl algebra.@result The reduced Groebner Basis of the given ideal.

#### Example

A1::=QQ[x,d]; --Define appropriate ring Use A1; L:=[x,d,1]; Weyl.WRGB(L); [1] -------------------------------

### See also

Introduction to Groebner Basis in CoCoA