# 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) | + | 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. |

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<see>Weyl.WNormalForm</see> | <see>Weyl.WNormalForm</see> | ||

<see>Weyl.WGB</see> | <see>Weyl.WGB</see> | ||

+ | <see>Weyl.WRGBS</see> | ||

+ | <see>Weyl.WRedGB</see> | ||

<see>Introduction to Groebner Basis in CoCoA</see> | <see>Introduction to Groebner Basis in CoCoA</see> | ||

<see>Introduction to CoCoAServer</see> | <see>Introduction to CoCoAServer</see> | ||

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<key>weyl.wrgb</key> | <key>weyl.wrgb</key> | ||

+ | <key>Weyl.WRGB</key> | ||

<key>wrgb</key> | <key>wrgb</key> | ||

<wiki-category>Package_weyl</wiki-category> | <wiki-category>Package_weyl</wiki-category> | ||

</command> | </command> |

## Revision as of 11:29, 24 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 Groebner basis `GB` computed by ApCoCoAServer into the reduced 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