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

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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 <tt>L</tt> such that <tt>Ideal(L) = Ideal(GB)</tt>. | ||

+ | This function is replaced by the function <ref>Weyl.WRGB</ref> inside the function <ref>Weyl.WGB</ref> to get a list of minimal Groebner basis elements for the ideal <tt>I</tt>. | ||

<par/> | <par/> | ||

− | + | <em>Note:</em> This function is faster than <ref>Weyl.WRGB</ref> for a list <tt>GB</tt> of large size. | |

− | This function is | ||

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<item>@param <em>GB</em> Groebner Basis of an ideal in the Weyl algebra.</item> | <item>@param <em>GB</em> Groebner Basis of an ideal in the Weyl algebra.</item> | ||

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− | <key>weyl. | + | <key>weyl.wredgb</key> |

− | <key> | + | <key>wredgb</key> |

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

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## Revision as of 15:56, 14 October 2009

## Weyl.WRedGB

Computes reduced Groebner basis of a D-ideal in Weyl algebra `A_n`.

### Syntax

Weyl.WRedGB(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)`.

This function is replaced by the function Weyl.WRGB inside the function Weyl.WGB to get a list of minimal Groebner basis elements for the ideal `I`.

*Note:* This function is faster than Weyl.WRGB for a list `GB` of large size.

@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.WRedGB(L); [1] -------------------------------

### See also

Introduction to Groebner Basis in CoCoA