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

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</syntax> | </syntax> | ||

<description> | <description> | ||

+ | <em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | ||

+ | <par/> | ||

This function converts Groebner basis GB computed by implementation in CoCoALib into reduced Groebner Basis. If GB is not a Groebner basis then the output will not be reduced Groebner basis. In fact, this function reduces a list GB of Weyl polynomals using <ref>Weyl.WNR</ref> into a new list L such that Ideal(L) = Ideal(GB). | This function converts Groebner basis GB computed by implementation in CoCoALib into reduced Groebner Basis. If GB is not a Groebner basis then the output will not be reduced Groebner basis. In fact, this function reduces a list GB of Weyl polynomals using <ref>Weyl.WNR</ref> into a new list L such that Ideal(L) = Ideal(GB). | ||

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

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<example> | <example> | ||

− | A1::=QQ[x,d]; --Define | + | A1::=QQ[x,d]; --Define appropriate ring |

Use A1; | Use A1; | ||

L:=[x,d,1] | L:=[x,d,1] | ||

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

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

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

</seealso> | </seealso> | ||

<types> | <types> |

## Revision as of 12:19, 24 April 2009

## Weyl.WRGB

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

### Syntax

Weyl.WRGB(GB:LIST):LIST

### Description

*Please note:* The function(s) explained on this page is/are using the *ApCoCoAServer*. You will have to start the ApCoCoAServer in order to use it/them.

This function converts Groebner basis GB computed by implementation in CoCoALib into reduced Groebner Basis. If GB is not a Groebner basis then the output will not be reduced Groebner basis. In fact, this function reduces a list GB of Weyl polynomals using Weyl.WNR into a new list L such that Ideal(L) = Ideal(GB).

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

@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