ApCoCoA-1:Weyl.WRGB: Difference between revisions
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<command> | <command> | ||
<title>Weyl.WRGB</title> | <title>Weyl.WRGB</title> | ||
<short_description>Reduced Groebner basis of an ideal I in Weyl algebra < | <short_description>Reduced Groebner basis of an ideal I in Weyl algebra <tt>A_n</tt>.</short_description> | ||
<syntax> | <syntax> | ||
Weyl.WRGB( | Weyl.WRGB(GB:LIST):LIST | ||
</syntax> | </syntax> | ||
<description> | <description> | ||
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. | |||
<itemize> | |||
<item>@param <em>GB</em> Groebner Basis of an ideal in the Weyl algebra.</item> | |||
<item>@result The reduced Groebner Basis of the given ideal.</item> | |||
</itemize> | |||
<example> | <example> | ||
A1::=QQ[x,d]; --Define appropraite ring | A1::=QQ[x,d]; --Define appropraite ring | ||
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<see>Weyl.WNormalForm</see> | <see>Weyl.WNormalForm</see> | ||
<see>Weyl.WGB</see> | <see>Weyl.WGB</see> | ||
<see>Groebner, and more</see> | |||
</seealso> | </seealso> | ||
<types> | <types> | ||
<type>cocoaserver</type> | <type>cocoaserver</type> | ||
<type>groebner</type> | |||
</types> | </types> | ||
<key>weyl.wrgb</key> | <key>weyl.wrgb</key> | ||
<key>wrgb</key> | |||
<wiki-category>Package_weyl</wiki-category> | <wiki-category>Package_weyl</wiki-category> | ||
</command> | </command> | ||
Revision as of 13:07, 23 April 2009
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 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 appropraite ring Use A1; L:=[x,d,1] Weyl.WRGB(L); [1] -------------------------------
See also
