Difference between revisions of "ApCoCoA-1:Weyl.WRedGB"
(New page: <command> <title>Weyl.WRedGB</title> <short_description>Computes reduced Groebner basis of a D-ideal in Weyl algebra <tt>A_n</tt>.</short_description> <syntax> Weyl.WRedGB(GB:LIS...) |
|||
| Line 6: | Line 6: | ||
</syntax> | </syntax> | ||
<description> | <description> | ||
| + | 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 | ||
| − | |||
<itemize> | <itemize> | ||
<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> | ||
| Line 35: | Line 35: | ||
<type>groebner</type> | <type>groebner</type> | ||
</types> | </types> | ||
| − | <key>weyl. | + | <key>weyl.wredgb</key> |
| − | <key> | + | <key>wredgb</key> |
<wiki-category>Package_weyl</wiki-category> | <wiki-category>Package_weyl</wiki-category> | ||
</command> | </command> | ||
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
