ApCoCoA-1:Weyl.WRGB: Difference between revisions
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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. | ||
<itemize> | <itemize> | ||
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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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</types> | </types> | ||
<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
