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 <short_description>Performs a FGLM Groebner Basis conversion using ApCoCoAServer.</short_description>

<syntax> FGLM(GBInput:LIST, M:MAT):LIST FGLM(GBInput:LIST):LIST </syntax>


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. <par/> The function FGLM calls the ApCoCoAServer to perform a FGLM Groebner Basis conversion. Please note that the ideal generated by the given Groebner Basis must be zero-dimensional. The Groebner Basis contained in list GBInput will be converted into a Groebner Basis with respect to term ordering <ref>Ord</ref>(M), i.e. M must be a matrix specifying a term ordering. If the parameter M is not specified, ApCoCoA will assume M = <ref>Ord</ref>(). Please note that the resulting polynomials belong to a different ring than the ones in GBInput. <par/> The return value will be the transformed Groebner basis polynomials. <itemize>

 <item>@param GBInput A Groebner basis of a zero-dimensional ideal.</item>
 <item>@return A Groebner basis of the ideal generated by the polynomials of GBInput. The polynomials of the new Groebner basis will belong to the polynomial ring with term ordering specified by M or <ref>Ord</ref>() in case M is not given.</item>

</itemize> The following parameter is optional. <itemize>

 <item>@param M A matrix representing a term ordering.</item>

</itemize> <example> Use QQ[x, y, z], DegRevLex; GBInput := [z^4 -3z^3 - 4yz + 2z^2 - y + 2z - 2, yz^2 + 2yz - 2z^2 + 1, y^2 - 2yz + z^2 - z, x + y - z]; M := LexMat(3); GBNew := FGLM.FGLM(GBInput, M); Use QQ[x, y, z], Ord(M); -- New basis (Lex) BringIn(GBNew);

[z^6 - z^5 - 4z^4 - 2z^3 + 1, y - 4/7z^5 + 5/7z^4 + 13/7z^3 + 10/7z^2 - 6/7z - 2/7,

x + 4/7z^5 - 5/7z^4 - 13/7z^3 - 10/7z^2 - 1/7z + 2/7]


 <see>GBasis5, and more</see>
 <see>Introduction to CoCoAServer</see>
 <key>groebner basis conversion</key>