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Perform a FGLM Groebner Basis conversion using ApCoCoAServer.




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.

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 GBOld will be converted into a Groebner Basis with respect to term ordering Ord(M), i.e. M must be a matrix specifying a term ordering. If the parameter M is not specified, ApCoCoA will assume M = Ord(). Please note that the resulting polynomials belong to a different ring than the ones in GBOld.

The return value will be the transformed Groebner basis polynomials.

  • @param GBOld A Groebner basis of a zero-dimensional ideal.

  • @param M A matrix representing a term ordering.

  • @return A Groebner basis of the ideal generated by the polynomials of GBOld. The polynomials of the new Groebner basis will belong to the polynomial ring with term ordering specified by M or Ord() in case M is not given.


Use QQ[x, y, z], DegRevLex;
GBOld := [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(GBOld, M);
Use QQ[x, y, z], Ord(M);
-- New basis (Lex)

GBasis5, and more

Introduction to CoCoAServer