# ApCoCoA-1:FGLM.FGLM

## FGLM.FGLM

Perform a FGLM Groebner Basis conversion using ApCoCoAServer.

### Syntax

FGLM(GBOld:LIST, M:MAT):LIST FGLM(GBOld:LIST):LIST

### Description

*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.

#### Example

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) BringIn(GBNew);