# Difference between revisions of "ApCoCoA-1: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, CoCoA will assume M = Ord(). Please note that the resulting polynomials belong to a different ring than the ones in GBOld.

Ther return value will be the transformed Groebner basis polynomials.

#### Example

```Use Q[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 Q[x, y, z], Ord(M);
-- New basis (Lex)
BringIn(GBNew);
```