# ApCoCoA-1:FGLM.FGLM

From ApCoCoAWiki

## FGLM

Perform a FGLM Groebner Basis conversion using ApCoCoAServer

### Syntax

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

### Description

The function `FGLM` calls the ApCoCoAServer to perform a

FGLM Groebner Basis conversion. 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.

#### 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);

### See also